tag:blogger.com,1999:blog-121333352018-07-13T04:22:30.009-04:00Walk Like a SabermetricianOccasional commentary on baseball and sabermetricsphttp://www.blogger.com/profile/18057215403741682609noreply@blogger.comBlogger568125tag:blogger.com,1999:blog-12133335.post-79604386149974536462018-05-23T09:35:00.000-04:002018-05-23T23:19:47.775-04:00Enby Distribution, pt. 7: Cigol at the Extremes--Runs Per WinNow that you presumably have some confidence in Cigol’s ability to do something fairly easy by the standards of classical sabermetrics, you may have some more interest in what Cigol says about a much harder question--how does W% vary by runs scored and runs allowed in extreme situations? This is the area in which Cigol (whether powered by Enby or any other run distribution model) has the potential to enhance our understanding of the relationship between runs and wins. Unfortunately, it is difficult to tell whether these results are reasonable, since we don’t have empirical data regarding extreme teams. If Cigol deviates from Pythagenpat, we won’t know which one to trust. Throughout this post, I am going to discuss these issues as if Cigol is in fact the “true” or “correct” estimate. This is simply for the sake of discussion--it would be unwieldy to have to issue a disclaimer every time we compare Cigol and Pythagenpat. Please note that I am not asserting that this is demonstrably the case.<br /><br />For a first look at how the two compare at the extreme, let’s assume that a team’s runs scored are fixed at an average 4.5, and look at their estimated W% at each interval of .5 in runs allowed from 1-15 RA/G using Cigol and Pythagenpat with three different exponents (.27, .28, and .29; I’ve always called this Pythagenpat constant z and will stick with that notation here, hoping that it will not be confused with the Enby z parameter):<br /><br /><a href="https://4.bp.blogspot.com/-IgUNAsJB8vQ/WwTc1SUaZ0I/AAAAAAAAChc/AaMj1YN4EZYfif_lrXL2ZUU9kQA75BgxgCLcBGAs/s1600/enby8-2.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://4.bp.blogspot.com/-IgUNAsJB8vQ/WwTc1SUaZ0I/AAAAAAAAChc/AaMj1YN4EZYfif_lrXL2ZUU9kQA75BgxgCLcBGAs/s400/enby8-2.JPG" width="240" height="400" data-original-width="307" data-original-height="511" /></a><br /><br />Just eyeballing the data, two things are evident. The first is that Pythagenpat with any of the exponent choices is a fairly decent match at any RA value. The largest differences come at the extremes, as you’d expect, but the maximum difference is .013 between the Cigol and z = .27 estimate for the 4.5 R/15 RA team. This is a difference of a little over 2 wins over the course of a 162 game schedule, which isn’t terrible since it represents close to the maximum discrepancy. While I have not figured Enby parameters past 15 RG, at some point the differences would begin to decline as both Cigol and Pythagenpat estimates converge at a 1.000 W%. For comparison, a Pythagorean fixed exponent of 1.83 predicts a W% of .099 for the 4.5/15 team, almost 8 wins/162 off of the Cigol estimate.<br /><br />The second thing that becomes apparent is that Cigol implies that as scoring increases, the Pythagenpat z constant is not fixed. For the lowest RPGs on the table (1-3 RA/G, which when combined with the 4.5 R/G is 5.5-7.5 RPG), .27 performs the best relative to Cigol. Once we cross 3.5 RA/G, .28 performs best, and maintains that advantage from 3.5-8 RA/G (8-12.5 RPG). Past that point (>8.5 RA/G, >13 RPG), .29 is the top-performer. This explains why studies have tended to peg z somewhere in the .28-.29 range, as such a value represents the best fit at normal major league scoring levels.<br /><br />A nice way to see the relationship is to plot the difference (Pythagenpat - Cigol) relative to RA/G for each exponent:<br /><br /><a href="https://1.bp.blogspot.com/-yDE-efbijos/WwTcT3nfEmI/AAAAAAAAChU/MROGsbkSmY0a0DurRnfnddA_QR4Vgf6jgCLcBGAs/s1600/enby8-1.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://1.bp.blogspot.com/-yDE-efbijos/WwTcT3nfEmI/AAAAAAAAChU/MROGsbkSmY0a0DurRnfnddA_QR4Vgf6jgCLcBGAs/s400/enby8-1.JPG" width="400" height="273" data-original-width="1227" data-original-height="838" /></a><br /><br />The point at which all converge is 4.5 RA/G, where R = RA and all estimators predict .500. As you can see, the differences converge as we approach either a .000 or 1.000 W%, since there is a hard cap on the linear difference at those points. <br /><br />This exercise gives us some direction on where to go, but it is not comprehensive enough to draw any conclusions. In order to do that, we need a more comprehensive set of data than simply fixing R/G at 4.5. To do so, I figured the Cigol W% for each interval of .25 runs scored and runs allowed between 1-15 RPG (removing all points at which R = RA). This yields 3,192 R/RA pairs, many of which are so extreme as to be absurd, which is the point.<br /><br />In order to make sense of this data, we will need to simplify the scope of what we are considering, so let’s start by trying to ascertain the relationship between runs and wins if we assume that a linear model should be used. Basically, the idea here is that we should be able to determine a runs per win (RPW) factor such that:<br /><br />W% = (R - RA)/RPW + .5<br /><br />From this, we can calculate RPW given W%, R, and RA as:<br /><br />RPW = (R - RA)/(W% - .5)<br /><br />In its most simple form, this type of equation assumes a fixed number of runs per win; for standard scoring contexts, 10 is a nice, round number that does the job and of course has become famous as a sabermetric rule of thumb. But it has long been known that RPW varies with the scoring context, and usually sabermetricians have attempted to express this by making RPW a function of RPG. So let’s graph our data in that manner:<br /><br /><a href="https://2.bp.blogspot.com/-eto0k7zXVgA/WwTdj4e6T9I/AAAAAAAACho/LE6hTxyYSjUthm0DZFhPFWNCseMKvU78gCLcBGAs/s1600/enby8-3.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://2.bp.blogspot.com/-eto0k7zXVgA/WwTdj4e6T9I/AAAAAAAACho/LE6hTxyYSjUthm0DZFhPFWNCseMKvU78gCLcBGAs/s400/enby8-3.JPG" width="400" height="277" data-original-width="1208" data-original-height="838" /></a><br /><br />As you can see, RPW is not even close to being a linear function of RPG when extreme teams are considered. The bulk of the observations scattered around a nice, linear-looking function, but the outliers are such that the linear function will fail horrifically at the extremes. And when I say extremes, I really mean extremes. For instance, a 15 R/1 RA team is at 16 RPG, but would need much more than 16 marginal runs for a marginal win--Cigol estimates that such a team would need 28.11 marginal runs (as would it’s 1/15 counterpart). This should make sense to you logically--the team’s W% is already so high, and so many of the games blowouts, that you need to scatter a large number of runs around to move the win needle. This point represents the maximum RPW for the points I’ve included--the minimum is 3.69 at 1.25/1.<br /><br />This is not to say that a linear model cannot be used to estimate W%; it is simply the case that one linear model cannot be used to estimate W% over a wide range of possible scoring contexts and/or disparities in team strength. Let’s suppose that we limit the scope of our data in each of these manners. First, let’s consider only cases in which a team’s runs are between 3-7 and its runs allowed are between 3-7. This essentially captures the range of teams in modern major league baseball and limits the sample to 272 data points:<br /><br /><a href="https://4.bp.blogspot.com/-k99A4re2GZY/WwYvRA6ZO4I/AAAAAAAACic/qCEV1CkNNRIUlB9dDsHi9ngQWFWEV6-6gCLcBGAs/s1600/enby8-8.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://4.bp.blogspot.com/-k99A4re2GZY/WwYvRA6ZO4I/AAAAAAAACic/qCEV1CkNNRIUlB9dDsHi9ngQWFWEV6-6gCLcBGAs/s400/enby8-8.JPG" width="400" height="242" data-original-width="1323" data-original-height="801" /></a><br /><br />I’ve taken the liberty of including a linear regression line, which now has the slope we’d expect (recall that Tango’s formula for RPW is .75*RPG + 3, and that this is <a href="http://walksaber.blogspot.com/2009/01/runs-per-win-from-pythagenpat.html">consistent with Pythagenpat</a>). The line is shifted up more than the best fit using normal teams or centering Pythagenpat at 9 RPG indicates, as there are still some extreme combinations here (for example, a 7 R/3 RA team is expected by Cigol to play .815 ball, well beyond anything we’ll ever see in modern MLB).<br /><br />We can also try limiting the data in another way--only looking at cases in which the resulting records are feasible in modern MLB. For simplicity, I’ll define this as cases in which the Cigol W% is between .300 and .700 (yes, I realize the 2001 Mariners and 2003 Tigers fall outside of this range in terms of actual W%, but in fact it’s probably too wide of a band if we consider only expected W% based on R and RA). Here are the results from our Cigol data points, including all intervals of R and RA between 1-15 (this leaves us with 1,126 cases):<br /><br /><a href="https://3.bp.blogspot.com/-suxTjnsQIEE/WwTfDg2rOEI/AAAAAAAACiE/DWDmjOUiv5AqvTbiA1_dVwDEvVSiQmIFwCLcBGAs/s1600/enby8-6.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://3.bp.blogspot.com/-suxTjnsQIEE/WwTfDg2rOEI/AAAAAAAACiE/DWDmjOUiv5AqvTbiA1_dVwDEvVSiQmIFwCLcBGAs/s400/enby8-6.JPG" width="400" height="249" data-original-width="1333" data-original-height="830" /></a><br /><br />Once again, the slope of the line is the ballpark of what we observe with normal teams, but the intercept is still off, shifting the line up to get closer to the extreme cases. If we make both adjustments simultaneously (look only at cases between 3-7 R, 3-7 RA, and .3-.7 Cigol W%), we are left with 202 data points and this graph:<br /><br /><a href="https://3.bp.blogspot.com/-Ku5lHCnGEEU/WwTeqBA7BXI/AAAAAAAACh8/0NiZMBYlT8MWF_yKPaUkybVmUEqMB784gCLcBGAs/s1600/enby8-5.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://3.bp.blogspot.com/-Ku5lHCnGEEU/WwTeqBA7BXI/AAAAAAAACh8/0NiZMBYlT8MWF_yKPaUkybVmUEqMB784gCLcBGAs/s400/enby8-5.JPG" width="400" height="248" data-original-width="1317" data-original-height="817" /></a><br /><br />Closer still, with the slope now essentially exactly where we expect it to be, but the intercept still shifting the line upwards. Why is this happening? We know that it’s not because of a breakdown of Cigol when estimating W% for normal teams--as we saw in the previous post, Cigol is of comparable accuracy to Pythagenpat and RPW = .75*RPG + 3 with normal teams. What’s happening is that we are not biasing our sample with near-.500 team as happens when we observe real major league data. All of our hypothetical teams have a run differential of at least +/- .25. In 1996-2006, about one quarter of teams had run differentials of less than +/- .25.<br />The standard deviation of W% for 1996-2006 was .073; the standard deviation of Cigol W% for this data is .111. This illustrates the point that I and other sabermetricians who seek theoretical soundness make repeatedly--using normal major league full season data, the variance is small enough that any halfway intelligible model will come close to predicting whatever it is your predicting. Anything that centers estimated W% at .500 and allows it to vary as run differential varies from zero will work just fine. But if you run into a sample that includes a lot of unusual cases, or you start looking at smaller sample sizes, or a higher variance league, or try to extrapolate results to individual player data, then many formulas that work just fine normally will begin to break down.<br /><br />A linear conversion between runs and wins breaks down in extreme cases for a few main reasons, including no bounds as is the case for real world W% [0,1] and the declining value of marginal runs on not one but two determinants--scoring context and differential between the two teams. There are some things we could attempt to do to salvage it, such as introducing run differential as a variable. If we did this, we could allow RPW to increase not only as RPG increases, but also as absolute value of RD increases.<br /><br />Let’s use the pared down in both dimensions data set to find a RPW estimator using both RPG and abs(RD) as predictors. I simply ran a multiple regression and got this equation:<br /><br />RPW = .732*RPG + .204*abs(R - RA) + 3.081<br /><br />If we assume that a team has R = RA, then this equation is a very good match for our expected .75*RPG + 3, as it would reduce to .732*RPG + 3.081. This is encouraging, since it should work with normal teams and offers the prospect for better performance with extreme teams. <br /><br />Remember, though, that “extreme” teams in the context of this dataset is a lot more restrictive than extreme teams in the broader set--we've limited the data to only 3-7 R, 3-7 RA, and .3-.7 Cigol W%. If we step outside of that range, the equation will break down again. For example, a 10 R/5 RA has a RPW of 15.081 according to this equation, which suggests a .832 W% versus the .819 expected by Cigol. While this is not a catastrophic error (and much better than the .851 suggested by .75*RPG + 3), don’t lose sight of the fact that the W% function is non-linear. <br /><br />If we use this equation on the rounded to nearest .05 1996-2006 major league data discussed in the last post, the RMSE times 162 is 3.858--just a tad worse than the RPW version that does not account for RD, but still comparable to (in fact, slightly lower RMSE than) the heavy hitters Pythagenpat and Cigol. It produces a very good match for Cigol over this dataset, in fact closer to Cigol than is Pythagenpat with z = .28.<br /><br />A similar equation to this one was previously developed by Tango Tiger (which is where I got the idea to use abs(R - RA) as the second variable; there might be some other ways one could construct the equation and achieve a similar outcome) and posted on FanHome in 2001:<br /><br />RPW = .756*RPG + .403*abs(R - RA) + 2.645<br /><br />In this version, the lower intercept is offset by the higher coefficient on RD. <br /><br />We can also attempt to improve the RPW estimate by using a non-linear equation. The best fit comes from a power regression, and again I will limit this to the 3-7 RPG, .300-.700 Cigol W% set of teams to produce this estimate:<br /><br /><a href="https://1.bp.blogspot.com/-Xf741cUmE5U/WwTg2qFoSaI/AAAAAAAACiQ/j7eYnu6gMuMFcvCe7kz4emxhmK1bkYMnQCLcBGAs/s1600/enby8-7.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://1.bp.blogspot.com/-Xf741cUmE5U/WwTg2qFoSaI/AAAAAAAACiQ/j7eYnu6gMuMFcvCe7kz4emxhmK1bkYMnQCLcBGAs/s400/enby8-7.JPG" width="400" height="248" data-original-width="1323" data-original-height="820" /></a><br />RPW = 2.171*RPG^.691<br /><br />This may look familiar, because as I have <a href="http://walksaber.blogspot.com/2009/01/runs-per-win-from-pythagenpat.html">demonstrated in the past</a>, the Pythagenpat implied RPW at a given RPG for a .500 team is 2*RPG^(1 - z). Here the implied z value of .309 is higher than we typically see (.27 - .29), but the form is essentially the same.<br /><br />Any linear approximation might work well near the RPG/team quality level where it was constructed, but will falter outside of that range. We could develop an equation based on teams similar to the 10/5 example that would work well for them, but we’d necessarily lose accuracy when looking at normal teams. Non-linear W% functions allow us to capture a wider range of contexts with one particular equation. We can push the envelope a little bit by using a non-linear estimate of RPW, but we’d still have to be very careful as we varied the scoring context and skill difference between the teams.<br /><br />Assuming we are not just satisfied with an equation to use for normal teams, all of this caution is a lot to go through to salvage a functional form that still allows for sub-zero or greater than one W% estimates. Instead, it makes more sense to attempt to construct a W% estimate that bounds W% between 0 and 1 and builds-in non-linearity. This of course is why Bill James and many sabermetricians who have followed have turned to the Pythagorean family of estimators.<br />phttp://www.blogger.com/profile/18057215403741682609noreply@blogger.com0tag:blogger.com,1999:blog-12133335.post-89658350754085586402018-04-26T08:33:00.000-04:002018-04-26T17:41:03.229-04:00Enby Distribution, pt. 6: Accuracy of Enby W% EstimateIn the last post, I demonstrated how one can estimate W% from any runs per game and runs per inning distribution by using the basic principles of how baseball games are decided. This model is simple conceptually, but a bear to implement computationally when compared to the other W% estimators that have been developed by sabermetricians over the last fifty years. As such, it is not a practical tool to use for common sabermetric applications of a winning percentage estimator. If you want to know how many games a team that scores 828 runs and allows 753 runs in a season can expect to win, there are any number of formulas that are better practical options than Enby. <br /><br />However, it is important to verify that Enby is able to hold its own when estimating W% for normal teams. If it does not work as well as our other tools for normal situations, it will be harder to put any stock in its results when looking at extreme situations.<br /><br />To check if Enby was up to the challenge, I performed a limited accuracy test based on 1996-2006 data (a sample of 326 teams). This was in no way intended to be a comprehensive accuracy test, but rather one with a sufficiently large sample to determine if Enby can predict normal teams with comparable accuracy to other approaches. <br /><br />Since I have only calculated Enby distribution parameters at intervals of .05 RG, I rounded all team’s R/G and RA/G to the nearest .05 and used these figures as the inputs for all of the estimators. This ensured that they were all on equal footing, rather than Enby only having some imprecision in terms of the actual R and RA counts. In addition to Enby, I tested four other estimators:<br /><br />* A simple assumption of 10 RPW <br />* Tango’s formula that varies RPW by RPG (runs per game for both teams): RPW = .75*RPG + 3. This formula (or at least something very close to it) can be derived by <a href="http://walksaber.blogspot.com/2009/01/runs-per-win-from-pythagenpat.html">using Pythagenpat</a>.<br />* Pythagorean with a fixed exponent of 1.83<br />* Pythagenpat using x = RPG^.28<br /><br />The resulting RMSE for each estimator (W% RMSE multiplied by 162 for ease of interpretation):<br /><br /><a href="https://2.bp.blogspot.com/-k8vOK6458EI/WuJFrA1dTuI/AAAAAAAACg8/eU4GBHDiHS0KvxFax9ORoNBSLL_0ccwOACLcBGAs/s1600/rmse.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://2.bp.blogspot.com/-k8vOK6458EI/WuJFrA1dTuI/AAAAAAAACg8/eU4GBHDiHS0KvxFax9ORoNBSLL_0ccwOACLcBGAs/s400/rmse.JPG" width="400" height="247" data-original-width="167" data-original-height="103" /></a><br /><br />The three methods which allow the relationship between runs and wins to vary by scoring context (either by explicitly changing the RPW factor or Pythagorean exponent, or by estimating the scoring distribution as Enby does) come out on top. The linear RPW formula wins here, although the best performer would be Pythagenpat with x = RPG^.29, edging it out at a 3.850 RMSE. Of course, we could also find the coefficients in Tango’s RPW formula that minimize error, and quite possibly push that method back ahead of Pythagenpat.<br /><br />In any event, the three formulas allowing for customization are close enough that we can safely conclude that none is grossly deficient for the task of estimating W% for normal teams. That means that Enby has passed the first hurdle towards being taken seriously as a model for W% based on average runs scored and allowed.<br /><br />I also thought it would be interesting to test the RMSE of using each W% estimator to predict Pythagenpat. This is obviously a biased approach, assuming that Pythagenpat is the standard by which other estimators should be compared. The real reason to do this is to see how closely Enby tracks Pythagenpat with normal teams, since Pythagenpat is the closest W% estimator in theory to Enby. Both attempt to dynamically model the relationship between runs and wins; the other approaches, even the dynamic RPW estimator, assume that there is a fixed relationship between runs and wins. We should expect Pythagenpat and Enby to be in general agreement. And they are (RMSE once again multiplied by 162):<br /><br /><a href="https://1.bp.blogspot.com/-7kLwUQb3vr0/WuJGHE2J9JI/AAAAAAAAChE/PBCJYUE3Tf8NpdESG3aLaUW0lFODHamUACLcBGAs/s1600/rmse2.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://1.bp.blogspot.com/-7kLwUQb3vr0/WuJGHE2J9JI/AAAAAAAAChE/PBCJYUE3Tf8NpdESG3aLaUW0lFODHamUACLcBGAs/s400/rmse2.JPG" width="400" height="206" data-original-width="167" data-original-height="86" /></a><br /><br />Enby and Pythagenpat are essentially in lockstep. In fact, the largest discrepancy between the two is for 2002 Braves, who scored 4.40 and allowed 3.50 runs per game (rounded). Pythagenpat expects that such a team would have a W% of .6007, while Enby predicts a .5997 W%, a difference of .15 wins over the course of a season. <br /><br />The minimum RMSE between Pythagenpat and Enby occurs when the Pythagenpat exponent is dropped slightly to .279 (.026 RMSE). As the exponent varies, the discrepancy increases; with a Pythagenpat exponent of .29, the RMSE is .274. <br /><br />At this point, I’d like to pause for a moment and change the name of the Enby estimate of W%. This is just for my own sanity as I write and hopefully use these tools in the future, but I want to draw a distinction between the Enby distribution, which is used to estimate the probability of scoring k runs in a game, and the methodology described for estimating W%. I’m a little hesitant to put a name on it, since I haven’t earned that right--the logic is based in reality, not my insight, and has been used by many sabermetricians long before me. Plus, I’m not very good at making up these kinds of names--if you don’t believe me, re-examine the name of the blog.<br /><br />This methodology is compatible with any means of estimating the probability of scoring k runs a game, whether empirically, through the Enby distribution, solely through the Tango Distribution (as Enby itself borrows from the Tango Distribution), the Weibull distribution (as implemented by <a href="http://www.hardballtimes.com/main/article/consistency-is-key/">Sal Baxamusa</a> or <a href="http://web.williams.edu/Mathematics/sjmiller/public_html/399/handouts/PythagWonLoss_Paper.pdf">Steven Miller</a>), or any other approach that may be developed in the future. Going forward, I will be referring to this as the Cigol method. As Toirtap can attest, I like to spell things backwards when I am flummoxed. Since the W% estimator is based on simple logic, Cigol it is.<br />phttp://www.blogger.com/profile/18057215403741682609noreply@blogger.com0tag:blogger.com,1999:blog-12133335.post-78084223289457716682018-03-27T08:50:00.000-04:002018-03-27T08:50:16.624-04:002018 PredictionsSee the <a href="http://sportsdataresearch.com/difficulties-associated-with-preseason-projections/">standard disclaimers</a>. This is an exercise in fun more than analysis, although hopefully there's a touch of the latter or you're just wasting your time.<br /><br />AL EAST<br /><br />1. Boston<br />2. New York (wildcard)<br />3. Toronto (wildcard)<br />4. Baltimore<br />5. Tampa Bay<br /><br />Picking the Red Sox is something of a tradition in this space. I don’t do it on purpose, it’s just that my “model” (such as it is) has tended to pick them consistently. This year it’s a virtual tie with the Yankees; some projections agree with that, but others (notably PECOTA) see a huge advantage for the latter. The Yankees arguably were more impressive last season given their component statistics, and yet Boston’s offense should bounce back, their starting pitching should be better, their bullpen could benefit from some healthy pieces coming back...and if Aaron Judge and Giancarlo Stanton combine for even ninety homers the takes will be hot. The top-heaviness of the AL, with four teams that really stand out, leaves a team like the Blue Jays a stealthy wildcard contender. Incidentally, I have them +9 runs on both offense and defense. The Orioles added enough late and the Rays subtracted enough to make me flip-flop their places, but it would be surprising if either gets into this race.<br /><br />AL CENTRAL<br /><br />1. Cleveland<br />2. Minnesota<br />3. Kansas City<br />4. Detroit <br />5. Chicago<br /><br />As a partisan am I always queasy about picking the Indians, but last year it worked out okay, and again this year the on-paper gap is just too large to superstitiously pick someone else. But it’s easier to see how the Indians might lose to the Twins in 2018 than it was to compare them to the field in 2017. While it’s easy to overstate the impact of the Twins pitching additions (one could argue that Jake Odorozzi and Lance Lynn would be no more than #4 starters for the Tribe, even #5 if Danny Salazar could get it together), Cleveland’s bullpen is showing signs of vulnerability without a lot of clear candidates to step in, there are still injury questions surrounding Jason Kipnis and Michael Brantley, the outfield is unsettled...but it’s also sometimes easier to worry about these things as a fan. The Twins true quality for 2016-2017 might be matched by the win total, but the distribution was all off. A plexiglass principle year would not surprise. The Royals kept just enough of the band together to a) still be annoying and b) provide some measure of optimism for their partisans, but probably more of the former. I’ve been calling for the Tigers to dead cat bounce for a couple years; I’m surrendering and just expecting it for Miguel Cabrera. The White Sox have a lot of prospects and could well be the future of this division, but it’s still a year or two away.<br /><br />AL WEST<br /><br />1. Houston<br />2. Los Angeles<br />3. Seattle<br />4. Texas<br />5. Oakland<br /><br />The Astros, in my crude system, are the second-best team in the AL...on offense and defense. Just slightly behind the Yankees and the Indians, respectively; combined, that’s enough to declare them the best and most well-rounded team on paper. Prior to Shohei Ohtani’s rough showing in spring training, I was set to pick the Angels as the second wildcard. Is dropping them a small sample size overreaction? Quite possibly, yes, but there wasn’t much separating teams like the Angels, Blue Jays, and Twins to begin with. You have to feel bad (unless you’re a fan of the…wait, do they even have a rival of note) for the Mariners - they now have the longest playoff drought in North American sports. Longer than the Cleveland Browns (this has been true for years but it is a miscarriage of justice that it’s not the Browns that hold this dubious distinction). They’ve been good enough to squeak out a second wildcard for a few years, but it never came together, and the window may be closing. The Rangers franchise history from 2010 - 2017 will make a fascinating case study some day, but I don’t think 2018 will add another dramatic return from the dead to the story. I still like the A’s players and think they could contend in the coming years, but the starting pitching is too shaky to predict good things this season.<br /><br />NL EAST<br /><br />1. Washington<br />2. New York<br />3. Philadelphia<br />4. Atlanta <br />5. Miami<br /><br />The Nationals are basically what they have been for the last six years -- the clear favorite in the NL East. This is probably the last year for them to enjoy that status, but that’s a pretty impressive run in a division that features two big markets and a Braves franchise that until some point in the Washington run had basically contended for 25 years. As a neutral observer, it would be nice to at least see them get a NLCS out of the deal. Everyone talks about the health of the Mets rotation, but I think scoring runs might be a bigger question mark. I like the Phillies over the Braves this season, but over the next five years I’d flip that. Philly is a popular second wildcard pick--while that’s certainly within the realm of possibility, it will take better than forecast performances from some of the rookies (JP Crawford, Jorge Alfaro, Nick Williams) and Maikel Franko to make that happen. The Marlins are obviously a sad team to ponder, but the fact that Derek Jeter’s halo is being tarnished in the process makes it more entertaining than the usual Miami teardown.<br /><br />NL CENTRAL<br /><br />1. Chicago<br />2. St. Louis (wildcard)<br />3. Milwaukee<br />4. Pittsburgh<br />5. Cincinnati<br /><br />The Cubs have the best offense in the NL by my estimation (although they distributed their runs across games so unfortunately last season that it wasn’t evident in the standings), their rotation is stronger entering this season (relative to last April) with the acquisitions of Jose Quintana and Yu Darvish, and I think they’re ready to re-challenge the Dodgers for NL superiority. The Cardinals look like a solid 86 win team, which is enough to make them a wildcard favorite; if they win with it, it’s a departure from the Pujols-era Cardinal teams which always had big stars, although maybe Carlos Martinez will take a step forward or Marcell Ozuna will hold his level and people will recognize how good he is outside of Miami and Stanton’s shadow. I look at four sources for team win projections when writing these up: my own crude version (fueled by the Steamer projections published at Fangraphs and some manual overrides on my part), Fangraphs, PECOTA from Baseball Prospectus, and Clay Davenport’s. The Brewers projected wins range from 76 - 86, which is tied with PECOTA darling Tampa Bay for the largest spread. Mine is on the low end of the spectrum--it just doesn’t seem like they have the pitching, and they have an outfield/corners logjam that’s good for depth but bad for allowing all of their name hitters to fully contribute. Last year I held on to hope for the Pirates; now I think it’s safe to say their 2012 - 2015 revival is over (come here for the bold statements). Amazingly, they would have been better off to have been in the NL East. If the only baseball I was allowed to watch this year was the games of one of the teams I picked last, I’d go with the Reds. Joey Votto, Luis Castillo, some interesting bullpen pieces, Billy Hamilton as a side show…it’s a fun team if not a good one.<br /><br />NL WEST<br /><br />1. Los Angeles<br />2. Arizona (wildcard)<br />3. San Francisco<br />4. Colorado<br />5. San Diego<br /><br />I might be shortchanging the Dodgers by not picking them as the best team in the NL. They are still really good, they still have good depth, they still have the resources to address issues, but you know all that. There’s not much to say other than to tip one’s cap to the machine. I’m not bullish on the Diamondbacks, per se, but I’ll see your Zack Greinke decline concerns and raise you Zack Godley. I was surprised at how well the Giants came out when I put my forecast spreadsheet together; I was expecting 78-82 wins. A few more put them in prime wildcard contention position, but that was before Bumgarner and Shark became huge injury concerns. I don’t think the Rockies offense is all that good. I don’t think you can expect Charlie Blackmon to be as good, I still am skeptical of DJ LeMahieu, catcher and first base aren’t exactly settled. The Padres are definitely intriguing going forward, but it’s too soon to expect contention.<br /><br />WORLD SERIES<br /><br />Houston over Chicago<br /><br />AL ROY: RF Austin Hays, BAL<br />AL Cy Young: Trevor Bauer, CLE<br />I don’t actually think this is the most likely outcome, I just love Trevor Bauer.<br />AL MVP: SS Carlos Correa, HOU<br />NL ROY: SP Alex Reyes, STL<br />NL Cy Young: Stephen Strasburg, WAS<br />NL MVP: RF Bryce Harper, WAS<br />phttp://www.blogger.com/profile/18057215403741682609noreply@blogger.com0tag:blogger.com,1999:blog-12133335.post-18801905049897703622018-02-28T07:53:00.000-05:002018-02-28T07:53:16.345-05:00Enby Distribution, pt. 5: W% EstimateWhile an earlier post contained the full explanation of the methodology used to estimate W%, it’s an important enough topic to repeat in full here. The methodology is not unique to Enby; it could be implemented with any estimate of the frequency of runs scored per game (and in fact I first implemented it with the Tango Distribution). As I discussed last time, the math may look complicated and require a computer to implement, but the model itself is arguably the simplest conceptually because it is based on the simple logic of how games are decided.<br /><br />Let p(k) be the probability of scoring k runs in a game and q(m) be the probability of allowing m runs a game. If k is greater than m, then the team will win; if k is less than m, then the team will lose. If k and m are equal, then the game will go to extra innings. In setting it up this way, I am implicitly assuming that p(k) is the probability of scoring k runs in nine innings rather than in a game. This is not a horrible way to go about it since the average major league game has about 27 outs once the influences that cause shorter games (not batting in the ninth, rain) are balanced with the longer games created by extra innings. Still, it should be noted that the count of runs scored from a particular game does not necessarily arise from an equivalent opportunity context (as defined by innings or outs) of another game.<br /><br />Given this notation, we can express the probability of winning a game in the standard nine innings as:<br /><br />P(win 9) = p(1)*q(0) + p(2)*[q(0) +q(1)] +p(3)*[q(0) + q(1) + q(2)] + p(4)*[q(0) + q(1) + q(2) + q(3)] + ...<br /><br />Extra innings will occur whenever k and m are equal:<br /><br />P(X) = p(0)*q(0) + p(1)*q(1) + p(2)*q(2) + p(3)*q(3) + p(4)*q(4) + ...<br /><br />When the game goes to extra innings, it becomes an inning by inning contest. Let n(k) be the probability of scoring k runs in an inning and r(m) be the probability of allowing m runs in an inning. If k is greater than m, the team wins; if k is less than m, the team loses; and if k is equal to m, then the process will repeat until a winner is determined. <br /><br />To find the probability of each of the three possible outcomes of an extra inning, we can follow the same logic as used above for P(win 9). The probability of winning the inning is:<br /><br />P(win inning) = n(1)*r(0) +n(2)*[r(0) +r(1)] +n(3)*[r(0) + r(1) + r(2)] + n(4)*[r(0) + r(1) + r(2) + r(3)] + ...<br /><br />The probability of the game continuing (equivalent to tying the inning) is similar to P(extra innings above):<br /><br />P(tie inning) = n(0)*r(0) + n(1)*r(1) +n(2)*r(2) + n(3)*r(3) + n(4)*r(4) + ...<br /><br />The probability of winning in extra innings [P(win X)] is:<br /><br />P(win X) = P(win inning) + P(tie inning)*P(win inning) + P(tie inning)^2*P(win inning) + P(tie inning)^3*P(win inning) + ...<br /><br />This is a geometric series that simplifies to:<br /><br />P(win X) = P(win inning)*[P(tie inning) + P(tie inning)^2 + P(tie inning)^3 + ...] = P(win inning)*1/[1 - P(tie inning)] = P(win inning)/[1 - P(tie inning)]<br /><br />This could also be expressed in a very clever way using the <a href="https://en.wikipedia.org/wiki/Craps_principle">Craps Principle</a> if we had also computed P(lose inning); I did it that way last time, but it doesn’t really cut down on the amount of calculation necessary in this case.<br /><br />Since I want these last few posts to serve as a comprehensive explanation of how to calculate the Enby run and win estimates, it is necessary to take a moment to review how to use the Tango Distribution to estimate the runs per inning distribution. c of course is the constant, set at .852 when looking with a head-to-head matchup. RI is runs/inning, which I’ve defined as RG/9:<br /><br />a = c*RI^2<br />n(0) = RI/(RI + a)<br />d = 1 - c*f(0)<br />n(1) = (1 - n(0))*(1 - d)<br />n(k) = n(k - 1)*d for k >= 2<br /><br />Once we have these three key probabilities [P(win 9), P(X), and P(win X)], the formula for W% is obvious:<br /><br />W% = P(win 9) + P(X)*P(win X)<br /><br />We will use the Enby Distribution to determine p(k) and q(m), and the Tango Distribution to determine n(k) and r(m). In both cases, we’ll use the Tango Distribution constant c = .852 since this works best when looking at a head-to-head matchup, which certainly is the applicable context when discussing W%.<br /><br />I have put together a <a href="https://docs.google.com/spreadsheets/d/e/2PACX-1vRUts4tT5khcH1bBUjw5buCRdmn3xDnJoQEPDDN5xHu91_AUdJKOtIvyVtZwt1ZY2i-xzVH2PITeMJy/pub?output=xlsx">spreadsheet</a> that will handle all of the calculations for you. The yellow cells are the ones that you can edit, with the most important being R (cell B1) and RA (cell L1), which naturally are where you enter the average R/G and RA/G for the team whose W% you’d like to estimate. The other yellow cell is for the c value of Tango Distribution. Please note that editing this cell will do nothing to change the Enby Distribution parameters--those are fixed based on using c = .852. Editing c in this cell (B8) will only change the estimates of the per inning scoring probabilities estimated by the Tango Distribution. I don’t advise changing this value, since .852 has been found to work best for head-to-head matchups and leaving it there keeps the Tango Distribution estimates consistent with the Enby Distribution estimates. The sheet also calculates Pythagenpat W% for a given exponent (which you can change in cell B15). <br /><br />The calculator supports the same range of values as the one for single team run distribution introduced in part 9--RG at intervals of .25 between 0-3 and 7-15 runs, and at intervals of .05 between 3-7 runs. The vlookup function will round down to the next R/G value on the parameter sheet (for example, the two highest values supported are 14.75 and 15.00. You can enter 14.93 if you want, but the Enby calculation will be based on 14.75 (the Pythagenpat calculation will still be based on 14.93). Have some fun playing around with it, and next time we’ll look at how accurate the Enby estimate is compared to other W% models.phttp://www.blogger.com/profile/18057215403741682609noreply@blogger.com0tag:blogger.com,1999:blog-12133335.post-81325313025579644302018-02-13T17:48:00.001-05:002018-02-13T17:49:33.161-05:00Doubles or NothingIn previewing the season to come for any team, it is customary (for good reason) to start by taking a look back at the previous season. Sometimes this is a pleasant or at least unobjectionable experience. On some occasions, though, it forces one to review an absolute disaster of a season, as was turned in by the 2017 Ohio State Buckeyes.<br /><br />OSU went 22-34, which was the lowest W% by a Buckeye club since 1974. Their 8-16 Big Ten record was the worst since 1987. The seven years in which Beals have been at the helm have produced a .564 W%, which excepting the largely overlapping span of 2008-2014, is the worst since 1986-1992. Beals has taken the program build by Bob Todd, who inherited the late 80s malaise, and driven it right back into mediocrity.<br /><br />Yet merrily he rolls along, untroubled by the pressures of coaching at a school that fired its all-time winningest basketball coach for having two straight NCAA tournament misses, despite compiling a .500 record in Big Ten play over those two seasons. Beals and his unenlightened brand of baseball may be too small fry to draw the ire of AD Gene Smith, but tell that to the track, gymnastics, and women’s hockey coaches who have been pushed out in recent years. Beals record of doing less with a historically strong program is unmatched at the University.<br /><br />When one peruses the likely lineup for 2018, it’s hard to think that a turnaround is imminent. Stranger things have happened, of course, but eight years into his tenure in Columbus, enough time to have nearly turned over two whole recruiting classes with no overlap, he is still plugging roster wholes with unproven JUCO transfers, failing to develop the high school recruits he’s brought in. It’s gotten to the point that if a player doesn’t find a role as a freshman, you can basically write him off as a future contributor.<br /><br />Junior Jacob Barnwell is firmly ensconced at catcher; he was an average hitter last year and appears to have the coach seal of approval as a receiver, so he’s golden for playing time over the next two seasons. True freshman Dillon Dingler may be the heir apparent, with junior Andrew Fishel and redshirt freshman Scottie Seymour providing depth.<br /><br />Seniors Bo Coolen and Noah McGowan, both JUCO transfers a year ago, will compete for first base; Coolen was bad offensively in 2017 with no power (.074 ISO), McGowan a little better but still below average. Junior Brady Cherry will move from the hot corner to the keystone, a curious move to this observer; Cherry flashed power as a freshman but was middling with the bat last year. That opens up third for sophomore Connor Pohl, who filled in admirably at second last year but does look more like a third baseman; on a rate basis he was the second most productive returning hitter, although it wasn’t a huge sample size (89 PA and it was very BA-heavy with a .325 BA/.225 SEC). JUCO transfer junior Kobie Foppe is penciled in at shortstop. The utility infielders are both sophomores; Noah West played more as a freshman, getting starts at second base (he didn’t hit at .213/.278/.303) and serving as a defensive replacement for Pohl, while Carpenter had 14 hitless (one walk) PAs. True freshman Aaron Hughes rounds out the roster.<br /><br />Senior Tyler Cowles has the inside track at left field, coming off a first season as a JUCO transfer in which he hit .190/.309/.314 over 129 PA. McGowan could also contend for this spot, with backup outfield redshirt juniors Nate Romans and Ridge Winand also in the mix. JUCO transfer Malik Jones has been anointed as the centerfielder, with true freshman Jake Ruby as an understeady. Right field along with catcher is the only spot on the roster that features an established starter at the same position; sophomore Dominic Canzone is OSU’s best returning hitter, although it was BA heavy (.343 BA/.205 SEC). Some combination of Cowles, McGowan, and Fishel would appear to have the first crack at DH.<br /><br />OSU’s pitching was an utter disaster last year, partly due to injury and partly because, well, Greg Beals. The only sure bet for the rotation appears to be senior Adam Niemeyer, with junior lefty Connor Curlis and senior Yianni Pavlopoulos (who closed as a sophomore) most likely to join him. Their RAs were 6.23, 5.03, and 7.65 respectively in 2017, although only Curlis had good health. Junior Ryan Feltner pitched poorly last year (7.32 RA over 62 IP despite 8.2 K/9), then went to the Cape Cod league and was named Reliever of the Year. Sophomore Jake Vance had a 6.92 RA over 26 innings, largely thanks to 20 walks, and is the fifth rotation candidate.<br /><br />The perennial bright spot of the pitching staff is senior righty Seth Kinker, who easily led the team with 13 RAA over 58 innings, even getting 3 starts when everything fell to pieces. He figures to be the go-to reliever, with fifth-year senior righties Kyle Michalik, Austin Woody, and Curtiss Irving in middle relief. You’re not going to believe this, but their RAs ranged between 6.85 and 7.94 over a combined 66 innings. Sophomore Thomas Waning will follow Kinker and Michalik in one of Beals’ good traits, which is an affinity for sidearmers; Waning was effective (11 K, 4 W) in a 12 inning injury-shortened debut season. Junior Dustin Jourdan will be in the mix as well.<br /><br />Beals also has an affinity for lefty specialists, which he will have to cultivate anew from sophomore Andrew Magno (4 appearances in 2016) and true freshman Luke Duermit, Griffan Smith, and Alex Theis.<br /><br />The schedule is fairly typical, with the opening weekend (starting Friday) featuring a pair of games with both Canisus and UW-Milwaukee in Florida. The following weekend will see the Bucks in Arizona for the Big Ten/Pac-12 Challenge where they’ll play two each against Utah and Oregon State. Another trip to Florida to play low-level opponents (Nicholls State, Southern Miss, and Eastern Michigan) follows, followed by a trip to the Carolinas that will feature two games each against High Point, Coastal Carolina, and UNC-Wilmington.<br /><br />Bizarrely, the home schedule opens March 16 with a weekend series against Cal St-Northridge; usually any home dates with non-Northern opponents come later in the calendar. Another non-conference weekend series against Georgetown follows, and then Big Ten play: Nebraska, @ Iowa, @ Penn St, Indiana, Minnesota, Illinois, Purdue, @ Michigan St. Mixed in will be a typically home-heavy mid-week slate (Eastern Michigan, Toledo, Kent St, Ohio University, Miami, Campbell) with road games at Ball St and Cincinnati.<br /><br />As I wrote the roster outlook (which relied on my own knowledge and guesses but also heavily on the season preview released by the athletic department), two things that I already thought I knew struck me even more plainly.<br /><br />1) This team does not appear to be very good. One can construct a rosy scenario where the pitching woes of 2017 were due largely to injury, but we’re talking about pitcher injuries. It takes extra tint on those glasses. It has to be better than last year, when nine pitchers started at least three games, but this team was 22-34; “better” isn’t going to cut it. <br /><br />2) The offense has a couple solid returnees, but in the eighth year of Beals tenure, major positions on the diamond are still being papered over with JUCO transfers. There is no pipeline of young players getting their feet wet in utility roles and transitioning into starting as you would expect in a healthy program. There are no freshman studs to come in and commandeer lineup positions as you would expect in a strong program. It is quite easy to imagine a scenario in which five of the nine lineup spots are held by first or second-year JUCO transfers.<br /><br />Beals has failed in recruiting, he has failed in player development, and most importantly he has failed to win at the level to which an OSU program should aspire. I’ve devoted many words in previous season previews and recaps (and the hashtag #BealsBall) to his asinine tactics. I won’t rehash that here, but I will end with a quote from the Meet the Team Dinner that program icon Nick Swisher was roped into headlining, which makes one seriously question in what decade Mr. Beals thinks he coaches:<br /><br /><i>“Our goal in 2018 is to hit a lot of doubles,” said Beals on Saturday night.<br /></i>phttp://www.blogger.com/profile/18057215403741682609noreply@blogger.com0tag:blogger.com,1999:blog-12133335.post-18458610589190368612018-01-08T08:46:00.000-05:002018-01-08T08:46:14.880-05:00Run Distribution and W%, 2017I always start this post by looking at team records in blowout and non-blowout games. This year, after a Twitter discussion with Tom Tango, I’ve narrowed the definition of blowout to games in which the margin of victory is six runs or more (rather than five, the definition used by Baseball-Reference and that I had independently settled on). In 2017, the percentage of games decided by x runs and by >= x runs are:<br /><br /><a href="https://4.bp.blogspot.com/--bCvpRvNFZM/Wk6wEGfy3nI/AAAAAAAACeI/teJD3ayrAEkLDVUYgRNeoBRsRLGgTh4WgCLcBGAs/s1600/rd17a.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://4.bp.blogspot.com/--bCvpRvNFZM/Wk6wEGfy3nI/AAAAAAAACeI/teJD3ayrAEkLDVUYgRNeoBRsRLGgTh4WgCLcBGAs/s400/rd17a.jpg" width="395" height="400" data-original-width="322" data-original-height="326" /></a><br /><br />If you draw the line at 5 runs, then 21.6% of games are classified as blowouts. At 6 runs, it drops to 15.3%. Tango asked his Twitter audience two different but related poll questions. The <a href="https://twitter.com/tangotiger/status/826804266803265537">first</a> was “what is the minimum margin that qualifies a game as a blowout?”, for which the plurality was six (39%, with 5, 7, and 8 the other options). The <a href="https://twitter.com/tangotiger/status/827317071205769218">second</a> was “what percentage of games do you consider to be blowouts?”, for which the plurality was 8-10% (43%, with the other choices being 4%-7%, 11%-15%, and 17-21%). Using the second criterion, one would have to set the bar at a margin of seven, at least in 2017.<br /><br />As Tango pointed out, it is of interest that asking a similar question in different ways can produce different results. Of course this is well-known to anyone with a passing interest in public opinion polling. But here I want to focus more on some of the pros and cons of having a fixed standard for a blowout or one that varies depending on the actual empirical results from a given season. <br /><br />A variable standard would recognize that as the run environment changes, the distribution of victory margin will surely change (independent of any concurrent changes in the distribution of team strength), expanding when runs are easier to come by. Of course, this point also means that what is a blowout in Coors Field may not be a blowout in Petco Park. The real determining factor of whether a game is a blowout is whether the probability that the trailing team can make a comeback (of course, picking one standard and applying to all games ignores the flow of a game; if you want to make a win probability-based definition, go for it).<br /> <br />On the other hand, a fixed standard allows the percentage of blowouts to vary over time, and maybe it should. If the majority of games were 1-0, it would sure feel like there were vary few blowouts even if the probability of the trailing team coming back was very low. Ideally, I would propose a mixed standard, in which the margin necessary for a blowout would not be a fixed % of games but rather somehow tied to the average runs scored/game. However, for the purpose of this post, Tango’s audience answering the simpler question is sufficient for my purposes. I never had any strong rationale for using five, and it does seem like 22% of games as blowouts is excessive.<br /><br />Given the criterion that a blowout is a game in which the margin of victory was six or more, here are team records in non-blowouts:<br /><br /><a href="https://3.bp.blogspot.com/-crhrioRBAzE/Wk6xNzHlOZI/AAAAAAAACeM/gDlf-okw8J0FGwi7CaGPYIDIzk-K6AbSACLcBGAs/s1600/rd17b.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://3.bp.blogspot.com/-crhrioRBAzE/Wk6xNzHlOZI/AAAAAAAACeM/gDlf-okw8J0FGwi7CaGPYIDIzk-K6AbSACLcBGAs/s400/rd17b.jpg" width="195" height="400" data-original-width="257" data-original-height="528" /></a><br /><br />Records in blowouts:<br /><br /><a href="https://1.bp.blogspot.com/-LrEUPl6FqcA/Wk6xUJQbEmI/AAAAAAAACeQ/GUPFZbsI-qU7VXUgHeuGN0Q7QIiM5alQQCLcBGAs/s1600/rd17c.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://1.bp.blogspot.com/-LrEUPl6FqcA/Wk6xUJQbEmI/AAAAAAAACeQ/GUPFZbsI-qU7VXUgHeuGN0Q7QIiM5alQQCLcBGAs/s400/rd17c.jpg" width="195" height="400" data-original-width="258" data-original-height="528" /></a><br /><br />The difference between blowout and non-blowout records (B - N), and the percentage of games for each team that fall into those categories:<br /><br /><a href="https://3.bp.blogspot.com/-Imnd_gkWV78/Wk6xaYibybI/AAAAAAAACeU/lULCkbfVcfU5ZlutCd8_zMjlIFvCKbx0QCLcBGAs/s1600/rd17d.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://3.bp.blogspot.com/-Imnd_gkWV78/Wk6xaYibybI/AAAAAAAACeU/lULCkbfVcfU5ZlutCd8_zMjlIFvCKbx0QCLcBGAs/s400/rd17d.jpg" width="195" height="400" data-original-width="258" data-original-height="528" /></a><br /><br />Keeping in mind that I changed definitions this year (and in so doing increased random variation if for no reason other than the smaller percentage of games in the blowout bucket), it is an oddity to see two of the very best teams in the game (HOU and WAS) with worse records in blowouts. Still, the general pattern is for strong teams to be even better in blowouts, per usual. San Diego stands out as the most extreme team, with an outlier poor record in blowouts offsetting an above-.500 record in non-blowouts, although given that they play in park with the lowest PF, their home/road discrepancy between blowout frequency should theoretically be higher than most teams.<br /><br />A more interesting way to consider game-level results is to look at how teams perform when scoring or allowing a given number of runs. For the majors as a whole, here are the counts of games in which teams scored X runs:<br /><br /><a href="https://3.bp.blogspot.com/-0j3htPsYddw/Wk6ypfXsCKI/AAAAAAAACeY/qhPPg-Opy0kfFkyEhc1ho-FlWszk5YWngCLcBGAs/s1600/rd17e.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://3.bp.blogspot.com/-0j3htPsYddw/Wk6ypfXsCKI/AAAAAAAACeY/qhPPg-Opy0kfFkyEhc1ho-FlWszk5YWngCLcBGAs/s400/rd17e.jpg" width="400" height="363" data-original-width="449" data-original-height="408" /></a><br /><br />The “marg” column shows the marginal W% for each additional run scored. In 2017, three was the mode of runs scored, while the second run resulted in the largest marginal increase in W%.<br /><br />The major league average was 4.65 runs/game; at that level, here is the estimated probability of scoring x runs using the Enby Distribution (stopping at fifteen):<br /><br /><a href="https://2.bp.blogspot.com/-KtOsb1yVgKk/Wk6y2j7JA3I/AAAAAAAACec/kIE2SYk7HFMNj07A6v7b6pC3q73ztiDFQCLcBGAs/s1600/rd17f.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://2.bp.blogspot.com/-KtOsb1yVgKk/Wk6y2j7JA3I/AAAAAAAACec/kIE2SYk7HFMNj07A6v7b6pC3q73ztiDFQCLcBGAs/s400/rd17f.jpg" width="265" height="400" data-original-width="193" data-original-height="291" /></a><br /><br />In graph form (again stopping at fifteen):<br /><br /><a href="https://2.bp.blogspot.com/-upZMsDdB0fM/Wk6zLLOFk4I/AAAAAAAACeg/XPQ2eR96c0oSevxCGlvg_Cw8Zdc5Bw4lQCLcBGAs/s1600/rd17g.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://2.bp.blogspot.com/-upZMsDdB0fM/Wk6zLLOFk4I/AAAAAAAACeg/XPQ2eR96c0oSevxCGlvg_Cw8Zdc5Bw4lQCLcBGAs/s400/rd17g.jpg" width="400" height="266" data-original-width="1285" data-original-height="856" /></a><br /><br />This is a pretty typical visual for the Enby fit to the major league average. It’s not perfect, but it is a reasonable model.<br /><br />In previous years I’ve used this observed relationship to calculate metrics of team offense and defense based on the percentage of games in which they scored or allowed x runs. But I’ve always wanted to switch to using theoretical values based on the Enby Distribution, for a number of reasons:<br /><br />1. The empirical distribution is subject to sample size fluctuations. In 2016, all 58 times that a team scored twelve runs in a game, they won; meanwhile, teams that scored thirteen runs were 46-1. Does that mean that scoring 12 runs is preferable to scoring 13 runs? Of course not--it's a quirk in the data. Additionally, the marginal values don’t necessary make sense even when W% increases from one runs scored level to another.<br /><br />2. Using the empirical distribution forces one to use integer values for runs scored per game. Obviously the number of runs a team scores in a game is restricted to integer values, but not allowing theoretical fractional runs makes it very difficult to apply any sort of park adjustment to the team frequency of runs scored.<br /><br />3. Related to #2 (really its root cause, although the park issue is important enough from the standpoint of using the results to evaluate teams that I wanted to single it out), when using the empirical data there is always a tradeoff that must be made between increasing the sample size and losing context. One could use multiple years of data to generate a smoother curve of marginal win probabilities, but in doing so one would lose centering at the season’s actual run scoring rate. On the other hand, one could split the data into AL and NL and more closely match context, but you would lose sample size and introduce more quirks into the data. <br /><br />So this year I am able to use the Enby Distribution. I have Enby Distribution parameters at each interval of .05 runs/game. Since it takes a fair amount of manual work to calculate the Enby parameters, I have not done so at each .01 runs/game, and for this purpose it shouldn’t create too much distortion (more on this later). The first step is to take the major league average R/G (4.65) and park-adjust it. I could have park-adjusted home and road separately, and in theory you should be as granular as practical, but the data on teams scoring x runs or more is not readily available broken out between home and road. So each team’s standard PF which assumes a 50/50 split of home and road games is used. I then rounded this value to the nearest .05 and calculated the probability of scoring x runs using the Enby Distribution (with c = .852 since this exercise involves interactions between two teams).<br /><br />For example, there were two teams that had PFs that produced a park-adjusted expected average of 4.90 R/G (ARI and TEX). In other words, an average offense playing half their games in Arizona's environment should have scored 4.90 runs/game; an average defense doing the same should have allowed 4.90 runs/game. The Enby distribution probabilities of scoring x runs for a team averaging 4.90 runs/game are:<br /><br /><a href="https://2.bp.blogspot.com/-jwGlbd7fj3Q/Wk6zznybyEI/AAAAAAAACek/EyPB7cfTI48JAjx9HgRk2eKAYkO76lwvwCLcBGAs/s1600/rd17h.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://2.bp.blogspot.com/-jwGlbd7fj3Q/Wk6zznybyEI/AAAAAAAACek/EyPB7cfTI48JAjx9HgRk2eKAYkO76lwvwCLcBGAs/s400/rd17h.jpg" width="138" height="400" data-original-width="129" data-original-height="374" /></a><br /><br />For each x, it’s simple to estimate the probability of winning. If this team scores three runs in a particular game, then they will win if they allow 0 (4.3%), 1 (8.6%), or 2 runs (12.1%). As you can see, this construct assumes that their defense is league-average. If they allow three, then the game will go to extra innings, in which case they have a 50% chance of winning (this exercise doesn’t assume anything about inherent team quality), so in another 13.6% of games they win 50%. Thus, if this the Diamondbacks score three runs, they should win 31.8% of those games. If they allow three runs, it’s just the complement; they should win 68.2% of those games.<br /><br />Using these probabilities and each team’s actual frequency of scoring x runs in 2017, I calculate what I call Game Offensive W% (gOW%) and Game Defensive W% (gDW%). It is analogous to James’ original construct of OW% except looking at the empirical distribution of runs scored rather than the average runs scored per game. (To avoid any confusion, James in 1986 also proposed constructing an OW% in the manner in which I calculate gOW%, which is where I got the idea).<br /><br />As such, it is natural to compare the game versions of OW% and DW%, which consider a team’s run distribution, to their OW% and DW% figured using Pythagenpat in a traditional manner. Since I’m now using park-adjusted gOW%/gDW%, I have park-adjusted the standard versions as well. As a sample calculation, Detroit averaged 4.54 R/G and had a 1.02 PF, so their adjusted R/G is 4.45 (4.54/1.02). OW% The major league average was 4.65 R/G, and since they are assumed to have average defense we use that as their runs allowed. The Pythagenpat exponent is (4.45 + 4.65)^.29 = 1.90, and so their OW% is 4.45^1.90/(4.45^1.90 + 4.65^1.90) = .479, meaning that if the Tigers had average defense they would be estimated to win 47.9% of their games.<br /><br />In previous year’s posts, the major league average gOW% and gDW% worked out to .500 by definition. Since this year I’m 1) using a theoretical run distribution from Enby 2) park-adjusting and 3) rounding team’s park-adjusted average runs to the nearest .05, it doesn’t work out perfectly. I did not fudge anything to correct for the league-level variation from .500, and the difference is small, but as a technical note do consider that the league average gOW% is .497 and the gDW% is .503.<br /><br />For most teams, gOW% and OW% are very similar. Teams whose gOW% is higher than OW% distributed their runs more efficiently (at least to the extent that the methodology captures reality); the reverse is true for teams with gOW% lower than OW%. The teams that had differences of +/- 2 wins between the two metrics were (all of these are the g-type less the regular estimate, with the teams in descending order of absolute value of the difference):<br /><br />Positive: SD, TOR<br />Negative: CHN, WAS, HOU, NYA, CLE<br /><br />The Cubs had a standard OW% of .542, but a gOW% of .516, a difference of 4.3 wins which is the largest such discrepancy for any team offense/defense in the majors this year. I always like to pick out this team and present a graph of their runs scored frequencies to offer a visual explanation of what is going on, which is that they distributed their runs less efficiently for the purpose of winning games than would have been expected. The Cubs average 5.07 R/G, which I’ll round to 5.05 to be able to use an estimated distribution I have readily available from Enby (using the parameters for c = .767 in this case since we are just looking at one team in isolation):<br /><br /><a href="https://3.bp.blogspot.com/-X1lf-NBJnPQ/Wk60J7uEPFI/AAAAAAAACeo/7ZygBuwcbEAnWUd1qZLpdW36gR7loZ9qgCLcBGAs/s1600/rd17i.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://3.bp.blogspot.com/-X1lf-NBJnPQ/Wk60J7uEPFI/AAAAAAAACeo/7ZygBuwcbEAnWUd1qZLpdW36gR7loZ9qgCLcBGAs/s400/rd17i.jpg" width="400" height="267" data-original-width="1237" data-original-height="825" /></a><br /><br />The Cubs were shutout or held to one run in eight more games than one would expect for a team that average 5.05 R/G; of course, these are games that you almost certainly will not win. They scored three, four, or six runs significantly less than would be expected; while three and four are runs levels at which in 2017 you would expect to lose more often then you win, even scoring three runs makes a game winnable (.345 theoretical W% for a team in the Cubs’ run environment). The Cubs had 4.5 fewer games scoring between 9-12 runs than expected, which should be good from an efficiency perspective, since even at eight runs they should have had a .857 W%. But they more than offset that by scoring 13+ runs in a whopping 6.8% of their games, compared to an expectation of 2.0%--7.8 games more than expected where they gratuitously piled on runs. Chicago scored 13+ runs in 11 games, with Houston and Washington next with nine, and it’s no coincidence that they were also very inefficient offensively.<br /><br />The preceding paragraph is an attempt to explain what happened; despite the choice of non-neutral wording, I’m not passing judgment. The question of whether run distribution is strongly predictive compared to average runs has not been studied in sufficient detail (by me at least), but I tend to think that the average is a reasonable indicator of quality going forward. Even if I’m wrong, it’s not “gratuitous” to continue to score runs after an arbitrary threshold with a higher probability of winning has been cleared. In some cases it may even be necessary, as the Cubs did have three games in which they allowed 13+ runs, although they weren’t the same games. As we saw earlier, major league teams were 111-0 when scoring 13+ runs, and 294-17 when scoring 10-12.<br /><br />Teams with differences of +/- 2 wins between gDW% and standard DW%:<br /><br />Positive: SD, CIN, NYN, MIN, TOR, DET<br />Negative: CLE, NYA<br /><br />San Diego and Toronto had positive differences on both sides of the ball; the Yankees and Cleveland had negative difference for both. Thus it is no surprise that those teams show up on the list comparing gEW% to EW% (standard Pythagenpat). gEW% combines gOW% and gDW% indirectly by converting both to equivalent runs/game using Pythagenpat (see <a href="http://walksaber.blogspot.com/2009/01/perfunctory-look-at-run-distribution.html">this post</a> for the methodology):<br /><br />Positive: SD, TOR, NYN, CIN, OAK<br />Negative: WAS, CHN, CLE, NYA, ARI, HOU<br /><br />The Padres EW% was .362, but based on the manner in which they actually distributed their runs and runs allowed per game, one would have expected a .405 W%, a difference of 6.9 wins which is an enormous difference for these two approaches. In reality, they had a .438 W%, so Pythagenpat’s error was 12.3 wins which is enormous in its own right.<br /><br />gEW% is usually (but not always!) a more accurate predictor of actual W% than EW%, which it should be since it has the benefit of additional information. However, gEW% assumes that runs scored and allowed are independent of each other on the game-level. Even if that were true theoretically (and given the existence of park factors alone it isn’t), gEW% would still be incapable of fully explaining discrepancies between actual records and Pythagenpat.<br /><br />The various measures discussed are provided below for each team.<br /><br /><a href="https://2.bp.blogspot.com/-f_HUgpsp7wQ/Wk61DdiuyNI/AAAAAAAACes/fwXfxNc-45EzOISUOGB-qj_o8LBvsZmiQCLcBGAs/s1600/rd17j.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://2.bp.blogspot.com/-f_HUgpsp7wQ/Wk61DdiuyNI/AAAAAAAACes/fwXfxNc-45EzOISUOGB-qj_o8LBvsZmiQCLcBGAs/s400/rd17j.jpg" width="322" height="400" data-original-width="426" data-original-height="529" /></a><br /><br />Finally, here are the <a href="http://walksaber.blogspot.com/2017/12/crude-team-ratings-2017.html">Crude Team Ratings</a> based on gEW% since I hadn’t yet calculated gEW% when that post was published:<br /><br /><a href="https://4.bp.blogspot.com/-1yR2MC_vS7c/Wk614W0gQzI/AAAAAAAACew/I6Xj_H6cnjQZCQujTtTG09I_8ksKvHkUwCLcBGAs/s1600/rd17k.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://4.bp.blogspot.com/-1yR2MC_vS7c/Wk614W0gQzI/AAAAAAAACew/I6Xj_H6cnjQZCQujTtTG09I_8ksKvHkUwCLcBGAs/s400/rd17k.jpg" width="285" height="400" data-original-width="377" data-original-height="529" /></a><br />phttp://www.blogger.com/profile/18057215403741682609noreply@blogger.com0tag:blogger.com,1999:blog-12133335.post-66760394830228435672017-12-18T09:53:00.000-05:002017-12-18T09:53:37.229-05:00Crude Team Ratings, 2017For the last several years I have published a set of team ratings that I call "Crude Team Ratings". The name was chosen to reflect the nature of the ratings--they have a number of limitations, of which I documented several when I introduced the <a href="http://walksaber.blogspot.com/2011/01/crude-team-ratings.html">methodology</a>. <br /><br />I explain how CTR is figured in the linked post, but in short:<br /><br />1) Start with a win ratio figure for each team. It could be actual win ratio, or an estimated win ratio.<br /><br />2) Figure the average win ratio of the team’s opponents.<br /><br />3) Adjust for strength of schedule, resulting in a new set of ratings.<br /><br />4) Begin the process again. Repeat until the ratings stabilize.<br /><br />The resulting rating, CTR, is an adjusted win/loss ratio rescaled so that the majors’ arithmetic average is 100. The ratings can be used to directly estimate W% against a given opponent (without home field advantage for either side); a team with a CTR of 120 should win 60% of games against a team with a CTR of 80 (120/(120 + 80)).<br /><br />First, CTR based on actual wins and losses. In the table, “aW%” is the winning percentage equivalent implied by the CTR and “SOS” is the measure of strength of schedule--the average CTR of a team’s opponents. The rank columns provide each team’s rank in CTR and SOS:<br /><br /><a href="https://1.bp.blogspot.com/-yKLWxOoghjI/WjWIKmggzaI/AAAAAAAACdU/fxuDh85YDDArfiDjsZjs9EelTwKHKpwhQCLcBGAs/s1600/ctr17a.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://1.bp.blogspot.com/-yKLWxOoghjI/WjWIKmggzaI/AAAAAAAACdU/fxuDh85YDDArfiDjsZjs9EelTwKHKpwhQCLcBGAs/s400/ctr17a.jpg" width="286" height="400" data-original-width="377" data-original-height="528" /></a><br /><br />The top ten teams were the playoff participants, with the two pennant winners coming from the group of three teams that formed a clear first-tier. The #9 and #10 teams lost the wildcard games. Were it not for the identity of the one of those three that did not win the pennant, it would have been about as close to perfect a playoff outcome as I could hope for. What stood out the most among the playoff teams to me is that Arizona ranked slightly ahead of Washington. As we’ll see in a moment, the NL East was bad, and as the best team in the worst division, the Nationals had the lowest SOS in the majors, with their average opponent roughly equivalent to the A’s, while the Diamondbacks’ average opponent was roughly equivalent to the Royals.<br /> <br />Next are the division averages. Originally I gave the arithmetic average CTR for each divison, but that’s mathematically wrong--you can’t average ratios like that. Then I switched to geometric averages, but really what I should have done all along is just give the arithemetic average aW% for each division/league. aW% converts CTR back to an “equivalent” W-L record, such that the average across the major leagues will be .50000. I do this by taking CTR/(100 + CTR) for each team, then applying a small fudge factor to force the average to .500. In order to maintain some basis for comparison to prior years, I’ve provided the geometric average CTR alongside the arithmetric average aW%, and the equivalent CTR by solving for CTR in the equation:<br /><br />aW% = CTR/(100 + CTR)*F, where F is the fudge factor (it was 1.0005 for 2017 lest you be concerned there is a massive behind-the-scenes adjustment taking place).<br /><br /><a href="https://1.bp.blogspot.com/-tJ1O9x342H4/WjWIqoPvE0I/AAAAAAAACdg/Z9MQ5Ysf1ZML1Cts1CYEWaasbC0lKrd9gCLcBGAs/s1600/ctr17b.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://1.bp.blogspot.com/-tJ1O9x342H4/WjWIqoPvE0I/AAAAAAAACdg/Z9MQ5Ysf1ZML1Cts1CYEWaasbC0lKrd9gCLcBGAs/s400/ctr17b.jpg" width="400" height="243" data-original-width="280" data-original-height="170" /></a><br /><br />The league gap closed after expanding in 2016, but the AL maintained superiority, with only the NL West having a higher CTR than any AL division. It was a good bounceback for the NL West after being the worst division in 2016, especially when you consider that the team that had been second-best for several years wound up as the second-worst team in the majors. The NL East was bad, but not as bad as it was just two years ago.<br /><br />I also figure CTRs based on various alternate W% estimates. The first is based Expected W%, (Pythagenpat based on actual runs scored and allowed):<br /><br /><a href="https://3.bp.blogspot.com/-B_N79UqRf-Q/WjWIenDA52I/AAAAAAAACdY/iW9VPrq20FMdDK3AW9oP97ThjbixphaiwCLcBGAs/s1600/ctr17c.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://3.bp.blogspot.com/-B_N79UqRf-Q/WjWIenDA52I/AAAAAAAACdY/iW9VPrq20FMdDK3AW9oP97ThjbixphaiwCLcBGAs/s400/ctr17c.jpg" width="286" height="400" data-original-width="378" data-original-height="528" /></a><br /><br />The second is CTR based on Predicted W% (Pythagenpat based on runs created and allowed, actually Base Runs):<br /><br /><a href="https://2.bp.blogspot.com/-eHS6h1dojQI/WjWI5T-1JOI/AAAAAAAACdk/E6rvZClqK28-Imi91O237NqdvAAwioQDQCLcBGAs/s1600/ctr17d.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://2.bp.blogspot.com/-eHS6h1dojQI/WjWI5T-1JOI/AAAAAAAACdk/E6rvZClqK28-Imi91O237NqdvAAwioQDQCLcBGAs/s400/ctr17d.jpg" width="286" height="400" data-original-width="377" data-original-height="528" /></a><br /><br />Usually I include a version based on Game Expected Winning %, but this year I’m finally switching to using the Enby distribution so it’s going to take a little bit more work, and I’d like to get one of these two posts up before the end of the year. So I will include the CTRs based on gEW% in the Run Distribution post.<br /><br />A few seasons ago I started including a CTR version based on actual wins and losses, but including the postseason. I am not crazy about this set of ratings, the reasoning behind which I tried very poorly to explain last year. A shorter attempt follows: Baseball playoff series have different lengths depending on how the series go. This has a tendency to exaggerate the differences between the teams exhibited by the series, and thus have undue influence on the ratings. When the Dodgers sweep the Diamondbacks in the NLDS, this is certainly additional evidence that we did not previously have which suggests that the Dodgers are a stronger team than the Diamondbacks. But counting this as 3 wins to 0 losses exaggerates the evidence. I don’t mean this in the (equally true) sense that W% over a small sample size will tend to be more extreme than a W% estimate based on components (R/RA, RC/RCA, etc.) This we could easily account for by using EW% or PW%. What I’m getting at is that the number of games added to the sample is dependent on the outcomes of the games that are played. If series were played through in a non-farcical manner (i.e. ARI/LA goes five games regardless of the outcomes), than this would be a moot point. <br /> <br />I doubt that argument swayed even one person, so the ratings including playoff performance are:<br /><br /><a href="https://3.bp.blogspot.com/-2BfZLtNhu_I/WjWJIFqMLpI/AAAAAAAACdo/UimIJR3Upd0TCKXUaq3pwftvf-r4EKuRACLcBGAs/s1600/ctr17e.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://3.bp.blogspot.com/-2BfZLtNhu_I/WjWJIFqMLpI/AAAAAAAACdo/UimIJR3Upd0TCKXUaq3pwftvf-r4EKuRACLcBGAs/s400/ctr17e.jpg" width="286" height="400" data-original-width="378" data-original-height="528" /></a><br /><br />With the Dodgers holding a 161 to 156 lead over the Astros before the playoffs, romping through the NL playoffs at 7-1 while the Astros went 7-4 in the AL playoffs, and taking the World Series to seven games, they actually managed to increase their position as the #1 ranked team. I’m not sure I’ve seen that before--certainly it is common for the World Series winner to not be ranked #1, but usually they get closer to it than further away.<br /><br />And the differences between ratings include playoffs (pCTR) and regular season only (rCTR):<br /><br /><a href="https://2.bp.blogspot.com/-KUQhTsb-p_o/WjWJWtxGtcI/AAAAAAAACdw/pY8cWfj9--oTLBULcjGNRsTYnMZTYkBzgCLcBGAs/s1600/ctr17f.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://2.bp.blogspot.com/-KUQhTsb-p_o/WjWJWtxGtcI/AAAAAAAACdw/pY8cWfj9--oTLBULcjGNRsTYnMZTYkBzgCLcBGAs/s400/ctr17f.jpg" width="158" height="400" data-original-width="208" data-original-height="528" /></a>phttp://www.blogger.com/profile/18057215403741682609noreply@blogger.com0tag:blogger.com,1999:blog-12133335.post-89071655628365699042017-12-11T07:03:00.000-05:002017-12-11T07:03:03.486-05:00Hitting by Position, 2017Of all the annual repeat posts I write, this is the one which most interests me--I have always been fascinated by patterns of offensive production by fielding position, particularly trends over baseball history and cases in which teams have unusual distributions of offense by position. I also contend that offensive positional adjustments, when carefully crafted and appropriately applied, remain a viable and somewhat more objective competitor to the defensive positional adjustments often in use, although this post does not really address those broad philosophical questions.<br /><br />The first obvious thing to look at is the positional totals for 2016, with the data coming from Baseball-Reference.com. "MLB” is the overall total for MLB, which is not the same as the sum of all the positions here, as pinch-hitters and runners are not included in those. “POS” is the MLB totals minus the pitcher totals, yielding the composite performance by non-pitchers. “PADJ” is the position adjustment, which is the position RG divided by the overall major league average (this is a departure from past posts; I’ll discuss this a little at the end). “LPADJ” is the long-term positional adjustment that I use, based on 2002-2011 data. The rows “79” and “3D” are the combined corner outfield and 1B/DH totals, respectively:<br /><br /><a href="https://2.bp.blogspot.com/-qh3yMDIMae4/Winb-_6jRkI/AAAAAAAACbM/9OG3nvruufEmbRlF86ZIGqoOLFgIGRM8gCLcBGAs/s1600/hitpos17a.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://2.bp.blogspot.com/-qh3yMDIMae4/Winb-_6jRkI/AAAAAAAACbM/9OG3nvruufEmbRlF86ZIGqoOLFgIGRM8gCLcBGAs/s400/hitpos17a.jpg" width="400" height="105" data-original-width="981" data-original-height="257" /></a><br /><br />After their record-smashing performance in 2016, second basemen regressed to the mean, although they still outproduced the league average. The mid-defensive spectrum positions, third base and centerfield, were both similarly about 3% above their historical norms, but the real story of 2017 positional offense was DH. DHs were essentially as productive as shortstops. Looking at the two positions’ respective slash lines, DH had the better secondary average, SS the better batting average for the same run output. While DH has been down in recent years, they were at a much more respectable 109 last year. One year of this data tends to yield more blips than trends, although after a league average performance in 2016 left fielders only improved slightly to 102.<br /><br />Moving on to looking at more granular levels of performance, I always start by looking at the NL pitching staffs and their RAA. I need to stress that the runs created method I’m using here does not take into account sacrifices, which usually is not a big deal but can be significant for pitchers. Note that all team figures from this point forward in the post are park-adjusted. The RAA figures for each position are baselined against the overall major league average RG for the position, except for left field and right field which are pooled.<br /><br /><a href="https://3.bp.blogspot.com/-MR9F8I_rurY/WincFBfIDSI/AAAAAAAACbQ/iHTXP68O1goNs1CHVT1UeFxgUcCLR3RcgCLcBGAs/s1600/hitpos17b.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://3.bp.blogspot.com/-MR9F8I_rurY/WincFBfIDSI/AAAAAAAACbQ/iHTXP68O1goNs1CHVT1UeFxgUcCLR3RcgCLcBGAs/s400/hitpos17b.jpg" width="400" height="282" data-original-width="393" data-original-height="277" /></a><br /><br />While positions relative to the league bounce around each year, it seems that the most predictable thing about this post is that the difference between the best and worst NL pitching staffs will be about twenty runs at the plate. As a whole, pitchers were at 0.00 runs created/game, which is the first time I’ve estimated them at 0, although they dipped into the negative in 2014 then crept back into positive territory for two years.<br /><br />I don’t run a full chart of the leading positions since you will very easily be able to go down the list and identify the individual primarily responsible for the team’s performance and you won’t be shocked by any of them, but the teams with the highest RAA at each spot were:<br /><br />C--CHN, 1B--CIN, 2B--HOU, 3B--CHN, SS--HOU, LF--NYN, CF--LAA, RF--MIA, DH—SEA<br /><br />More interesting are the worst performing positions; the player listed is the one who started the most games at that position for the team:<br /><br /><a href="https://2.bp.blogspot.com/-E2wnqXiwz4c/WincKwr7MaI/AAAAAAAACbU/0h-LZvFnmCYumGvxwUw6-Scu1T2oZjx5wCLcBGAs/s1600/hitpos17d.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://2.bp.blogspot.com/-E2wnqXiwz4c/WincKwr7MaI/AAAAAAAACbU/0h-LZvFnmCYumGvxwUw6-Scu1T2oZjx5wCLcBGAs/s400/hitpos17d.jpg" width="400" height="144" data-original-width="481" data-original-height="173" /></a><br /><br />Usually this list is more funny than sad, but almost every player that led one of these teams in starts was at one time considered (by some, maybe, in the case of Alcides Escobar) to be an outstanding player. Mercifully Mark Trumbo led Oriole DHs to a worse composite performance than the Angels or it would have been a veritable tragedy. Although the depressing nature of this list is offset significantly by the presence of the Kansas City shortstops and their Esky Magic, it is also not fair to Eduardo Nunez, who hit fine as a SF 3B (764 OPS in 199 PA). The real culprits for the Giants were, well, everyone else who played third base, with a max 622 OPS out of Christian Arroyo, Pablo Sandoval, Kelby Tomlinson, Jae-gyun Hwan, Connor Gillaspie, Ryder Jones, Aaron Hill, and Orlando Calixte. Giant third basemen other than Nunez hit a combined un-park adjusted 174/220/246. Props to Austin Slater who had a single in his only PA as Giant third basemen, joining Nunez as the only non-horrible performer of the bunch.<br /><br />I like to attempt to measure each team’s offensive profile by position relative to a typical profile. I’ve found it frustrating as a fan when my team’s offensive production has come disproportionately from “defensive” positions rather than offensive positions (“Why can’t we just find a corner outfielder who can hit?”) The best way I’ve yet been able to come up with to measure this is to look at the correlation between RG at each position and the long-term positional adjustment. A positive correlation indicates a “traditional” distribution of offense by position--more production from the positions on the right side of the defensive spectrum. (To calculate this, I use the long-term positional adjustments that pool 1B/DH as well as LF/RF, and because of the DH I split it out by league.) There is no value judgment here--runs are runs whether they are created by first basemen or shortstops:<br /><br /><a href="https://2.bp.blogspot.com/-cQKvfnA7KXE/WincWsGQkiI/AAAAAAAACbY/rSV2Pf7CVFA4KRs3CLT_TOvZlGfymoASwCLcBGAs/s1600/hitpos17c.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://2.bp.blogspot.com/-cQKvfnA7KXE/WincWsGQkiI/AAAAAAAACbY/rSV2Pf7CVFA4KRs3CLT_TOvZlGfymoASwCLcBGAs/s400/hitpos17c.jpg" width="399" height="400" data-original-width="277" data-original-height="278" /></a><br /><br />The two teams with the most extreme correlations did so because of excellence (which we’ll see further evidence of in the next set of charts) from either a position group that is expected to provide offense (Miami’s outfielders) or from one that is not (Houston’s middle infielders). The signing of Edwin Encarnacion helped the Indians record a high correlation, as the rest of the positions didn’t strongly match expectations and the middle infielders hit very well.<br /><br />The following tables, broken out by division, display RAA for each position, with teams sorted by the sum of positional RAA. Positions with negative RAA are in red, and positions that are +/-20 RAA are bolded:<br /><br /><a href="https://1.bp.blogspot.com/-dm8gScZcxpA/WincciRDG6I/AAAAAAAACbc/IytDsGKNj0wEhLK64mwAPmf9LWMIInflACLcBGAs/s1600/hitpos17e.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://1.bp.blogspot.com/-dm8gScZcxpA/WincciRDG6I/AAAAAAAACbc/IytDsGKNj0wEhLK64mwAPmf9LWMIInflACLcBGAs/s400/hitpos17e.jpg" width="400" height="80" data-original-width="518" data-original-height="104" /></a><br /><br />In 2016, the Yankees were last in the division in RAA; this year they were the only above-average offense, led by the AL’s most productive outfield. The Red Sox nearly did the opposite, going from the best offense in the AL to a lot of red, highlighted by the AL’s worst corner infield production. They were the only AL team to have just one above average positon. To what extent the Blue Jays hit, it was from the right side of the defensive spectrum; their catchers and middle infielders were the worst in MLB.<br /><br /><a href="https://4.bp.blogspot.com/-IjzR6ntjLWA/Winchv0CRXI/AAAAAAAACbg/7l8LMIDAO4M45hEcyA8vLsdlYfLPJ_p0wCLcBGAs/s1600/hitpos17f.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://4.bp.blogspot.com/-IjzR6ntjLWA/Winchv0CRXI/AAAAAAAACbg/7l8LMIDAO4M45hEcyA8vLsdlYfLPJ_p0wCLcBGAs/s400/hitpos17f.jpg" width="400" height="80" data-original-width="518" data-original-height="104" /></a><br /><br />The Indians had very balanced offensive contributions relative to position, with the +36 for DH inflated by the fact that here DH are compared to the (historically-low) 2017 positional average rather than a longer-term benchmark. Seeing the Detroit first basemen at -20 is sad. Kansas City had the worst outfield in the AL, as it seems it takes more than Esky Magic and “timely hitting” and “putting the ball in play” (yes, I realize their frequency of doing the latter has tailed off) to score runs.<br /><br /><a href="https://2.bp.blogspot.com/-1hnodP84SDk/WincmOZg0oI/AAAAAAAACbk/6YoVGzqocaoLJJQwxE-W5wCjPWPysrq3QCLcBGAs/s1600/hitpos17g.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://2.bp.blogspot.com/-1hnodP84SDk/WincmOZg0oI/AAAAAAAACbk/6YoVGzqocaoLJJQwxE-W5wCjPWPysrq3QCLcBGAs/s400/hitpos17g.jpg" width="400" height="80" data-original-width="518" data-original-height="103" /></a><br /><br />Houston led all of MLB in infield and middle infield RAA, and they were the only AL team to have just one below average position. Los Angeles had the worst infield in MLB, and shortstop was the only position that chipped in to help Mike Trout.<br /><br /><a href="https://4.bp.blogspot.com/-MOyIuywvEHA/Wincq0eMQWI/AAAAAAAACbo/xb7S4sjoNVEK9IjjiHiS4pAksAwSAKXEwCLcBGAs/s1600/hitpos17h.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://4.bp.blogspot.com/-MOyIuywvEHA/Wincq0eMQWI/AAAAAAAACbo/xb7S4sjoNVEK9IjjiHiS4pAksAwSAKXEwCLcBGAs/s400/hitpos17h.jpg" width="400" height="89" data-original-width="471" data-original-height="105" /></a><br /><br />Miami led MLB in outfield RAA; of course Giancarlo Stanton was the driving force but all three spots were outstanding. Washington had the NL’s top infield, Philadelphia the worst. But what jumped out at me in the NL East was how good Atlanta’s catchers were. Only the Cubs had a higher RAA. Atlanta’s unlikely duo was Tyler Flowers (282/382/447 in 368 PA overall) and Kurt Suzuki (284/355/539 in 306 PA). I have to admit I watch a lot of Braves games this year, so I am floored to see that Suzuki pulled a .255 ISO out of a hat; non-park adjusted, it was his career high by 94 points, and the .160 came a full decade ago.<br /><br /><a href="https://2.bp.blogspot.com/-kLRPqYbewyA/WindJgsFLcI/AAAAAAAACbw/6bKKjmdbhmcaBH4tV88PaWS6bp5Swrm9ACLcBGAs/s1600/hitpos17i.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://2.bp.blogspot.com/-kLRPqYbewyA/WindJgsFLcI/AAAAAAAACbw/6bKKjmdbhmcaBH4tV88PaWS6bp5Swrm9ACLcBGAs/s400/hitpos17i.jpg" width="400" height="88" data-original-width="472" data-original-height="104" /></a><br /><br />The Cubs had two positions that led the majors in RAA, a good showing from first base--and otherwise a lot of average and below average. Cincinnati led the majors in RAA from corner infielders; Joey Votto is obvious, but Eugenio Suarez led the third basemen to a fine showing as well. Pittsburgh was the only NL team to have just one position show up in black font, but there’s a reason I’m not constructing that to say anything about “below average”...<br /><br /><a href="https://3.bp.blogspot.com/-3BSqUgmLIfQ/WindOZ2-wNI/AAAAAAAACb0/QqOugGImAbIUUfJXMDHqavs_lhB7Ja5ZQCLcBGAs/s1600/hitpos17j.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://3.bp.blogspot.com/-3BSqUgmLIfQ/WindOZ2-wNI/AAAAAAAACb0/QqOugGImAbIUUfJXMDHqavs_lhB7Ja5ZQCLcBGAs/s400/hitpos17j.jpg" width="400" height="88" data-original-width="472" data-original-height="104" /></a><br /><br />The Dodgers joined the Nationals as the only NL teams to have just one below-average position and led the NL in middle infield RAA. Arizona and San Diego tied for the worst middle infield RAA in the NL, while the Giants had the worst corner infielders and outfielders in the majors. The remarkably bad third basemen, the single worst position in the majors, were discussed in greater detail above. But the Padres might have the most dubious distinction on this list; they had not a single position that was above average. It doesn’t stand out here because I zero is displayed in black font rather than red, and to be fair they had two positions at zero, as well as single positions at -1, -2, and -4; it’s not as if every position was making outs with no redeeming value. And their pitchers were +9, so they can hang their hat on that.<br /><br />The full spreadsheet with data is available <a href="https://docs.google.com/spreadsheets/d/e/2PACX-1vRUeWHv74vqkknEe8S7ST4piLLAPxssP_kzxZoQOwSYR6PgvncZEZsCPECLruA4gLXr_0qRERB9hMTk/pub?output=html">here</a>.<br />phttp://www.blogger.com/profile/18057215403741682609noreply@blogger.com0tag:blogger.com,1999:blog-12133335.post-29478843310169413452017-11-28T07:53:00.000-05:002017-11-28T07:53:01.128-05:00Leadoff Hitters, 2017I will try to make this as clear as possible: the statistics are based on the players that hit in the #1 slot in the batting order, whether they were actually leading off an inning or not. It includes the performance of all players who batted in that spot, including substitutes like pinch-hitters. <br /><br />Listed in parentheses after a team are all players that started in twenty or more games in the leadoff slot--while you may see a listing like "COL (Blackmon)" this does not mean that the statistic is only based solely on Blackmon's performance; it is the total of all Colorado batters in the #1 spot, of which Blackmon was the only one to start in that spot in twenty or more games. I will list the top and bottom three teams in each category (plus the top/bottom team from each league if they don't make the ML top/bottom three); complete data is available in a spreadsheet linked at the end of the article. There are also no park factors applied anywhere in this article.<br /><br />That's as clear as I can make it, and I hope it will suffice. I always feel obligated to point out that as a sabermetrician, I think that the importance of the batting order is often overstated, and that the best leadoff hitters would generally be the best cleanup hitters, the best #9 hitters, etc. However, since the leadoff spot gets a lot of attention, and teams pay particular attention to the spot, it is instructive to look at how each team fared there.<br /><br />The conventional wisdom is that the primary job of the leadoff hitter is to get on base, and most simply, score runs. It should go without saying on this blog that runs scored are heavily dependent on the performance of one’s teammates, but when writing on the internet it’s usually best to assume nothing. So let's start by looking at runs scored per 25.5 outs (AB - H + CS):<br /><br />1. COL (Blackmon), 7.9<br />2. HOU (Springer), 7.0<br />3. STL (Carpenter/Fowler), 6.7<br />Leadoff average, 5.5<br />ML average, 4.6<br />28. CHA (Garcia/Anderson/Sanchez), 4.4<br />29. KC (Merrifield/Escobar), 4.3<br />30. SD (Margot/Pirela), 3.9<br /><br />That’s Leury Garcia for the White Sox, in case you were wondering. One of my favorite little tidbits from the 2017 season was their all-Garcia outfield: Willy, Leury, and Avasail. Sadly, one of my favorite tidbits from the last few season was no more as Kansas City finally decided that Esky Magic had run its course. Alcides Escobar only got 25 starts leading off, with Whit Merrifield leading the way with 115. The Royals still made plenty of appearances in the trailer portions of these lists.<br /><br />The most basic team independent category that we could look at is OBA (figured as (H + W + HB)/(AB + W + HB)):<br /><br />1. COL (Blackmon), .399<br />2. STL (Carpenter/Fowler), .374<br />3. HOU (Springer), .374<br />Leadoff average, .333<br />ML average, .327<br />28. CIN (Hamilton), .295<br />29. TOR (Pillar/Bautista), .287<br />30. KC (Merrifield/Escobar), .282<br /><br />Even if we were to park-adjust Colorado’s .399, they’d be at .370, so it was a fine performance by Blackmon and company (mostly Blackmon, with 156 starts), but not the best in the league. There’s no good reason I don’t park-adjust, although my excuse is that park adjustments don’t apply (or at least can’t be based off the runs park factor) for some of the metrics presented here. Of the categories mentioned in this post, R/G, OBA, 2OPS, RG, and LE could be if one was so inclined.<br /><br />The next statistic is what I call Runners On Base Average. The genesis for ROBA is the A factor of Base Runs. It measures the number of times a batter reaches base per PA--excluding homers, since a batter that hits a home run never actually runs the bases. It also subtracts caught stealing here because the BsR version I often use does as well, but BsR versions based on initial baserunners rather than final baserunners do not. Here ROBA = (H + W + HB - HR - CS)/(AB + W + HB).<br /><br />This metric has caused some confusion, so I’ll expound. ROBA, like several other methods that follow, is not really a quality metric, it is a descriptive metric. A high ROBA is a good thing, but it's not necessarily better than a slightly lower ROBA plus a higher home run rate (which would produce a higher OBA and more runs). Listing ROBA is not in any way, shape or form a statement that hitting home runs is bad for a leadoff hitter. It is simply a recognition of the fact that a batter that hits a home run is not a baserunner. Base Runs is an excellent model of offense and ROBA is one of its components, and thus it holds some interest in describing how a team scored its runs. As such it is more a measure of shape than of quality:<br /><br />1. STL (Carpenter/Fowler), .341<br />2. COL (Blackmon), .336<br />3. PHI (Hernandez), .327<br />5. SEA (Segura/Gamel), .319<br />Leadoff average, .295<br />ML average, .288<br />28. CIN (Hamilton), .265<br />29. KC (Merrifield/Escobar), .248<br />30. TOR (Pillar/Bautista), .241<br /><br />With the exception of Houston, the top and bottom three are the same as the OBA list, just in different order (HOU was eighth at .313, their 38 homers out of the leadoff spot tied with Colorado; Minnesota, the Mets, Cleveland, and Tampa Bay also got 30 homers out of the top spot). <br /><br />I also include what I've called Literal OBA--this is just ROBA with HR subtracted from the denominator so that a homer does not lower LOBA, it simply has no effect. It “literally” (not really, thanks to errors, out stretching, caught stealing after subsequent plate appearances, etc.) is the proportion of plate appearances in which the batter becomes a baserunner able to be advanced by his teammates. You don't really need ROBA and LOBA (or either, for that matter), but this might save some poor message board out there twenty posts, by not implying that I think home runs are bad. LOBA = (H + W + HB - HR - CS)/(AB + W + HB - HR):<br /><br />1. COL (Blackmon), .354<br />2. STL (Carpenter/Fowler), .352<br />3. PHI (Hernandez), .332<br />4. HOU (Springer), .330<br />Leadoff average, .303<br />ML average, .298<br />28. CIN (Hamilton), .268<br />29. KC (Merrifield/Escobar), .253<br />30. TOR (Pillar/Bautista), .251<br /><br />The next two categories are most definitely categories of shape, not value. The first is the ratio of runs scored to RBI. Leadoff hitters as a group score many more runs than they drive in, partly due to their skills and partly due to lineup dynamics. Those with low ratios don’t fit the traditional leadoff profile as closely as those with high ratios (at least in the way their seasons played out, and of course using R and RBI incorporates the quality and style of the hitters in the adjacent lineup spots rather then attributes of the leadoff hitters’ performance in isolation):<br /><br />1. MIA (Gordon), 2.5<br />2. TEX (DeShields/Choo/Gomez), 2.2<br />3. CIN (Hamilton), 2.2<br />Leadoff average, 1.5<br />ML average, 1.0<br />27. SD (Margot/Pirela), 1.3<br />28. KC (Merrifield/Escobar), 1.2<br />29. MIN (Dozier), 1.1<br />30. CLE (Kipnis/Lindor/Santana), 1.1<br /><br />Cleveland only settled on a permanent leadoff fixture (Lindor) late in the season, but all three of their 20+ game leadoff men were of the same general type. They didn’t really have a player who saw regular time who fit anything like the leadoff profile. It worked OK; their .328 OBA was lower than the leadoff average, but as we’ll see later their 5.2 RG was above average.<br /><br />A similar gauge, but one that doesn't rely on the teammate-dependent R and RBI totals, is Bill James' Run Element Ratio. RER was described by James as the ratio between those things that were especially helpful at the beginning of an inning (walks and stolen bases) to those that were especially helpful at the end of an inning (extra bases). It is a ratio of "setup" events to "cleanup" events. Singles aren't included because they often function in both roles. <br /><br />Of course, there are RBI walks and doubles are a great way to start an inning, but RER classifies events based on when they have the highest relative value, at least from a simple analysis:<br /> <br />1. CIN (Hamilton), 1.7<br />2. MIA (Gordon), 1.6<br />3. TEX (DeShields/Choo/Gomez), 1.3<br />Leadoff average, .8<br />ML average, .6<br />28. TB (Dickerson/Kiermaier/Smith/Souza), .5<br />29. BAL (Smith/Beckham/Jones/Rickard), .5<br />30. COL (Blackmon), .5<br /><br />Both Tampa Bay and Baltimore followed the Cleveland pattern of using multiple leadoff hitters, although one of the four for each (Mallex Smith and Joey Rickard) fit more of a traditional profile. The Rays got 5.1 RG out of this hodgepodge, which is above-average; the Orioles’ 4.3 was not. For the record, I’m basing my assessment of Joey Rickard’s traditional leadoff style bona fides on his career minor league line (.280/.388/.392), and not his major league line (.255/.298/.361) for which the only stylistic interpretation is “bad”. <br /><br />Since stealing bases is part of the traditional skill set for a leadoff hitter, I've included the ranking for what some analysts call net steals, SB - 2*CS. I'm not going to worry about the precise breakeven rate, which is probably closer to 75% than 67%, but is also variable based on situation. The ML and leadoff averages in this case are per team lineup slot:<br /><br />1. WAS (Turner/Goodwin), 37<br />2. CIN (Hamilton), 36<br />3. MIA (Gordon), 25<br />4. NYA (Gardner), 21<br />Leadoff average, 8<br />ML average, 2<br />28. CHN (Jay/Zobrist/Schwarber), -2<br />29. COL (Blackmon), -5<br />30. HOU (Springer), -7<br /><br />A lot of the leaders and trailers are flipped on this list from the overall quality measures.<br /><br />Shifting back to said quality measures, first up is one that David Smyth proposed when I first wrote this annual leadoff review. Since the optimal weight for OBA in a x*OBA + SLG metric is generally something like 1.7, David suggested figuring 2*OBA + SLG for leadoff hitters, as a way to give a little extra boost to OBA while not distorting things too much, or even suffering an accuracy decline from standard OPS. Since this is a unitless measure anyway, I multiply it by .7 to approximate the standard OPS scale and call it 2OPS:<br /><br />1. COL (Blackmon), 979<br />2. HOU (Springer), 887<br />3. MIN (Dozier), 865<br />Leadoff average, 763<br />ML average, 755<br />28. TOR (Pillar/Bautista), 678<br />29. KC (Merrifield/Escobar), 658<br />30. CIN (Hamilton), 651<br /><br />Along the same lines, one can also evaluate leadoff hitters in the same way I'd go about evaluating any hitter, and just use Runs Created per Game with standard weights (this will include SB and CS, which are ignored by 2OPS):<br /><br />1. COL (Blackmon), 7.8<br />2. HOU (Springer), 6.4<br />3. MIN (Dozier), 6.1<br />Leadoff average, 4.8<br />ML average, 4.6<br />28. TOR (Pillar/Bautista), 3.7<br />29. CIN (Hamilton), 3.6<br />30. KC (Merrifield/Escobar), 3.5<br /><br />Allow me to close with a crude theoretical measure of linear weights supposing that the player always led off an inning (that is, batted in the bases empty, no outs state). There are weights out there (see The Book) for the leadoff slot in its average situation, but this variation is much easier to calculate (although also based on a silly and impossible premise). <br /><br />The weights I used were based on the 2010 run expectancy table from Baseball Prospectus. Ideally I would have used multiple seasons but this is a seat-of-the-pants metric. The 2010 post goes into the <a href="http://walksaber.blogspot.com/2010/12/leadoff-hitters-2010.html">detail of how this measure is figured</a>; this year, I’ll just tell you that the out coefficient was -.230, the CS coefficient was -.597, and for other details refer you to that post. I then restate it per the number of PA for an average leadoff spot (750 in 2017):<br /><br /><br />1. COL (Blackmon), 45<br />2. HOU (Springer), 26<br />3. MIN (Dozier), 25<br />Leadoff average, 2<br />ML average, 0<br />28. CIN (Hamilton), -17<br />29. TOR (Pillar/Bautista), -18<br />30. KC (Merrifield/Escobar), -24<br /><br />Esky Magic has residual effects, apparently. I don’t recall seeing the same teams in the leaders and trailers list for 2OPS, RG, and LE before, but they are all very similar in terms of their construction, with 2OPS arbitrarily but logically tilted towards OBA and LE attempting to isolate run value that would be contributed if all plate appearances came in a leadoff situation. RG represents the approximate run value of a player’s performance in an “average” situation on an average team.<br /><br />The spreadsheet with full data is available <a href="https://docs.google.com/spreadsheets/d/e/2PACX-1vT-sOJtAtgLkuqJOAFc1FHLWTZG0UEjeaM_FljWRSjTi4hGONMcKSzQAguwU797p6g_uFD4nx_GTXhS/pub?output=html">here</a>.<br />phttp://www.blogger.com/profile/18057215403741682609noreply@blogger.com0tag:blogger.com,1999:blog-12133335.post-11360152046090888362017-11-15T17:55:00.000-05:002017-11-15T17:55:00.158-05:00Hypothetical Ballot: MVPMy heart’s just not in writing this, since it’s the first time in the brilliant career of Mike Trout that he will not top my AL MVP ballot. This is made a little better by noting that, prorated to 150 games, he contributed 90 RAR to my choice’s 76, but you add no value to your team when you’re sitting at home. I should note that there have been many less deserving MVP winners than Mike Trout would be in 2017.<br /><br />Jose Altuve leads Aaron Judge by four RAR, not considering baserunning or fielding. Judge’s fielding metrics are better than one might expect from a man of his size--5 FRAA, 6 UZR, 9 DRS--but Altuve ranks as average, and per Fangraphs was worth another run on the basepaths, so I don’t think it’s enough to bump him. It’s well within any margin of error and Judge would certainly be a fine choice as MVP.<br /><br />The other candidate for the top spot is Corey Kluber--with 81 RAR, he’d would my choice by default. But while Kluber’s RAR using his peripherals (78) and DIPS (71) are good, they are basically a match for Altuve’s 77 (after baserunning). Our analytical approach for evaluating hitters is much more like using pitcher’s peripherals than their actual runs allowed, and there should be some consideration that some of the value attributed to a pitcher is actually due to his fielders (if you’re not making an explicit adjustment for that). For me, if a pitcher doesn’t clearly rank ahead of a hitter, he doesn’t get the benefit of the doubt on a MVP ballot.<br /><br />The rest of the ballot is pretty straightforward by RAR, mixing the top pitchers in, as the top-performing hitters were all solid in the field and didn’t change places:<br /><br />1. 2B Jose Altuve, HOU<br />2. RF Aaron Judge, NYA<br />3. SP Corey Kluber, CLE<br />4. SP Chris Sale, BOS<br />5. CF Mike Trout, LAA<br />6. SP Carlos Carrasco, CLE<br />7. 3B Jose Ramirez, CLE<br />8. SP Luis Severino, NYA<br />9. SP Justin Verlander, DET/HOU<br />10. SS Carlos Correa, HOU<br /><br />In the NL, Joey Votto has a two-run RAR lead over Giancarlo Stanton, but Fangraphs has him at a whopping -10 baserunning runs to Stanton’s -2. BP has the same margin, but -8 to 0. Their fielding numbers (FRAA, UZR, DRS) are almost identical--(10, 11, 7) for Votto and (9, 10, 7) for Stanton. I’m not sure I’ve ever determined the top spot on my ballot on the basis of baserunning value before, but even if you were to be extremely conservative and regress it by 50%, it makes the difference. Paul Goldschmidt will get a lot of consideration, but even as a good baserunner and fielder I don’t think his 52 RAR offensively gets him in the picture for the top of the ballot.<br /><br />Max Scherzer’s case is similar to Kluber’s, except with an even more pronounced gap between his actual runs allowed-based RAR (77), his peripherals (71), and DIPS (61). <br /><br />The rest of my ballot follows RAR, as there were no players who made a huge difference in the field. I might be more inclined to accept an argument that Buster Posey was more valuable than the statistics suggest in a season in which San Francisco didn’t have the second-worst record in the league. But one player is missing from my ballot who will be high on many (although not in the top three of the BBWAA vote) is Nolan Arenado, and I feel that deserves a little explanation.<br /><br />Rather than comparing Arenado to every player on my ballot, let’s look at my last choice, Marcell Ozuna. Ozuna starts with a ten run lead in RAR (56 to 46). Arenado is widely regarded as an excellent fielder, but the metrics aren’t in agreement--1 FRAA, 7 UZR, 20 DRS. Ozuna’s figures are (5, 11, 3). If you believe that Arenado is +20 fielder, than he would rank about dead even with Kris Bryant at 66 RAR (bumping Bryant from 61 on the strength of his own (especially) baserunning and fielding). It’s certainly not out of the realm of possibility. But if you only give Arenado credit for 10 fielding runs, that only pulls him even with Ozuna, before giving Ozuna any credit for his fielding.<br /><br />I was going to write a bit more about how it might be easy for writers to consider Coors Field but understate how good of a hitter’s park it is (116 PF). If you used 110 instead, then Arenado starts at 51. But given that he didn’t finish in the top three, I don’t think there’s any evidence of not taking park into account. As discussed, there are perfectly reasonable views on Arenado’s fielding value that justify fourth-place. I’m not sure Arenado would be 11th or 12th or 13th if I went further, as Tommy Pham, Corey Seager, Clayton Kershaw, Gio Gonzalez, and Zack Greinke are all worthy of consideration for the bottom of the ballot themselves:<br /><br />1. RF Giancarlo Stanton, MIA<br />2. 1B Joey Votto, CIN<br />3. SP Max Scherzer, WAS<br />4. 3B Kris Bryant, CHN<br />5. CF Charlie Blackmon, COL<br />6. 3B Anthony Rendon, WAS<br />7. 1B Paul Goldschmidt, ARI<br />8. 3B Justin Turner, LA<br />9. SP Stephen Strasburg, WAS <br />10. LF Marcell Ozuna, MIAphttp://www.blogger.com/profile/18057215403741682609noreply@blogger.com2tag:blogger.com,1999:blog-12133335.post-70572829978076769832017-11-14T17:29:00.001-05:002017-11-14T18:03:00.067-05:00Hypothetical Ballot: Cy YoungThe starting pitchers (and they’re the only ones that can possibly accrue enough value to be serious Cy Young candidates if you subscribe to the school of thought that all innings are created equal and the only leveraging effect appropriate to credit to relief aces is that they are used in close games) did a very nice job of separating themselves by RAR into groups of five or six, with a five run gap to the next pitcher. This makes a very convenient cut point to define the ballot candidates:<br /><br />AL: Kluber 81, Sale 71, Carrasco 62, Verlander 61, Severino 59, Santana 59, <i>Stroman 52</i><br /><br />NL: Scherzer 77, Gonzalez 66, Kershaw 64, Strasburg 62, Greinke 57, <i>Ray 51</i><br /><br />Corey Kuber has a clear edge over Chris Sale in RAR, but it’s closer (78 to 73) in RAR based on eRA, and in RAR based on DIPS theory (assuming an average rate of hits on balls in play), Sale flips the standard list almost perfectly (80 to 71). My philosophy has always been that the actual runs allowed takes precedence, and while DIPS can serve to narrow the difference, Kluber is still outstanding when viewed in that light (e.g. this is not a Joe Mays or Esteban Loaiza situation). I don’t think it comes close to making up the difference. FWIW, <u>Baseball Prospects</u> WARP, which attempts to account for all matter of situational effects not captured in the conventional statistical record, sees Kluber’s performance as slightly more valuable (8.0 to 7.6). <br /><br />The rest of my AL ballot goes in order except to flip Severino and Verlander. Severino had significantly better marks in both eRA (3.15 to 3.73) and dRA (3.40 to 4.12). Santana had an even more marked disparity between his actual runs allowed and the component measures (3.82 eRA, 4.75 dRA) which also triggers confirmation bias as he and Jason Vargas’ first-half performances were quite vexing to this Cleveland fan.<br /><br />1. Corey Kluber, CLE<br />2. Chris Sale, BOS<br />3. Carlos Carrasco, CLE<br />4. Luis Severino, NYA<br />5. Justin Verlander, DET/HOU<br /><br />In the NL, I was a little surprised to see that in some circles, Clayton Kershaw is the choice for the award and may well win it. Tom Tango pointed out that Kershaw’s edges over Scherzer in both W-L (18-4 to 16-6) and ERA (2.31 to 2.51) give him a clear edge in the normal thought process of voters. I have been more detached than normal this season from the award debates as you might hear on MLB Tonight, and so seeing a 13 run gap in RAR I didn’t even consider that there might be a groundswell of support for Kershaw. With respect to ERA, Scherzer has a lower RRA (based on runs allowed, adjusting for park, and crudely accounting for bullpen support) and Kershaw’s raw .20 ERA lead drops to just .08 (2.41 to 2.49) when park-adjusting.<br /><br />What’s more is that Scherzer has a larger edge over Kershaw in eRA (2.71 to 3.26) and dRA (3.20 to 3.73) than he does in RRA (2.56 to 2.72)--leading in all three with a 25 inning advantage. Scherzer led the NL in RRA and eRA, was a narrow second to his teammate Strasburg (3.07 to 3.20) in dRA, and was just seven innings off the league lead (albeit in seventh place). For Cy Young races in non-historic pitcher seasons, I don’t think it gets much more clear than this. <br /><br />As a final note on Kershaw v. Scherzer, perhaps some of the pro-Kershaw sentiment goes beyond W-L and ERA and into the notion that Kershaw is the best pitcher in baseball. I don’t think this is relevant to a single season award, and I think it would have a much more obvious application to the AL MVP race, where not only is Mike Trout the best player in baseball, but the best by a tremendous margin, and was easily the most valuable player on a rate basis in the league (NOTE: I am not advocating that Trout should be the MVP, only that he has a better case using this argument than Kershaw). But it may be time to re-evaluate Kershaw as the best pitcher in baseball as a fait accompli. Over the last three seasons, Scherzer has pitched 658 innings with a 2.84 RRA and 211 RAR; Kershaw has pitched 557 innings with a 2.37 RRA and 206 RAR. At some point, the fact that Scherzer has consistently been more durable than Kershaw should factor into the discussion of “best”.<br /><br />Strasburg placed second to Scherzer in eRA, and as discussed bettered him in dRA, recording one more out than Kershaw did. That’s enough for me to move him into second over teammate Gonzalez as well, who had an even larger peripheral gap than Kershaw (basing RAR on eRA, Strasburg beats Gonzalez 62 to 56; on dRA, 56 to 37), so I see it as:<br /><br />1. Max Scherzer, WAS<br />2. Stephen Strasburg, WAS<br />3. Clayton Kershaw, LA<br />4. Gio Gonzalez, WAS<br />5. Zack Greinke, ARI<br />phttp://www.blogger.com/profile/18057215403741682609noreply@blogger.com0tag:blogger.com,1999:blog-12133335.post-40882757647570966852017-11-06T17:36:00.003-05:002017-11-06T17:36:36.367-05:00Hypothetical Ballot: Rookie of the YearLet's assume for a moment that you care about post-season awards (I've lost at least 30% of you).<br /><br />Then let's suppose you care about my opinion about how should win them (another 50% gone...I'd guess higher but you are reading this blog after all).<br /><br />So for the 20% of you left (those percentages were based on the original population for those checking math), do you care about who I think should finish second - fifth on a ballot for awards which will almost certainly and deservedly be unanimously decided? Especially if the awards in question are Rookie of the Year?<br /><br />I didn't think so. Rookie of the Year is the least interesting award for a number of reasons, including but not limited to:<br /><br />1. For as much as people like to argue about what "valuable" means, RoY has even more contentious questions: how much should perceived future potential outweigh current year performance, and how should players who are new to the Major Leagues but veterans of high-level professional baseball in other countries (or in segregated leagues when the award was young) be treated?<br /><br />2. While winning a RoY award might become a part of the standard broadcaster rundown and a line in the <U>Baseball Register</U> (RIP), it rarely takes on any significance beyond that. In contrast, Cy Youngs and MVPs enter a feedback loop of subjective awards when they are cited in Hall of Fame discussions.<br /><br />Because of this, particularly #2, downballot selections on the Cy Young or MVP ballot take on a little more importance, even if the winner of the award gets so many first place votes that the downballot choices don't factor into the outcome. Award shares, top 5 MVP finishes, etc. may not be that important in the grand scheme of things--but compared to who finished fourth in the RoY voting, they might as well be the list of pennant winners.<br /><br />This is a long-winded way of saying that: <br /><br />1) Aaron Judge and Cody Bellinger are going to, and should, easily win the 2017 RoYs<br />2) The 20% of you who might theoretically have some interest in this post really aren't going to care who I say should be fourth. It was more fun to write this explanation than to write a detailed breakdown of why I think <br />Yuli Gurriel deserved to rank ahead of Trey Mancini while still having a respectable word count for a blog post:<br /><br />AL:<br />1. RF Aaron Judge, NYA<br />2. SP Jordan Montgomery, NYA<br />3. 1B Yuli Gurriel, HOU<br />4. RF Mitch Haniger, SEA<br />5. 1B Trey Mancini, BAL<br /><br />NL:<br />1. 1B Cody Bellinger, LA<br />2. SS Paul DeJong, STL<br />3. SP German Marquez, COL<br />4. SP Kyle Freeland, COL<br />5. SP Trevor Williams, PIT<br /><br />phttp://www.blogger.com/profile/18057215403741682609noreply@blogger.com0tag:blogger.com,1999:blog-12133335.post-84496559428856971392017-10-03T17:39:00.001-04:002017-10-03T17:40:37.431-04:00End of Season Statistics, 2017The spreadsheets are published as Google Spreadsheets, which you can download in Excel format by changing the extension in the address from "=html" to "=xls". That way you can download them and manipulate things however you see fit. <br /><br />The data comes from a number of different sources. Most of the data comes from Baseball-Reference. KJOK's park database is extremely helpful in determining when park factors should reset. Data on bequeathed runners for relievers comes from Baseball Prospectus. <br /><br />The basic philosophy behind these stats is to use the simplest methods that have acceptable accuracy. Of course, "acceptable" is in the eye of the beholder, namely me. I use Pythagenpat not because other run/win converters, like a constant RPW or a fixed exponent are not accurate enough for this purpose, but because it's mine and it would be kind of odd if I didn't use it. <br /><br />If I seem to be a stickler for purity in my critiques of others' methods, I'd contend it is usually in a theoretical sense, not an input sense. So when I exclude hit batters, I'm not saying that hit batters are worthless or that they *should* be ignored; it's just easier not to mess with them and not that much less accurate. <br /><br />I also don't really have a problem with people using sub-standard methods (say, Basic RC) as long as they acknowledge that they are sub-standard. If someone pretends that Basic RC doesn't undervalue walks or cause problems when applied to extreme individuals, I'll call them on it; if they explain its shortcomings but use it regardless, I accept that. Take these last three paragraphs as my acknowledgment that some of the statistics displayed here have shortcomings as well, and I've at least attempted to describe some of them in the discussion below.<br /><br />The League spreadsheet is pretty straightforward--it includes league totals and averages for a number of categories, most or all of which are explained at appropriate junctures throughout this piece. The advent of interleague play has created two different sets of league totals--one for the offense of league teams and one for the defense of league teams. Before interleague play, these two were identical. I do not present both sets of totals (you can figure the defensive ones yourself from the team spreadsheet, if you desire), just those for the offenses. The exception is for the defense-specific statistics, like innings pitched and quality starts. The figures for those categories in the league report are for the defenses of the league's teams. However, I do include each league's breakdown of basic pitching stats between starters and relievers (denoted by "s" or "r" prefixes), and so summing those will yield the totals from the pitching side. The one abbreviation you might not recognize is "N"--this is the league average of runs/game for one team, and it will pop up again.<br /><br />The Team spreadsheet focuses on overall team performance--wins, losses, runs scored, runs allowed. The columns included are: Park Factor (PF), Home Run Park Factor (PFhr), Winning Percentage (W%), Expected W% (EW%), Predicted W% (PW%), wins, losses, runs, runs allowed, Runs Created (RC), Runs Created Allowed (RCA), Home Winning Percentage (HW%), Road Winning Percentage (RW%) [exactly what they sound like--W% at home and on the road], Runs/Game (R/G), Runs Allowed/Game (RA/G), Runs Created/Game (RCG), Runs Created Allowed/Game (RCAG), and Runs Per Game (the average number of runs scored an allowed per game). Ideally, I would use outs as the denominator, but for teams, outs and games are so closely related that I don’t think it’s worth the extra effort.<br /><br />The runs and Runs Created figures are unadjusted, but the per-game averages are park-adjusted, except for RPG which is also raw. Runs Created and Runs Created Allowed are both based on a simple Base Runs formula. The formula is:<br /><br />A = H + W - HR - CS<br />B = (2TB - H - 4HR + .05W + 1.5SB)*.76<br />C = AB - H<br />D = HR<br />Naturally, A*B/(B + C) + D.<br /><br />I have explained the methodology used to figure the PFs before, but the cliff’s notes version is that they are based on five years of data when applicable, include both runs scored and allowed, and they are regressed towards average (PF = 1), with the amount of regression varying based on the number of years of data used. There are factors for both runs and home runs. The initial PF (not shown) is:<br /><br />iPF = (H*T/(R*(T - 1) + H) + 1)/2<br />where H = RPG in home games, R = RPG in road games, T = # teams in league (14 for AL and 16 for NL). Then the iPF is converted to the PF by taking x*iPF + (1-x), where x = .6 if one year of data is used, .7 for 2, .8 for 3, and .9 for 4+. <br /><br />It is important to note, since there always seems to be confusion about this, that these park factors already incorporate the fact that the average player plays 50% on the road and 50% at home. That is what the adding one and dividing by 2 in the iPF is all about. So if I list Fenway Park with a 1.02 PF, that means that it actually increases RPG by 4%. <br /><br />In the calculation of the PFs, I did not take out “home” games that were actually at neutral sites (of which there were a rash this year).<br /><br />There are also Team Offense and Defense spreadsheets. These include the following categories:<br /><br />Team offense: Plate Appearances, Batting Average (BA), On Base Average (OBA), Slugging Average (SLG), Secondary Average (SEC), Walks and Hit Batters per At Bat (WAB), Isolated Power (SLG - BA), R/G at home (hR/G), and R/G on the road (rR/G) BA, OBA, SLG, WAB, and ISO are park-adjusted by dividing by the square root of park factor (or the equivalent; WAB = (OBA - BA)/(1 - OBA), ISO = SLG - BA, and SEC = WAB + ISO).<br /><br />Team defense: Innings Pitched, BA, OBA, SLG, Innings per Start (IP/S), Starter's eRA (seRA), Reliever's eRA (reRA), Quality Start Percentage (QS%), RA/G at home (hRA/G), RA/G on the road (rRA/G), Battery Mishap Rate (BMR), Modified Fielding Average (mFA), and Defensive Efficiency Record (DER). BA, OBA, and SLG are park-adjusted by dividing by the square root of PF; seRA and reRA are divided by PF.<br /><br />The three fielding metrics I've included are limited it only to metrics that a) I can calculate myself and b) are based on the basic available data, not specialized PBP data. The three metrics are explained in this post, but here are quick descriptions of each:<br /><br />1) BMR--wild pitches and passed balls per 100 baserunners = (WP + PB)/(H + W - HR)*100<br /><br />2) mFA--fielding average removing strikeouts and assists = (PO - K)/(PO - K + E)<br /><br />3) DER--the Bill James classic, using only the PA-based estimate of plays made. Based on a suggestion by Terpsfan101, I've tweaked the error coefficient. Plays Made = PA - K - H - W - HR - HB - .64E and DER = PM/(PM + H - HR + .64E)<br /><br />Next are the individual player reports. I defined a starting pitcher as one with 15 or more starts. All other pitchers are eligible to be included as a reliever. If a pitcher has 40 appearances, then they are included. Additionally, if a pitcher has 50 innings and less than 50% of his appearances are starts, he is also included as a reliever (this allows some swingmen type pitchers who wouldn’t meet either the minimum start or appearance standards to get in).<br /><br />For all of the player reports, ages are based on simply subtracting their year of birth from 2017. I realize that this is not compatible with how ages are usually listed and so “Age 27” doesn’t necessarily correspond to age 27 as I list it, but it makes everything a heckuva lot easier, and I am more interested in comparing the ages of the players to their contemporaries than fitting them into historical studies, and for the former application it makes very little difference. The "R" category records rookie status with a "R" for rookies and a blank for everyone else; I've trusted Baseball Prospectus on this. Also, all players are counted as being on the team with whom they played/pitched (IP or PA as appropriate) the most. <br /><br />For relievers, the categories listed are: Games, Innings Pitched, estimated Plate Appearances (PA), Run Average (RA), Relief Run Average (RRA), Earned Run Average (ERA), Estimated Run Average (eRA), DIPS Run Average (dRA), Strikeouts per Game (KG), Walks per Game (WG), Guess-Future (G-F), Inherited Runners per Game (IR/G), Batting Average on Balls in Play (%H), Runs Above Average (RAA), and Runs Above Replacement (RAR).<br /><br />IR/G is per relief appearance (G - GS); it is an interesting thing to look at, I think, in lieu of actual leverage data. You can see which closers come in with runners on base, and which are used nearly exclusively to start innings. Of course, you can’t infer too much; there are bad relievers who come in with a lot of people on base, not because they are being used in high leverage situations, but because they are long men being used in low-leverage situations already out of hand.<br /><br />For starting pitchers, the columns are: Wins, Losses, Innings Pitched, Estimated Plate Appearances (PA), RA, RRA, ERA, eRA, dRA, KG, WG, G-F, %H, Pitches/Start (P/S), Quality Start Percentage (QS%), RAA, and RAR. RA and ERA you know--R*9/IP or ER*9/IP, park-adjusted by dividing by PF. The formulas for eRA and dRA are based on the same Base Runs equation and they estimate RA, not ERA.<br /><br />* eRA is based on the actual results allowed by the pitcher (hits, doubles, home runs, walks, strikeouts, etc.). It is park-adjusted by dividing by PF.<br /><br />* dRA is the classic DIPS-style RA, assuming that the pitcher allows a league average %H, and that his hits in play have a league-average S/D/T split. It is park-adjusted by dividing by PF.<br /><br />The formula for eRA is:<br /><br />A = H + W - HR<br />B = (2*TB - H - 4*HR + .05*W)*.78<br />C = AB - H = K + (3*IP - K)*x (where x is figured as described below for PA estimation and is typically around .93) = PA (from below) - H - W<br />eRA = (A*B/(B + C) + HR)*9/IP<br /><br />To figure dRA, you first need the estimate of PA described below. Then you calculate W, K, and HR per PA (call these %W, %K, and %HR). Percentage of balls in play (BIP%) = 1 - %W - %K - %HR. This is used to calculate the DIPS-friendly estimate of %H (H per PA) as e%H = Lg%H*BIP%.<br /><br />Now everything has a common denominator of PA, so we can plug into Base Runs:<br /><br />A = e%H + %W<br />B = (2*(z*e%H + 4*%HR) - e%H - 5*%HR + .05*%W)*.78<br />C = 1 - e%H - %W - %HR<br />cRA = (A*B/(B + C) + %HR)/C*a<br /><br />z is the league average of total bases per non-HR hit (TB - 4*HR)/(H - HR), and a is the league average of (AB - H) per game.<br /><br />In the past I presented a couple of batted ball RA estimates. I’ve removed these, not just because batted ball data exhibits questionable reliability but because these metrics were complicated to figure, required me to collate the batted ball data, and were not personally useful to me. I figure these stats for my own enjoyment and have in some form or another going back to 1997. I share them here only because I would do it anyway, so if I’m not interested in certain categories, there’s no reason to keep presenting them.<br /><br />Instead, I’m showing strikeout and walk rate, both expressed as per game. By game I mean not nine innings but rather the league average of PA/G. I have always been a proponent of using PA and not IP as the denominator for non-run pitching rates, and now the use of per PA rates is widespread. Usually these are expressed as K/PA and W/PA, or equivalently, percentage of PA with a strikeout or walk. I don’t believe that any site publishes these as K and W per equivalent game as I am here. This is not better than K%--it’s simply applying a scalar multiplier. I like it because it generally follows the same scale as the familiar K/9.<br /><br />To facilitate this, I’ve finally corrected a flaw in the formula I use to estimate plate appearances for pitchers. Previously, I’ve done it the lazy way by not splitting strikeouts out from other outs. I am now using this formula to estimate PA (where PA = AB + W):<br /><br />PA = K + (3*IP - K)*x + H + W<br />Where x = league average of (AB - H - K)/(3*IP - K)<br /><br />Then KG = K*Lg(PA/G) and WG = W*Lg(PA/G).<br /><br />G-F is a junk stat, included here out of habit because I've been including it for years. It was intended to give a quick read of a pitcher's expected performance in the next season, based on eRA and strikeout rate. Although the numbers vaguely resemble RAs, it's actually unitless. As a rule of thumb, anything under four is pretty good for a starter. G-F = 4.46 + .095(eRA) - .113(K*9/IP). It is a junk stat. JUNK STAT JUNK STAT JUNK STAT. Got it?<br /><br />%H is BABIP, more or less--%H = (H - HR)/(PA - HR - K - W), where PA was estimated above. Pitches/Start includes all appearances, so I've counted relief appearances as one-half of a start (P/S = Pitches/(.5*G + .5*GS). QS% is just QS/(G - GS); I don't think it's particularly useful, but Doug's Stats include QS so I include it.<br /><br />I've used a stat called Relief Run Average (RRA) in the past, based on Sky Andrecheck's article in the August 1999 By the Numbers; that one only used inherited runners, but I've revised it to include bequeathed runners as well, making it equally applicable to starters and relievers. I use RRA as the building block for baselined value estimates for all pitchers. I explained RRA in this article, but the bottom line formulas are:<br /><br />BRSV = BRS - BR*i*sqrt(PF)<br />IRSV = IR*i*sqrt(PF) - IRS<br />RRA = ((R - (BRSV + IRSV))*9/IP)/PF<br /><br />The two baselined stats are Runs Above Average (RAA) and Runs Above Replacement (RAR). Starting in 2015 I revised RAA to use a slightly different baseline for starters and relievers as described here. The adjustment is based on patterns from the last several seasons of league average starter and reliever eRA. Thus it does not adjust for any advantages relief pitchers enjoy that are not reflected in their component statistics. This could include runs allowed scoring rules that benefit relievers (although the use of RRA should help even the scales in this regard, at least compared to raw RA) and the talent advantage of starting pitchers. The RAR baselines do attempt to take the latter into account, and so the difference in starter and reliever RAR will be more stark than the difference in RAA.<br /><br />RAA (relievers) = (.951*LgRA - RRA)*IP/9<br />RAA (starters) = (1.025*LgRA - RRA)*IP/9<br />RAR (relievers) = (1.11*LgRA - RRA)*IP/9<br />RAR (starters) = (1.28*LgRA - RRA)*IP/9<br /><br />All players with 250 or more plate appearances (official, total plate appearances) are included in the Hitters spreadsheets (along with some players close to the cutoff point who I was interested in). Each is assigned one position, the one at which they appeared in the most games. The statistics presented are: Games played (G), Plate Appearances (PA), Outs (O), Batting Average (BA), On Base Average (OBA), Slugging Average (SLG), Secondary Average (SEC), Runs Created (RC), Runs Created per Game (RG), Speed Score (SS), Hitting Runs Above Average (HRAA), Runs Above Average (RAA), Hitting Runs Above Replacement (HRAR), and Runs Above Replacement (RAR).<br /><br />Starting in 2015, I'm including hit batters in all related categories for hitters, so PA is now equal to AB + W+ HB. Outs are AB - H + CS. BA and SLG you know, but remember that without SF, OBA is just (H + W + HB)/(AB + W + HB). Secondary Average = (TB - H + W + HB)/AB = SLG - BA + (OBA - BA)/(1 - OBA). I have not included net steals as many people (and Bill James himself) do, but I have included HB which some do not.<br /><br />BA, OBA, and SLG are park-adjusted by dividing by the square root of PF. This is an approximation, of course, but I'm satisfied that it works well (I plan to post a couple articles on this some time during the offseason). The goal here is to adjust for the win value of offensive events, not to quantify the exact park effect on the given rate. I use the BA/OBA/SLG-based formula to figure SEC, so it is park-adjusted as well.<br /><br />Runs Created is actually Paul Johnson's ERP, more or less. Ideally, I would use a custom linear weights formula for the given league, but ERP is just so darn simple and close to the mark that it’s hard to pass up. I still use the term “RC” partially as a homage to Bill James (seriously, I really like and respect him even if I’ve said negative things about RC and Win Shares), and also because it is just a good term. I like the thought put in your head when you hear “creating” a run better than “producing”, “manufacturing”, “generating”, etc. to say nothing of names like “equivalent” or “extrapolated” runs. None of that is said to put down the creators of those methods--there just aren’t a lot of good, unique names available. <br /><br />For 2015, I refined the formula a little bit to:<br /><br />1. include hit batters at a value equal to that of a walk<br />2. value intentional walks at just half the value of a regular walk<br />3. recalibrate the multiplier based on the last ten major league seasons (2005-2014)<br /><br />This revised RC = (TB + .8H + W + HB - .5IW + .7SB - CS - .3AB)*.310<br /><br />RC is park adjusted by dividing by PF, making all of the value stats that follow park adjusted as well. RG, the Runs Created per Game rate, is RC/O*25.5. I do not believe that outs are the proper denominator for an individual rate stat, but I also do not believe that the distortions caused are that bad. (I still intend to finish my rate stat series and discuss all of the options in excruciating detail, but alas you’ll have to take my word for it now).<br /><br />Several years ago I switched from using my own "Speed Unit" to a version of Bill James' Speed Score; of course, Speed Unit was inspired by Speed Score. I only use four of James' categories in figuring Speed Score. I actually like the construct of Speed Unit better as it was based on z-scores in the various categories (and amazingly a couple other sabermetricians did as well), but trying to keep the estimates of standard deviation for each of the categories appropriate was more trouble than it was worth.<br /><br />Speed Score is the average of four components, which I'll call a, b, c, and d:<br /><br />a = ((SB + 3)/(SB + CS + 7) - .4)*20<br />b = sqrt((SB + CS)/(S + W))*14.3<br />c = ((R - HR)/(H + W - HR) - .1)*25<br />d = T/(AB - HR - K)*450<br /><br />James actually uses a sliding scale for the triples component, but it strikes me as needlessly complex and so I've streamlined it. He looks at two years of data, which makes sense for a gauge that is attempting to capture talent and not performance, but using multiple years of data would be contradictory to the guiding principles behind this set of reports (namely, simplicity. Or laziness. You're pick.) I also changed some of his division to mathematically equivalent multiplications.<br /><br />There are a whopping four categories that compare to a baseline; two for average, two for replacement. Hitting RAA compares to a league average hitter; it is in the vein of Pete Palmer’s Batting Runs. RAA compares to an average hitter at the player’s primary position. Hitting RAR compares to a “replacement level” hitter; RAR compares to a replacement level hitter at the player’s primary position. The formulas are:<br /><br />HRAA = (RG - N)*O/25.5<br />RAA = (RG - N*PADJ)*O/25.5<br />HRAR = (RG - .73*N)*O/25.5<br />RAR = (RG - .73*N*PADJ)*O/25.5<br /><br />PADJ is the position adjustment, and it is based on 2002-2011 offensive data. For catchers it is .89; for 1B/DH, 1.17; for 2B, .97; for 3B, 1.03; for SS, .93; for LF/RF, 1.13; and for CF, 1.02. I had been using the 1992-2001 data as a basis for some time, but finally updated for 2012. I’m a little hesitant about this update, as the middle infield positions are the biggest movers (higher positional adjustments, meaning less positional credit). I have no qualms for second base, but the shortstop PADJ is out of line with the other position adjustments widely in use and feels a bit high to me. But there are some decent points to be made in favor of offensive adjustments, and I’ll have a bit more on this topic in general below.<br /><br />That was the mechanics of the calculations; now I'll twist myself into knots trying to justify them. If you only care about the how and not the why, stop reading now. <br /><br />The first thing that should be covered is the philosophical position behind the statistics posted here. They fall on the continuum of ability and value in what I have called "performance". Performance is a technical-sounding way of saying "Whatever arbitrary combination of ability and value I prefer".<br /><br />With respect to park adjustments, I am not interested in how any particular player is affected, so there is no separate adjustment for lefties and righties for instance. The park factor is an attempt to determine how the park affects run scoring rates, and thus the win value of runs.<br /><br />I apply the park factor directly to the player's statistics, but it could also be applied to the league context. The advantage to doing it my way is that it allows you to compare the component statistics (like Runs Created or OBA) on a park-adjusted basis. The drawback is that it creates a new theoretical universe, one in which all parks are equal, rather than leaving the player grounded in the actual context in which he played and evaluating how that context (and not the player's statistics) was altered by the park.<br /><br />The good news is that the two approaches are essentially equivalent; in fact, they are precisely equivalent if you assume that the Runs Per Win factor is equal to the RPG. Suppose that we have a player in an extreme park (PF = 1.15, approximately like Coors Field pre-humidor) who has an 8 RG before adjusting for park, while making 350 outs in a 4.5 N league. The first method of park adjustment, the one I use, converts his value into a neutral park, so his RG is now 8/1.15 = 6.957. We can now compare him directly to the league average:<br /><br />RAA = (6.957 - 4.5)*350/25.5 = +33.72<br /><br />The second method would be to adjust the league context. If N = 4.5, then the average player in this park will create 4.5*1.15 = 5.175 runs. Now, to figure RAA, we can use the unadjusted RG of 8:<br /><br />RAA = (8 - 5.175)*350/25.5 = +38.77<br /><br />These are not the same, as you can obviously see. The reason for this is that they take place in two different contexts. The first figure is in a 9 RPG (2*4.5) context; the second figure is in a 10.35 RPG (2*4.5*1.15) context. Runs have different values in different contexts; that is why we have RPW converters in the first place. If we convert to WAA (using RPW = RPG, which is only an approximation, so it's usually not as tidy as it appears below), then we have:<br /><br />WAA = 33.72/9 = +3.75<br />WAA = 38.77/10.35 = +3.75<br /><br />Once you convert to wins, the two approaches are equivalent. The other nice thing about the first approach is that once you park-adjust, everyone in the league is in the same context, and you can dispense with the need for converting to wins at all. You still might want to convert to wins, and you'll need to do so if you are comparing the 2015 players to players from other league-seasons (including between the AL and NL in the same year), but if you are only looking to compare Jose Bautista to Miguel Cabrera, it's not necessary. WAR is somewhat ubiquitous now, but personally I prefer runs when possible--why mess with decimal points if you don't have to? <br /><br />The park factors used to adjust player stats here are run-based. Thus, they make no effort to project what a player "would have done" in a neutral park, or account for the difference effects parks have on specific events (walks, home runs, BA) or types of players. They simply account for the difference in run environment that is caused by the park (as best I can measure it). As such, they don't evaluate a player within the actual run context of his team's games; they attempt to restate the player's performance as an equivalent performance in a neutral park.<br /><br />I suppose I should also justify the use of sqrt(PF) for adjusting component statistics. The classic defense given for this approach relies on basic Runs Created--runs are proportional to OBA*SLG, and OBA*SLG/PF = OBA/sqrt(PF)*SLG/sqrt(PF). While RC may be an antiquated tool, you will find that the square root adjustment is fairly compatible with linear weights or Base Runs as well. I am not going to take the space to demonstrate this claim here, but I will some time in the future. <br /><br />Many value figures published around the sabersphere adjust for the difference in quality level between the AL and NL. I don't, but this is a thorny area where there is no right or wrong answer as far as I'm concerned. I also do not make an adjustment in the league averages for the fact that the overall NL averages include pitcher batting and the AL does not (not quite true in the era of interleague play, but you get my drift). <br /><br />The difference between the leagues may not be precisely calculable, and it certainly is not constant, but it is real. If the average player in the AL is better than the average player in the NL, it is perfectly reasonable to expect the average AL player to have more RAR than the average NL player, and that will not happen without some type of adjustment. On the other hand, if you are only interested in evaluating a player relative to his own league, such an adjustment is not necessarily welcome.<br /><br />The league argument only applies cleanly to metrics baselined to average. Since replacement level compares the given player to a theoretical player that can be acquired on the cheap, the same pool of potential replacement players should by definition be available to the teams of each league. One could argue that if the two leagues don't have equal talent at the major league level, they might not have equal access to replacement level talent--except such an argument is at odds with the notion that replacement level represents talent that is truly "freely available".<br /><br />So it's hard to justify the approach I take, which is to set replacement level relative to the average runs scored in each league, with no adjustment for the difference in the leagues. The best justification is that it's simple and it treats each league as its own universe, even if in reality they are connected.<br /><br />The replacement levels I have used here are very much in line with the values used by other sabermetricians. This is based both on my own "research", my interpretation of other's people research, and a desire to not stray from consensus and make the values unhelpful to the majority of people who may encounter them.<br /><br />Replacement level is certainly not settled science. There is always going to be room to disagree on what the baseline should be. Even if you agree it should be "replacement level", any estimate of where it should be set is just that--an estimate. Average is clean and fairly straightforward, even if its utility is questionable; replacement level is inherently messy. So I offer the average baseline as well.<br /><br />For position players, replacement level is set at 73% of the positional average RG (since there's a history of discussing replacement level in terms of winning percentages, this is roughly equivalent to .350). For starting pitchers, it is set at 128% of the league average RA (.380), and for relievers it is set at 111% (.450). <br /><br />I am still using an analytical structure that makes the comparison to replacement level for a position player by applying it to his hitting statistics. This is the approach taken by Keith Woolner in VORP (and some other earlier replacement level implementations), but the newer metrics (among them Rally and Fangraphs' WAR) handle replacement level by subtracting a set number of runs from the player's total runs above average in a number of different areas (batting, fielding, baserunning, positional value, etc.), which for lack of a better term I will call the subtraction approach.<br /><br />The offensive positional adjustment makes the inherent assumption that the average player at each position is equally valuable. I think that this is close to being true, but it is not quite true. The ideal approach would be to use a defensive positional adjustment, since the real difference between a first baseman and a shortstop is their defensive value. When you bat, all runs count the same, whether you create them as a first baseman or as a shortstop. <br /><br />That being said, using "replacement hitter at position" does not cause too many distortions. It is not theoretically correct, but it is practically powerful. For one thing, most players, even those at key defensive positions, are chosen first and foremost for their offense. Empirical research by Keith Woolner has shown that the replacement level hitting performance is about the same for every position, relative to the positional average.<br /><br />Figuring what the defensive positional adjustment should be, though, is easier said than done. Therefore, I use the offensive positional adjustment. So if you want to criticize that choice, or criticize the numbers that result, be my guest. But do not claim that I am holding this up as the correct analytical structure. I am holding it up as the most simple and straightforward structure that conforms to reality reasonably well, and because while the numbers may be flawed, they are at least based on an objective formula that I can figure myself. If you feel comfortable with some other assumptions, please feel free to ignore mine.<br /><br />That still does not justify the use of HRAR--hitting runs above replacement--which compares each hitter, regardless of position, to 73% of the league average. Basically, this is just a way to give an overall measure of offensive production without regard for position with a low baseline. It doesn't have any real baseball meaning. <br /><br />A player who creates runs at 90% of the league average could be above-average (if he's a shortstop or catcher, or a great fielder at a less important fielding position), or sub-replacement level (DHs that create 3.5 runs per game are not valuable properties). Every player is chosen because his total value, both hitting and fielding, is sufficient to justify his inclusion on the team. HRAR fails even if you try to justify it with a thought experiment about a world in which defense doesn't matter, because in that case the absolute replacement level (in terms of RG, without accounting for the league average) would be much higher than it is currently. <br /><br />The specific positional adjustments I use are based on 2002-2011 data. I stick with them because I have not seen compelling evidence of a change in the degree of difficulty or scarcity between the positions between now and then, and because I think they are fairly reasonable. The positions for which they diverge the most from the defensive position adjustments in common use are 2B, 3B, and CF. Second base is considered a premium position by the offensive PADJ (.97), while third base and center field have similar adjustments in the opposite direction (1.03 and 1.02).<br /><br />Another flaw is that the PADJ is applied to the overall league average RG, which is artificially low for the NL because of pitcher's batting. When using the actual league average runs/game, it's tough to just remove pitchers--any adjustment would be an estimate. If you use the league total of runs created instead, it is a much easier fix.<br /><br />One other note on this topic is that since the offensive PADJ is a stand-in for average defensive value by position, ideally it would be applied by tying it to defensive playing time. I have done it by outs, though.<br /><br />The reason I have taken this flawed path is because 1) it ties the position adjustment directly into the RAR formula rather than leaving it as something to subtract on the outside and more importantly 2) there’s no straightforward way to do it. The best would be to use defensive innings--set the full-time player to X defensive innings, figure how Derek Jeter’s innings compared to X, and adjust his PADJ accordingly. Games in the field or games played are dicey because they can cause distortion for defensive replacements. Plate Appearances avoid the problem that outs have of being highly related to player quality, but they still carry the illogic of basing it on offensive playing time. And of course the differences here are going to be fairly small (a few runs). That is not to say that this way is preferable, but it’s not horrible either, at least as far as I can tell.<br /><br />To compare this approach to the subtraction approach, start by assuming that a replacement level shortstop would create .86*.73*4.5 = 2.825 RG (or would perform at an overall level of equivalent value to being an average fielder at shortstop while creating 2.825 runs per game). Suppose that we are comparing two shortstops, each of whom compiled 600 PA and played an equal number of defensive games and innings (and thus would have the same positional adjustment using the subtraction approach). Alpha made 380 outs and Bravo made 410 outs, and each ranked as dead-on average in the field.<br /><br />The difference in overall RAR between the two using the subtraction approach would be equal to the difference between their offensive RAA compared to the league average. Assuming the league average is 4.5 runs, and that both Alpha and Bravo created 75 runs, their offensive RAAs are:<br /><br />Alpha = (75*25.5/380 - 4.5)*380/25.5 = +7.94<br /><br />Similarly, Bravo is at +2.65, and so the difference between them will be 5.29 RAR.<br /><br />Using the flawed approach, Alpha's RAR will be:<br /><br />(75*25.5/380 - 4.5*.73*.86)*380/25.5 = +32.90<br /><br />Bravo's RAR will be +29.58, a difference of 3.32 RAR, which is two runs off of the difference using the subtraction approach.<br /><br />The downside to using PA is that you really need to consider park effects if you do, whereas outs allow you to sidestep park effects. Outs are constant; plate appearances are linked to OBA. Thus, they not only depend on the offensive context (including park factor), but also on the quality of one's team. Of course, attempting to adjust for team PA differences opens a huge can of worms which is not really relevant; for now, the point is that using outs for individual players causes distortions, sometimes trivial and sometimes bothersome, but almost always makes one's life easier.<br /><br />I do not include fielding (or baserunning outside of steals, although that is a trivial consideration in comparison) in the RAR figures--they cover offense and positional value only). This in no way means that I do not believe that fielding is an important consideration in player evaluation. However, two of the key principles of these stat reports are 1) not incorporating any data that is not readily available and 2) not simply including other people's results (of course I borrow heavily from other people's methods, but only adapting methodology that I can apply myself).<br /><br />Any fielding metric worth its salt will fail to meet either criterion--they use zone data or play-by-play data which I do not have easy access to. I do not have a fielding metric that I have stapled together myself, and so I would have to simply lift other analysts' figures. <br /><br />Setting the practical reason for not including fielding aside, I do have some reservations about lumping fielding and hitting value together in one number because of the obvious differences in reliability between offensive and fielding metrics. In theory, they absolutely should be put together. But in practice, I believe it would be better to regress the fielding metric to a point at which it would be roughly equivalent in reliability to the offensive metric.<br /><br />Offensive metrics have error bars associated with them, too, of course, and in evaluating a single season's value, I don't care about the vagaries that we often lump together as "luck". Still, there are errors in our assessment of linear weight values and players that collect an unusual proportion of infield hits or hits to the left side, errors in estimation of park factor, and any number of other factors that make their events more or less valuable than an average event of that type. <br /><br />Fielding metrics offer up all of that and more, as we cannot be nearly as certain of true successes and failures as we are when analyzing offense. Recent investigations, particularly by Colin Wyers, have raised even more questions about the level of uncertainty. So, even if I was including a fielding value, my approach would be to assume that the offensive value was 100% reliable (which it isn't), and regress the fielding metric relative to that (so if the offensive metric was actually 70% reliable, and the fielding metric 40% reliable, I'd treat the fielding metric as .4/.7 = 57% reliable when tacking it on, to illustrate with a simplified and completely made up example presuming that one could have a precise estimate of nebulous "reliability").<br /><br />Given the inherent assumption of the offensive PADJ that all positions are equally valuable, once RAR has been figured for a player, fielding value can be accounted for by adding on his runs above average relative to a player at his own position. If there is a shortstop that is -2 runs defensively versus an average shortstop, he is without a doubt a plus defensive player, and a more valuable defensive player than a first baseman who was +1 run better than an average first baseman. Regardless, since it was implicitly assumed that they are both average defensively for their position when RAR was calculated, the shortstop will see his value docked two runs. This DOES NOT MEAN that the shortstop has been penalized for his defense. The whole process of accounting for positional differences, going from hitting RAR to positional RAR, has benefited him.<br /><br />I've found that there is often confusion about the treatment of first baseman and designated hitters in my PADJ methodology, since I consider DHs as in the same pool as first baseman. The fact of the matter is that first baseman outhit DH. There are any number of potential explanations for this; DHs are often old or injured, players hit worse when DHing than they do when playing the field, etc. This actually helps first baseman, since the DHs drag the average production of the pool down, thus resulting in a lower replacement level than I would get if I considered first baseman alone.<br /><br />However, this method does assume that a 1B and a DH have equal defensive value. Obviously, a DH has no defensive value. What I advocate to correct this is to treat a DH as a bad defensive first baseman, and thus knock another five or so runs off of his RAR for a full-time player. I do not incorporate this into the published numbers, but you should keep it in mind. However, there is no need to adjust the figures for first baseman upwards --the only necessary adjustment is to take the DHs down a notch. <br /><br />Finally, I consider each player at his primary defensive position (defined as where he appears in the most games), and do not weight the PADJ by playing time. This does shortchange a player like Ben Zobrist (who saw significant time at a tougher position than his primary position), and unduly boost a player like Buster Posey (who logged a lot of games at a much easier position than his primary position). For most players, though, it doesn't matter much. I find it preferable to make manual adjustments for the unusual cases rather than add another layer of complexity to the whole endeavor.<br /><br /><a href="https://docs.google.com/spreadsheets/d/e/2PACX-1vRcb2zLEtaXv5GEGMLQuUUnb4KAOFcGWh6wfOn-MnY3gR9LbvvJJtGcqXmKSXqUBNQDeL9pQop6zFji/pub?output=html"><br />2017 League</a><br /><br /><a href="https://docs.google.com/spreadsheets/d/e/2PACX-1vTqqWsLzxQ9uSkyzgLcHmoEKSAGrx6zoadd6sZNK8EgG_sMwlr1uJvsW6qbtaGH7Bpo32hsCpvXMNhh/pub?output=html">2017 Park Factors</a><br /><br /><a href="https://docs.google.com/spreadsheets/d/e/2PACX-1vTbe9Bvv3L4pwYb5qJC1AAiIZwV2invYT5HKIqYKWhGHweE9zEyzewU-80OrLbT6uPc6Kfkigs-J5BF/pub?output=html">2017 Teams</a><br /><br /><a href="https://docs.google.com/spreadsheets/d/e/2PACX-1vQxpPvgc4bmrHqBYXxOlfFGhcDhefJqwp0wa4-O6RM6VnzTlTNxjRhAsxlxGEdgLqgH3EhVBIyfwqNQ/pub?output=html">2017 Team Offense</a><br /><br /><a href="https://docs.google.com/spreadsheets/d/e/2PACX-1vR6-vk6pPcXPiF7OjlxKSOAx6dpKrpM72Lv9aHRTTmt2vE5VrBCP2ZuMlC-IQ6N0_cjZo3_aBkl6rZN/pub?output=html">2017 Team Defense</a><br /><br /><a href="https://docs.google.com/spreadsheets/d/e/2PACX-1vSqgjP8LES2aBeI4vY7Z1GiWZQ_o5xifZepKEBqYstzMCGMcwB1XTehljVBUjsEc__-8B0J95wgKBUV/pub?output=html">2017 AL Relievers</a><br /><br /><a href="https://docs.google.com/spreadsheets/d/e/2PACX-1vQAxZzDcveBMh_b78cQbtf_5vPPcJ-47L17uSNNuzoPE5XjrrDWNfOmjO1TBGw_uiiCrHhNGc_czbeq/pub?output=html">2017 NL Relievers<br /></a><br /><a href="https://docs.google.com/spreadsheets/d/e/2PACX-1vQrMIiv_ufFUHoH3P5r6F_-S7bBGKQ00HKJGCeq57UjA6j24QFLYUV238Dgca5yih1GJNxpDUhTSlf1/pub?output=html">2017 AL Starters</a><br /><br /><a href="https://docs.google.com/spreadsheets/d/e/2PACX-1vRXa-m_byBIx9TQ5Jqqto4Am-xiP4X22tUlMrm3xWXGdwz9A5TauYM23asTQ_2btMMeCzNU9V0380p4/pub?output=html">2017 NL Starters</a><br /><br /><a href="https://docs.google.com/spreadsheets/d/e/2PACX-1vQpRFDFgsnkk8de6PBS6a-nqDZfQrVVqyo3TJCP9y2sJjRBGjJRrnLZZOWYU26GarOheT_RWEzcPyf1/pub?output=html">2017 AL Hitters</a><br /><br /><a href="https://docs.google.com/spreadsheets/d/e/2PACX-1vQfxVtrW43CPz227jxGKq_Gc0gGus6OVKvLUID0D578iymbKBNmdB9xTHKa9FofYpIoTGgBHUQT_u2u/pub?output=html">2017 NL Hitters</a>phttp://www.blogger.com/profile/18057215403741682609noreply@blogger.com0tag:blogger.com,1999:blog-12133335.post-23113546112861404382017-10-02T17:58:00.000-04:002017-10-03T19:54:55.134-04:00Crude Playoff Odds--2017These are very simple playoff odds, based on my crude rating system for teams using an equal mix of W%, EW% (based on R/RA), PW% (based on RC/RCA), and 69 games of .500. They account for home field advantage by assuming a .500 team wins 54.2% of home games (major league average 2006-2015). They assume that a team's inherent strength is constant from game-to-game. They do not generally account for any number of factors that you would actually want to account for if you were serious about this, including but not limited to injuries, the current construction of the team rather than the aggregate seasonal performance, pitching rotations, estimated true talent of the players, etc.<br /><br />The CTRs that are fed in are:<br /><br /><a href="https://4.bp.blogspot.com/-QNp2ZSN6m9I/WdK1v7wd4_I/AAAAAAAACZA/gyJrCH3OwZMaZloWqdWH7ptfau7kHmElwCLcBGAs/s1600/playodd17a.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://4.bp.blogspot.com/-QNp2ZSN6m9I/WdK1v7wd4_I/AAAAAAAACZA/gyJrCH3OwZMaZloWqdWH7ptfau7kHmElwCLcBGAs/s400/playodd17a.jpg" width="400" height="387" data-original-width="217" data-original-height="210" /></a><br /><br />Notable here is that three AL teams rank ahead of the Dodgers, which includes New York rather than Boston. NYA’s raw EW% and PW% are very close to LA, and LA played the second-weakest schedule in MLB while the Red Sox and Yankees played the toughest schedules of any playoff teams.<br /><br />Wilcard game odds (the least useful since the pitching matchups aren’t taken into account, and that matters most when there is just one game):<br /><br /><a href="https://2.bp.blogspot.com/-brFOMr65c2Q/WdK114T01uI/AAAAAAAACZE/Sk99AOCRB_cdjwK7xDCoMAaBV9IMPRuMACLcBGAs/s1600/playodd17b.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://2.bp.blogspot.com/-brFOMr65c2Q/WdK114T01uI/AAAAAAAACZE/Sk99AOCRB_cdjwK7xDCoMAaBV9IMPRuMACLcBGAs/s400/playodd17b.jpg" width="400" height="81" data-original-width="288" data-original-height="58" /></a><br /><br />LDS:<br /><br /><a href="https://4.bp.blogspot.com/-ZE-Biq7wL18/WdK1_Pxm9SI/AAAAAAAACZI/6Ur1aAuRthITXbD4_Vz_z7BzDAyEVT4rQCLcBGAs/s1600/playodd17c.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://4.bp.blogspot.com/-ZE-Biq7wL18/WdK1_Pxm9SI/AAAAAAAACZI/6Ur1aAuRthITXbD4_Vz_z7BzDAyEVT4rQCLcBGAs/s400/playodd17c.jpg" width="400" height="106" data-original-width="505" data-original-height="134" /></a><br /><br />I think most people would pick WAS/CHN as the most compelling on paper, which is backed up by the odds. Unfortunately for me, CLE/NYA would be a sneaky-good series.<br /><br />LCS:<br /><br /><a href="https://3.bp.blogspot.com/-LEokV4AhuDc/WdK2GF0c7AI/AAAAAAAACZM/XtYznK2rgN0w0nBJ_hG4yfdwWdYi1HwmQCLcBGAs/s1600/playodd17d.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://3.bp.blogspot.com/-LEokV4AhuDc/WdK2GF0c7AI/AAAAAAAACZM/XtYznK2rgN0w0nBJ_hG4yfdwWdYi1HwmQCLcBGAs/s400/playodd17d.jpg" width="400" height="197" data-original-width="505" data-original-height="249" /></a><br /><br />World Series:<br /><br /><a href="https://4.bp.blogspot.com/-JM5tFMYAvFA/WdK2LnluBpI/AAAAAAAACZQ/3keRDCdRoREd93iJ1zO4WvouAbVKl021ACLcBGAs/s1600/playodd17e.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://4.bp.blogspot.com/-JM5tFMYAvFA/WdK2LnluBpI/AAAAAAAACZQ/3keRDCdRoREd93iJ1zO4WvouAbVKl021ACLcBGAs/s400/playodd17e.jpg" width="400" height="394" data-original-width="503" data-original-height="495" /></a><br /><br />Because I set this spreadsheet up when home field advantage went to a particular league (as it has been for the entire history of the World Series prior to this year), all of the NL teams are listed as the home team. But the probabilities all consider which team would actually have the home field advantage in each matchup.<br /><br />Put it all together:<br /><br /><a href="https://4.bp.blogspot.com/-ogVSkEB2mJo/WdK2RfTpZCI/AAAAAAAACZU/YXyXMcHqC6MJ9EPc3hRNQty9ETCDVMu5QCLcBGAs/s1600/playodd17f.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://4.bp.blogspot.com/-ogVSkEB2mJo/WdK2RfTpZCI/AAAAAAAACZU/YXyXMcHqC6MJ9EPc3hRNQty9ETCDVMu5QCLcBGAs/s400/playodd17f.jpg" width="400" height="234" data-original-width="361" data-original-height="211" /></a><br /><br />This one should make it clear why I don’t have much to say this year.phttp://www.blogger.com/profile/18057215403741682609noreply@blogger.com0tag:blogger.com,1999:blog-12133335.post-24173031964119195442017-08-22T10:23:00.000-04:002017-08-22T10:23:06.181-04:00Enby Distribution, pt. 4: Revisiting W%In my first series about runs per game distributions, I wrote about how to use estimates of the probability of scoring k runs (however these probabilities were estimated, Enby distribution or an alternative approach) to estimate a team’s winning percentage. I’m going to circle back to that here, and most of the content is a repeat of the earlier post. <br /><br />However, I think this is an important enough topic to rehash. In fact, a winning percentage estimator strikes me as the most logical application for a runs per game distribution, albeit one that is not particularly helpful to everyday sabermetric practice. After all, multiple formulas to estimate W% as a function of runs scored and runs allowed have been developed, and most of them work quite well when working with normal major league teams--well enough to make it difficult to imagine that there is any appreciable gain in accuracy to be had. Better yet, these W% estimators are fairly simple--even the most complex versions in common use, Pythagenport/pat, can be quickly tapped out on a calculator in about thirty seconds.<br /><br />Given that there are powerful, relatively simple W% models already in use, why even bother to examine a model based on the estimated scoring distribution? There are three obvious reasons that come to my mind. The first is that such a model serves as a check on the others. Depending on how much confidence one has in the underlying run distribution model, it is possible that the resulting W% estimator will produce a batter estimate, at least at the extremes. We know of course that some of the easier models don’t hold up well in extreme situations--linear estimators will return negative or greater than one figures at some point, and fixed Pythagorean exponents will fray at some point. While we know that Pythagenpat works at the known point of 1 RPG and appears to work well at other extreme values, it doesn’t hurt to have another way of estimating W% in those extremes to see if Pythagenpat is corroborated, or whether the models disagree. This can also serve as a check on Enby--if the results vary too much from what we expect, it may imply that Enby does not hold up well at extremes itself.<br /><br />A second reason is that it’s plain fun if you like esoteric sabermetrics (and if you’re reading this blog, it’s a good bet that you do). I’ve never needed an excuse to mess around with alternative methods, particularly when it comes to W% estimators, which along with run estimators are my own personal favorite sabermetric tools.<br /><br />But the third reason is the one that I want to focus on here, which is that a W% estimator based on an underlying estimate of the run distribution is from one perspective the simplest possible estimator. This may seem to be an absurd statement given all of the steps that are necessary to compute Enby estimates, let alone plugging these into a W% formula. But from a first principles standpoint, the distribution-based W% estimator is the simplest to explain, because it is defined by the laws of the game itself.<br /><br />If you score no runs, you don’t win. If you score one run, you win if you allow zero runs. If you score two runs, you win if you allow either zero or one run, and on it goes ad infinitum. If at the end of nine innings you have scored and allowed an equal number of runs, you play on until there is an inning in which an unequal, greater than zero number of runs are scored. This fundamental identity is what all of the other W% estimators attempt to approximate, the mechanics which they attempt to sweep under the rug by taking shortcuts to approximate. The distribution-based approach is computationally dense but conceptually easy (and correct). Of course, to bring points one and three together, the definition may be correct, but the resulting estimates are useless if the underlying model (Enby in this case) does not work.<br /><br />In order to produce our W% estimate, we first need to use Enby to estimate the scoring distribution for the two teams. This is not as simple as using the Enby parameters we have already developed based on the Tango Distribution with c = .767. Tango has found that his method produces more accurate results for two teams when c is set equal to .852 instead.<br /><br />In the previous post, I walked through the computations for the Enby distribution with any c value, so this is an easy substitution to make. But why is it necessary? I don’t have a truly satisfactory answer to that question--it's trite to just assert that it works better for head-to-head matchups because of the covariance between runs scored and runs allowed, even if that is in fact the right answer.<br /><br />How will modifying the control value alter the Enby distribution? All of the parameters will be effected, because all depend on the control value in one way or another. First, B and r (the latter as it is initially figured before zero modification):<br /><br />VAR = RG^2/9 + (2/c - 1)*RG<br />r = RG^2/(VAR - RG)<br />B = VAR/RG - 1<br /><br />When c is larger, the variance of runs scored will be smaller. We can see this by examining the equations for variance with c = .767 and .852:<br /><br />VAR (.767) = RG^2/9 + 1.608*RG<br />VAR (.852) = RG^2/9 + 1.347*RG<br /><br />This results in a larger value for r and a smaller value for B, but these parameters don’t have an intuitive baseball explanation, unlike variance. It’s difficult to explain (for me at least) why variance of a single team’s runs scored should be lower when considering a head-to-head matchup, but that’s the way it works out.<br /><br />It should be noted that if the sole purpose of this exercise is to estimate W%, we don’t have to care whether the actual probability of each team scoring k runs is correct. All we need to do is have an accurate estimate of how often Team A’s runs scored are greater than Team B’s. <br /> <br />By increasing c, we also reduce the probability of a shutout, as can be seen from the formula for z:<br /><br />z =(RI/(RI + c*RI^2))^9<br /><br />Originally, I had intended to display some graphs showing the behavior of the three parameters by RG with each choice of c, but these turned out to be not of any particular interest. I ran <a href="http://walksaber.blogspot.com/2012/07/on-run-distributions-pt-6.html">similar graphs</a> earlier in the series with parameters based on the earlier variance model, and the shape of the resulting functions are quite similar. The only real visual difference when c varies is what appears to be linear shifts for r and B (the B shift is linear, the r not quite).<br /><br />What might be more interesting is looking at how c shapes the estimated run distribution for a team with a given RG. I’ll look at three teams--one average (4.5 RG), one extremely low-scoring (2.25 RG), and one extremely high-scoring (9 RG). First, the 4.5 RG team:<br /><br /><a href="https://3.bp.blogspot.com/-Y_-NRFvlIeQ/WZpFjKn9TQI/AAAAAAAACYk/LJWiJj0acHYpr90_3ntBtw31E4lJQZiHwCLcBGAs/s1600/45rg.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://3.bp.blogspot.com/-Y_-NRFvlIeQ/WZpFjKn9TQI/AAAAAAAACYk/LJWiJj0acHYpr90_3ntBtw31E4lJQZiHwCLcBGAs/s400/45rg.jpg" width="400" height="203" data-original-width="1566" data-original-height="796" /></a><br /><br />As you may recall from earlier, Enby consistently overestimates the frequency with which a normal major league team will score 2-4 runs. Using the .852 c value exacerbates this issue; in fact, the main thing to take away from this set of graphs is that the higher c value clusters more probability around the mean, while the lower c value leaves more probability for the tails.<br /><br />The 2.25 RG team:<br /><br /><a href="https://1.bp.blogspot.com/-yp_tHHSKr6o/WZpFnug1eFI/AAAAAAAACYo/BFBoMYBTB3USxlMx1eUPjQNN93RbK9UFwCLcBGAs/s1600/225rg.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://1.bp.blogspot.com/-yp_tHHSKr6o/WZpFnug1eFI/AAAAAAAACYo/BFBoMYBTB3USxlMx1eUPjQNN93RbK9UFwCLcBGAs/s400/225rg.jpg" width="400" height="204" data-original-width="1563" data-original-height="799" /></a><br /><br />And the 9 RG team:<br /><br /><a href="https://1.bp.blogspot.com/-hE2EmLUqMX4/WZpFukgTScI/AAAAAAAACYs/_OrCcur9k3UknSQbfssFwg5LGitMl9sPgCLcBGAs/s1600/9rg.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://1.bp.blogspot.com/-hE2EmLUqMX4/WZpFukgTScI/AAAAAAAACYs/_OrCcur9k3UknSQbfssFwg5LGitMl9sPgCLcBGAs/s400/9rg.jpg" width="400" height="202" data-original-width="1554" data-original-height="783" /></a><br />phttp://www.blogger.com/profile/18057215403741682609noreply@blogger.com0tag:blogger.com,1999:blog-12133335.post-45693263701828212692017-08-10T16:38:00.000-04:002017-08-10T16:38:24.296-04:00Bottoming OutOn June 5, OSU Athletic Director Gene Smith unceremoniously fired Thad Matta, the winningest men’s basketball coach in the history of the school. He did so months after the normal time to fire coaches had passed, and he did so in a way that ensured that the end of Matta’s tenure would be the dominant story in college basketball over the next week. Matta won four regular season Big Ten championships, went to two Final Fours, and was as close to universally respected and beloved by his former players as you will ever find in college basketball. He did all of this while dealing with a debilitating condition that made routine tasks like walking and taking off his shoes a major challenge; it was a side effect of a surgery performed at the university’s own hospital. OSU was coming off a pair of seasons without making the NCAA Tournament, but basketball is a sport in which a roster can get turned around in a hurry, and this author feels that Matta had more than earned another year or two in which to have the opportunity to do just that. Gene Smith felt otherwise.<br /><br />On May 20, the OSU baseball team lost to Indiana 4-3 at home. This brought an end to a season in which they went 22-34, the school’s worst record since going 6-12 in 1974. They went 8-16 in the Big Ten, the worst showing since going 4-12 in 1987. The season brought Greg Beals’ seven-year record at OSU to 225-167 (.574) and his Big Ten record to 85-83 (.506). Setting aside 2008-2014, a seven-year stretch in which OSU had a .564 W% (since four of the seasons were coached by Beals), the seven-year record is OSU’s worst since 1986-1992. The seven-year stretch in the Big Ten is the worst since 1984-1990 (.486). The Buckeyes finished eleventh in the Big Ten, which in fairness wasn’t possible until the addition of Nebraska, but since the Big Ten eliminated divisions in 1988, the lowest previous conference standing had been seventh (out of 10 in 2010, out of 11 in 2014, out of 13 in 2015).<br /><br />The OSU season is hardly worth recapping in detail, except to point out that baseball is such that Oregon State could go 56-6 on the year let have one of those losses come to the Buckeyes (February 24, 6-1; the Beavers won a rematch 5-1 two days later). The other noteworthy statistical oddity is that in eight Big Ten series, Ohio won just one (2-1 at Penn State). They were swept once (home against Minnesota) and the other six were all 1-2 for the opposition. The top eight teams in the conference qualify for the tournament; OSU finished four games out of the running, eliminated even before the final weekend.<br /><br />The Buckeyes’ .393 overall W% and .412 EW% were both eleventh of thirteen Big Ten teams (the forces of darkness led at .724 and .748 respectively), and their .463 PW% was eighth (again, the forces of darkness led with .699). OSU was twelfth with 5.07 R/G and tenth with 6.05 RA/G, although Bill Davis Staidum is a pitcher’s park and those are unadjusted figures. OSU’s .659 DER was last in the conference.<br /><br />None of this was surprising; OSU lost a tremendous amount of production from 2016, which was Beals’ most successful team, notching his only championship (Big Ten Tournament) and NCAA appearance. With individual exceptions, outside of the 2016 draft class, Beals has failed to recruit and develop talent, often patching his roster with copious amounts of JUCO transfers rather than underclassmen developed in the program. Never was this more acute than in 2017. None of this is meant to be an indictment of the players, who did the best they could to represent their school. It is not their fault that the coach put them in situations that they couldn’t handle or weren’t ready for.<br /><br />Sophomore catcher Jacob Barnwell had a solid season, hitting .254/.367/.343 for only -1 RAA; his classmate and backup Andrew Fishel only got 50 PA but posted a .400 OBA. First base/DH was a real problem position, as senior Zach Ratcliff was -8 RAA and JUCO transfer junior Bo Coolen chipped in -6; both had secondary averages well below the team average. Noah McGowan, another JUCO transfer started at second (and got time in left as well), with -3 RAA in 162 PA before getting injured. True freshman Noah West followed him into the lineup, but a lack of offense (.213/.278/.303 in 105 PA) gave classmate Connor Pohl a shot. Pohl is 6’5” and his future likely lies at third, but his bat gave a boost to the struggling offense (.325/.386/.450 in 89 PA).<br /><br />Senior Jalen Washington manned shortstop and acquitted himself fine defensively and at the plate (.266/.309/.468), and was selected by San Diego in the 28th round. Sophomore third baseman Brady Cherry did not build on the power potential his freshman year seemed to show, hitting four homers in 82 more PA than he had when he hit four in 2016. His overall performance (.260/.333/.410) was about average (-2 RAA). <br /><br />Outfield was definitely the bright spot for the offense, despite getting little production out of JUCO transfer Tyler Cowles (.190/.309/.314 in 129 PA). Senior Shea Murray emerged from a pitching career marred by injuries to provide adequate production and earn the left field job (.252/.331/.449, 0 RAA) and was drafted in the 18th round by Pittsburgh, albeit as a pitcher. Junior center fielder Tre’ Gantt was the team MVP, hitting .314/.426/.426, leading the team with 18 RAA, and was drafted in the 29th round by Cleveland. True freshman right fielder Dominic Canzone was also a key contributor, challenging for the Big Ten batting average lead (.343/.398/.458 for 8 RAA).<br /><br />On the mound, OSU never even came close to establishing a starting rotation due to injuries and ineffectiveness. Nine pitchers started a game, and only one of them had greater than 50% of his appearances as a starter. That was senior Jake Post, who went 1-7 over 13 starts with a 6.41 eRA. Sophomore lefty Connor Curlis was most effective, starting eight times for +3 RAA with 8.3/2.7 K/W. He tied for team innings lead with classmate Ryan Feltner, who was -13 RAA with a 6.71 eRA. Junior Yianni Pavloupous, the closer a year ago, was -10 RAA over 40 innings between both roles. Junior Adam Niemeyer missed time with injuries, appearing in just ten games (five starts) for -3 RAA over 34 innings. Freshman Jake Vance was rushed into action and allowed 20 runs and walks in 26 innings (-4 RAA). And JUCO transfer Reece Calvert gave up a shocking 39 runs in 39 innings.<br /><br />I thought the bullpen would be the strength of the team before the season. In the case of Seth Kinker, I was right. The junior slinger was terrific, pitching 58 innings (21 relief appearances, 3 starts) and leading the team by a huge margin with 13 RAA (8.4/2.0 K/W). But the rest of the bullpen was less effective. Junior Kyle Michalik missed much of the season with injuries and wasn’t that effective when on the mound (6.85 RA and just 4.8 K/9 over 22 innings). Senior Joe Stoll did fine in the LOOGY role, something Beals has brought to OSU, with 3 RAA in 23 innings over 25 appearances. Junior Austin Woodby had a 6.00 RA over 33 innings but deserved better with a 4.79 eRA and 5.5/1.8 K/W. The only other reliever to work more than ten innings was freshman sidearmer Thomas Waning (3 runs, 11 K, 4 W over 12 innings). Again, it’s hard to describe the roles because almost everyone was forced to both start and relieve.<br /><br />It’s too early to hazard a prognosis for 2018, but given the lack of promising performances from young players, it’s hard to be optimistic. What remains to be seen is whether Smith’s ruthlessness can be transferred from coaches who do not deserve it to those who have earned it in spades. No, baseball is not a revenue sport, and no, baseball is not bringing the athletic department broad media exposure. But when properly curated, the OSU baseball program is a top-tier Big Ten program, with the potential to make runs in the NCAA Tournament, and bring in more revenue than most of the “other” 34 programs that are not football or men’s basketball. Neglected in the hands of a failed coach, it is capable of putting up a .333 W% in conference play. Smith, not Beals, is the man who will most directly impact the future success of the program.<br />phttp://www.blogger.com/profile/18057215403741682609noreply@blogger.com0tag:blogger.com,1999:blog-12133335.post-26196007280938452472017-07-12T07:21:00.000-04:002017-07-12T07:21:02.283-04:00Enby Distribution, pt. 3: Enby Distribution CalculatorAt this point, I want to re-explain how to use the Enby distribution, step-by-step. While I already did this in part 6 of the original series, I now have the new variance estimator as found by Alan Jordan to plug in, and so to avoid any confusion and to make this is easy if anyone ever wants to implement it themselves, I will recount it all in one location. I will also re-introduce a spreadsheet that you can use to estimate the probability of scoring X runs based on the Enby distribution.<br /><br />Step 1: Estimate the variance of runs scored per game (VAR) as a function of mean runs/game (RG):<br /><br />VAR = RG^2/9 + (2/c - 1)*RG<br />where c is the control value from the <a href="http://tangotiger.net/wiki_archive/Tango_Distribution.html">Tango Distribution</a>. For normal applications, we’ll assume that c = .767.<br /><br />Step 2: Use the mean and variance to estimate the parameters (r and B) of the negative binomial distribution:<br /><br />r = RG^2/(VAR - RG)<br />B = VAR/RG - 1<br /><br />B will be retained as a parameter for the Enby distribution.<br /><br />Step 3: Find the probability of zero runs scored as estimated by the negative binomial distribution (we’ll call this value a):<br /><br />a = (1 + B)^(-r)<br /><br />Step 4: Use the Tango Distribution to estimate the probability of being shutout. This will become the Enby distribution parameter z:<br /><br />z =(RI/(RI + c*RI^2))^9<br />where RI is runs/inning, which we’ll estimate as RG/9. <br /><br />Step 5: Use trial and error to estimate a new value of r given the modified value at zero. B and z will stay constant, but r must be chosen so as to ensure that the correct mean RG is returned by the Enby distribution. Use the following formula to estimate the probability of k runs scored per game using the non-modified negative binomial distribution:<br /><br />q(0) = a<br />q(k) = (r)(r + 1)(r + 2)(r + 3)…(r + k - 1)*B^k/(k!*(1 + B)^(r + k)) for k >=1<br /><br />Then modify by taking:<br /><br />p(0) = z<br />p(k) = (1 - z)*q(k)/(1 - a)for k >=1<br /><br />The mean is calculated as:<br /><br />mean = sum (from k = 1 to infinity) of (k*p(k)) = p(1) + 2*p(2) + 3*p(3) + ...<br /><br />Now you have the parameters r, B, and z and the probability of scoring k runs in a game. <br /><br />I previously published a spreadsheet that provided the approximate Enby distribution parameters at each .05 increment of RG between 3 and 7. The link below will take you to an updated version of this calculator. It is updated in two ways: first, the Tango Distribution estimate of variance developed by Alan Jordan is used as in the example above. Secondly, I have added lines for RG levels between 0-3 and 7-15 RG (at intervals of .25). Previously, you could enter in any value between 3-7 RG and the calculator would round it to nearest .05; now I’m going to make you enter a legitimate value yourself or accept whatever vlookup() gives you.<br /><br />P(x) is the probability of scoring x runs in a game, P(<= x) is the probability of scoring that many or fewer, and P(> x) is the probability of scoring more than x runs.<br /><br /><a href="https://docs.google.com/spreadsheets/d/1ibSqb1qjuBPVEaT7QHpEDpj75xkEIfcZqqOf7YpDALM/pub?output=xlsx">Enby Calculator</a>phttp://www.blogger.com/profile/18057215403741682609noreply@blogger.com0tag:blogger.com,1999:blog-12133335.post-80293292655783244672017-06-20T07:19:00.000-04:002017-06-20T07:19:05.726-04:00Enby Distribution, pt. 2: Revamping the Variance EstimateAll models are approximations of reality, but some are more useful than others. The notion of being able to estimate the runs per game distribution cleanly in one algorithm (rather than patching together runs per inning distributions or using simulators) is one that can be quite useful in estimating winning percentage or trying to distinguish between the effectiveness of team offense beyond similar noting their runs scored total. I’d argue that a runs per game distribution is a fundamentally useful tool in classical sabermetrics.<br /><br />However, while such a model would be useful, Enby as currently constructed falls well short of being an ideal tool. There are a few major issues:<br /><br />1) It is not mathematically feasible to solve directly for the parameters of a zero-modified negative binomial distribution, which forces me to use trial and error to estimate Enby coefficients. In doing so, the distribution is no longer able to exactly match the expected mean and variance--instead, I have chosen to match the mean precisely, and hope that the variance is not too badly distorted.<br /><br />2) The variance that we should expect for runs per game at any given level of average R/G is itself unknown. I developed a simple formula to estimate variance based on some actual team data, but that formula is far from perfect and there’s no particular reason to expect it to perform well outside of the R/G range represented by the data from which it was developed.<br /><br />3) An issue with run distribution models found by Tom Tango in the course of his research on runs per inning distribution is that the optimal fit for a single team’s distribution may not return optimal results in situations in which two teams are examined simultaneously (such as using the distribution to model winning percentage). One explanation for this phenomenon is the covariance between runs scored and runs allowed in a given game, due to either environmental or strategic causes.<br /><br />I have recently attempted to improve the Enby distribution by focusing on these obvious flaws. Unfortunately, my findings were not as useful as I had hoped they would be, but I would argue (hope?) that they represent at least small progress in this endeavor.<br /><br />During the course of writing the original series on this topic, I was made aware of work being done by Alan Jordan, who was developing a spreadsheet that used the Tango Distribution to estimate scoring distributions and winning percentage. One of the underpinnings was that he found (or found <a href="http://cupola.gettysburg.edu/cgi/viewcontent.cgi?article=1050&context=mathfac">work by Darren Glass and Phillip Lowry that demonstrated</a>) that the variance of runs scored per inning as predicted by the Tango Distribution could be calculated as follows (where RI = runs per inning and c is the Tango Distribution constant):<br /><br />Variance (inning) = RI*(2/c + RI - 1) = RI^2 + (2/c - 1)*RI<br /><br />Assuming independence of runs per inning (this is a necessary assumption to use the Tango Distribution to estimate runs per game), the variance of runs per game will simply be nine times the variance of runs per inning (assuming of course that there are precisely nine innings per game, as I did in estimating the z parameter of Enby from the Tango Distribution). If we attempt to simply this further by assuming that RI = RG/9, where RG = runs per game:<br /><br />Variance (game) = 9*(RI^2 + (2/c - 1)*RI) = 9*((RG/9)^2 + (2/c - 1)*RG/9) = RG^2/9 + (2/c - 1)*RG<br /><br />The traditional value of c used to estimate runs per inning for one team is .767, so if we substitute that for c, we wind up with:<br /><br />Variance (game) =1.608*RG + .111*RG^2<br /><br />When I worked on this problem previously, I did not have any theoretical basis for an estimator of variance as a function of RG, so I experimented with a few possibilities and found what appeared to be a workable correlation between mean RG and the ratio of variance to mean. I used linear regression on a set of actual team data (1981-1996) and wound up with an equation that could be written as:<br /><br />Variance (game) = 1.43*RG + .1345*RG^2<br /><br />Note the similarities between this equation and the equation based on the Tango Distribution - they both take the form of a quadratic equation less the constant (I purposefully avoided constants in developing my variance estimator so as to avoid unreasonable results at zero and near-zero RG). The coefficients are somewhat different, but the form of the equation is identical.<br /><br />On one hand, this is wonderful for me, because it vindicates my intuition that this was a reasonable way to estimate variance. On the other hand, this is very disappointing, because I had hoped that Jordan’s insight would allow me to significantly improve the variance estimate. Instead, any gains to be had here are limited to improving the equation by using a more theoretical basis to estimate its coefficients, but there is no change in the form of this equation.<br /><br />In fact, any revision to the estimator will reduce accuracy over the 1981-96 sample that I am using, since the linear regression already found optimal coefficients for this particular dataset. This by no means should be taken as a claim on my part that the regression-based equation should be used rather than the more theoretically-grounded Tango Distribution estimate, simply an observation that any improvement will not show up given the confines of the data I have at hand.<br /><br />What about data from out of that set? I have easy access to the four seasons from 2009-2012. In these seasons, major league teams have averaged 4.401 runs per game and the variance of runs scored per game is 9.373. My equation estimates the variance should be 8.90, while the Tango-based formula estimates 9.23. In this case, we could get a near-precise match by using c = .757.<br /><br />While we know how accurate each estimator is with respect to variance for this case, what happens when we put Enby to use to estimate the run distribution? The Enby parameters for 4.40 RG using my original equation are (B = 1.0218, r = 4.353, z = .0569). If we instead use the Tango estimated variance of 9.23, the parameters become (B = 1.0970, r = 4.041, z = .0569). With that, we can calculate the estimated frequencies of X runs scored using each estimator and compare to the empirical frequencies from 2009-2012:<br /><br /><a href="https://3.bp.blogspot.com/-WR4AxLkuSGA/WUhCRq6UyXI/AAAAAAAACYQ/LcwoxkOzBIwcYhOq905aR9IFU4ZQfPM0ACLcBGAs/s1600/freqest.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://3.bp.blogspot.com/-WR4AxLkuSGA/WUhCRq6UyXI/AAAAAAAACYQ/LcwoxkOzBIwcYhOq905aR9IFU4ZQfPM0ACLcBGAs/s400/freqest.jpg" width="300" height="400" data-original-width="307" data-original-height="409" /></a><br /><br />Eyeballing this, the Tango-based formula is closer for one run, but exacerbates the recurring issue of over-estimating the likelihood of two or three runs. It makes up for this by providing a better estimate at four and five runs, but a worse estimate at six. After that the two are similar, although the Tango estimate provides for more probability in the tail of the distribution, which in this case is consistent with empirical results.<br /><br />For now, I will move on to another topic, but I will eventually be coming back to this form of the Tango-based variance estimate, re-estimating the parameters for 3-7 RG, and providing an updated Enby calculator, as I do feel that there are distinct advantages to using the theoretical coefficients of the variance estimator rather than my empirical coefficients.<br />phttp://www.blogger.com/profile/18057215403741682609noreply@blogger.com0tag:blogger.com,1999:blog-12133335.post-77582682249648788522017-05-09T10:42:00.000-04:002017-05-09T10:42:00.964-04:00Enby Distribution, pt. 1: PioneersA few years ago, I attempted to <a href="http://walksaber.blogspot.com/2012/07/on-run-distributions-pt-6.html">demonstrate</a> that one could do a decent job of estimating the distribution of runs scored per game by using the negative binomial distribution, particularly a zero-modified version given the propensity of an unadulterated negative binomial distribution to underestimate the probability of a shutout. I dubbed this modified distribution Enby.<br /><br />I’m going to be re-introducing this distribution and adopting a modification to the key formula in this series, but I wanted to start by acknowledging that I am not the first sabermetrician to adopt the negative binomial distribution to the matter of the runs per game distribution. To my knowledge, a zero-modified negative binomial distribution had not been implemented prior to Enby, and while the zero-modification is a significant improvement to the model, it would be disingenuous not to acknowledge and provide an overview of the two previous efforts using the negative binomial distribution of which I am aware.<br /><br />I acknowledged one of these in the original iteration of this <a href="http://walksaber.blogspot.com/2012/06/on-run-distributions-pt1.html">series</a>, but inadvertently overlooked the first. In the early issues of Bill James’ <U>Baseball Analyst</u> newsletter, Dallas Adams published a series of articles on run distributions, ultimately developing an unwieldy formula I discussed in the linked post. What I overlooked was an article in the August 1983 edition in which the author noted that the Poisson distribution worked for hockey, it would not work for baseball because the variance of runs per game is not equal to the mean, but rather is twice the mean. But a "modified Poisson" distribution provided a solution.<br /><br />The author of the piece? Pete Palmer. Palmer is often overlooked to an undue extent when sabermetric history is recounted. While one could never omit Palmer from such a discussion, his importance is often downplayed. But the sheer volume of methods that he developed or refined is such that I have no qualms about naming him the most important technical sabermetrician by a wide margin. Park factors, run to win converters, linear weights, relative statistics, OPS for better or worse, the construct of an overall metric by adding together runs above average in various discrete components of the game...these were all either pioneered or greatly improved by Palmer. And while it is not nearly as widespread in use as his other innovations, you can add using the negative binomial distribution for the runs per game distribution the list.<br /><br />Palmer says that he learned about this “modified Poisson” in a book called <U>Facts From Figures</u> by Maroney. The relevant formulas were:<br /><br />Mean (u) = p/c<br />Variance (v) = u + u/c<br />p(0) = (c/(1 + c))^p<br />p(1) = p(0)*p/(1 + c)<br />p(2) = p(1)*(p + 1)/(2*(1 + c))<br />p(3) = p(2)*(p + 2)/(3*(1 + c))<br />p(n) = p(0)*(p*(p + 1)*(p + 2)*...*(p + n - 1)/(n!*(1 + c)^n)<br /><br />The text that I used renders the negative binomial distribution as:<br /><br />p(k) = (1 + B)^(-r) for k = 0<br />p(k) = (r)(r + 1)(r + 2)(r + 3)…(r + k - 1)*B^k/(k!*(1 + B)^(r + k)) for k >=1<br />mean (u) = r*B<br />variance(v) = r*B*(1 + B)<br /><br />You may be forgiven for not immediately recognizing these two as equivalent; I did not at first glance. But if you recognize that r = p and B = 1/c, then you will find that the mean and variance equations are equivalent and that the formulas for each n or k depending on the nomenclature used are equivalent as well.<br /><br />So Palmer was positing the negative binomial distribution to model runs scored. He noted that the variance of runs per game is about two times the mean, which is true. In my original Enby implementation, I estimated variance as 1.430*mean + .1345*mean^2, which for the typical mean value of around 4.5 R/G works out to an estimated variance of 9.159, which is 2.04 times the mean. Of course, the model can be made more accurate by allowing the ratio <br />if variance/mean to vary from two.<br /><br />The second use of the negative binomial distribution to model runs per game of which I am aware was implemented by Phil Melita. Mr. Melita used it to estimate winning percentage and sent me a copy of his paper (over a decade ago, which is profoundly disturbing in the existential sense). Unfortunately, I am not aware of the paper ever being published so I hesitate to share too much from the copy in my possession. <br /><br />Melita’s focus was on estimating W%, but he did use negative binomial to look at the run distribution in isolation as well. Unfortunately, I had forgotten his article when I started messing around with various distributions that could be used to model runs per game; when I tried negative binomial and got promising results, I realized that I had seen it before. <br /><br />So as I begin this update of what I call Enby, I want to be very clear that I am not claiming to have “discovered” the application of the negative binomial distribution in this context. To my knowledge using zero-modification is a new (to sabermetrics) application of the negative binomial, but obviously is a relatively minor twist on the more important task of finding a suitable distribution to use. So if you find that my work in this series has any value at all, remember that Pete Palmer and Phil Melita deserve much of the credit for first applying the negative binomial distribution to runs scored per game.<br />phttp://www.blogger.com/profile/18057215403741682609noreply@blogger.com0tag:blogger.com,1999:blog-12133335.post-19612886446556010922017-04-13T22:19:00.000-04:002017-04-13T22:19:20.964-04:00Great Moments in CBS Sports Box Scores<div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-JmDINVy9ces/WPAxnTEHCjI/AAAAAAAACYA/kHHq3a03rlg4_w3z_nxUJkhW9cclhxtIQCLcB/s1600/nicasio.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://2.bp.blogspot.com/-JmDINVy9ces/WPAxnTEHCjI/AAAAAAAACYA/kHHq3a03rlg4_w3z_nxUJkhW9cclhxtIQCLcB/s400/nicasio.jpg" width="400" height="102" /></a></div>phttp://www.blogger.com/profile/18057215403741682609noreply@blogger.com0tag:blogger.com,1999:blog-12133335.post-65544633692861292372017-04-01T15:04:00.000-04:002017-04-01T15:04:40.780-04:002017 PredictionsAll the <a href="http://sportsdataresearch.com/difficulties-associated-with-preseason-projections/">usual disclaimers</a>. This is not serious business.<br /><br />AL EAST<br /><br />1. Boston<br />2. Toronto (wildcard)<br />3. New York<br />4. Baltimore<br />5. Tampa Bay<br /><br />I have noted the last couple years that I always pick the Red Sox--last year was one of the years where that was the right call. Boston has question marks, and they have less talent on hand to fill holes than in past years, but no one else in the division is making a concerted push with the Blue Jays retrenching and the Yankees in transition. While much has been made of the NL featuring more of a clear dichotomy between contenders and rebuilders, the AL features three strong division favorites and a void for wildcard contention that Toronto may well once again fill. New York looks like a .500 team to me, and one with as strong a recent history of overperforming projections/Pythagorean as darlings like Baltimore and Kansas City, but get far less press for it. (I guess the mighty Yankees aren’t a good sell as a team being unfairly dismissed by the statheads). The Orioles offense has to take step back at some point with only Machado and Schoop being young, and if that happens the rotation can’t carry them. It’s not that I think the Rays are bad; this whole division is filled with potential wildcard contenders.<br /><br />AL CENTRAL<br /><br />1. Cleveland<br />2. Detroit<br />3. Kansas City<br />4. Minnesota<br />5. Chicago<br /><br />I have a general policy of trying to pick against the Indians when reasonable, out of irrational superstition and an attempt to counteract any unconscious fan-infused optimism. Last year I felt they were definitely the best team in this division on paper but picked against them regardless. But the gap is just too big to ignore this season, so I warily pick them in front. There are reasons to be pessimistic--while they didn’t get “every break in the world last season” as Chris Russo says in a commercial that hopefully will be off the air soon, it’s easy to overstate the impact of their pitching injuries since the division was basically wrapped up before the wheels came off the rotation. Consider the volatility of bullpens, the extra workload for the pitchers who were available in October, the fact that the two that weren’t aren’t the best health bets in the world, and you can paint a bleaker picture than the triumphalism that appears to be the consensus. On the other hand, Michael Brantley, the catchers, the fact that the offense didn’t score more runs than RC called for last year. I see them as the fourth-strongest team out of the six consensus division favorites. Detroit is the team best-positioned to challenge them; I used the phrase “dead cat bounce” last year and it remains appropriate. The less said about Kansas City the better, but as much fun as it was to watch the magic dissipate last season, the death throes of this infuriating team could be even better. The Twins have famously gone from worst to first in their franchise history; given the weakness of the division and some young players who may be much better than they’ve shown so far, it’s not that far-fetched, but it’s also more likely that they lose 95 again. The White Sox rebuilding might succeed in helping them compete down the road and finally ridding the world of the disease that is Hawk Harrelson.<br /><br />AL WEST<br /><br />1. Houston<br />2. Seattle (wildcard)<br />3. Los Angeles<br />4. Texas<br />5. Oakland<br /><br />Houston looks really good to me; if their rotation holds together (or if they patch any holes with the long awaited Jose Quintana acquisition), I see them as an elite team. Maybe the third time is the charm picking Seattle to win the wildcard. Truth be told, I find it hard to distinguish between most AL teams including the middle three in this division. Picking the Angels ahead of the Rangers is more a way to go on record disbelieving that the latter can do it again than an endorsement of the former, but even with a shaky rotation the Angels should be respectable. My Texas pick will probably look terrible when Nomar Mazara breaks out, Yu Darvish returns healthy, and Josh Hamilton rises from the dead or something. Oakland’s outlook for this year looks bleak, but am I crazy to have read their chapter in <U>Baseball Prospectus</U> and thought there were a number of really interesting prospects who could have a sneaky contender season in 2018? Probably.<br /><br />NL EAST<br /><br />1. Washington<br />2. New York (wildcard)<br />3. Miami <br />4. Atlanta<br />5. Philadelphia<br /><br />It’s very tempting to pick New York over Washington, based on the superficial like the Nationals sad-Giants even year pattern and cashing in most of their trade chits for Adam Eaton, but there remains a significant on-paper gap between the two. Especially since the Mets stood pat from a major league roster perspective. This might be the best division race out there in a season in which there are six fairly obvious favorites. Sadly, Miami is about one 5 WAR player away from being right in the mix…I wonder where on might have found such a player? Atlanta seems like a better bet than Philadelphia in both the present and future tense, but having a great deal of confidence in the ordering of the two seems foolhardy.<br /><br />NL CENTRAL<br /><br />1. Chicago<br />2. Pittsburgh<br />3. St. Louis<br />4. Milwaukee<br />5. Cincinnati<br /><br />The Cubs’ starting pitching depth is a little shaky? Kyle Schwarber doesn’t have a position and people might be a little too enthusiastic about him? Hector Rondon struggled late in the season and Wade Davis’ health is not a sure thing? These are the straws that one must grasp at to figure out how Chicago might be defeated. You also have to figure out whether Pittsburgh can get enough production from its non-outfielders while also having some good fortune with their pitching. Or whether St. Louis’ offense is good enough. Or whether Milwaukee or Cincinnati might have a time machine that could jump their rebuild forward a few years. You know, the normal questions you ask about a division.<br /><br />NL WEST<br /><br />1. Los Angeles<br />2. San Francisco<br />3. Arizona<br />4. Colorado<br />5. San Diego<br /><br />Last year I picked the Giants over the Dodgers despite the numbers suggesting otherwise because of injury concerns. I won’t make that mistake again, as it looks as if LA could once again juggle their rotation and use their resources to patch over any holes. The Giants are strong themselves, but while the two appear close in run prevention, the Dodgers have the edge offensively. The Diamondbacks should have a bounce back season, but one that would still probably break Tony LaRussa’s heart if he still cared. The Rockies seem like they should project better than they do, with more promise on the mound than they usually do. The Padres are the consensus worst team in baseball from all of the projection systems, which can be summed up with two words: Jered Weaver.<br /><br />WORLD SERIES<br /><br />Los Angeles over Houston<br /><br />Just about every projection system out there has the Dodgers ever so slightly ahead of the Cubs. That of course does not mean they are all right--perhaps there is some blind spot about these teams that player projection systems and/or collation of said projections into team win estimates share in common. On the other hand, none of these systems <i>dislike</i> the Cubs—everyone projects them to win a lot of games. I was leaning towards picking LA even before I saw that it was bordering on a consensus, because the two teams look fairly even to me but the Dodgers have more depth on hand, particularly in the starting pitching department (the natural rebuttal is that the Dodgers are likely to need that depth, while the Cubs have a four pretty reliable starters). The Dodgers bullpen looks better, and their offense is nothing to sneeze at. <br /><br />AL Rookie of the Year: LF Andrew Benintendi, BOS<br />AL Cy Young: Chris Sale, BOS<br />AL MVP: CF George Springer, HOU<br />NL Rookie of the Year: SS Dansby Swanson, ATL<br />NL Cy Young: Stephen Strasburg, WAS<br />NL MVP: 1B Anthony Rizzo, CHN<br />phttp://www.blogger.com/profile/18057215403741682609noreply@blogger.com0tag:blogger.com,1999:blog-12133335.post-45318868325340846342017-03-14T07:50:00.000-04:002017-03-14T07:50:06.276-04:00Win Value of Pitcher Adjusted Run AveragesThe most common class of metrics used in sabermetrics for cross-era comparisons use relative measures of actual or estimated runs per out or sother similar denominator. These include ERA+ for pitchers and OPS+ or wRC+ for batters (OPS+ being an estimate of relative runs per out, wRC+ using plate appearances in the denominator but accounting for the impact of avoiding outs). While these metrics provide an estimate of runs relative to the league average, they implicitly assume that the resulting relative scoring level is equally valuable across all run environments.<br /><br />This is in fact not the case, as it is well-established that the relationship between run ratio and winning percentage depends on the overall level of run scoring. A team with a run ratio of 1.25 will have a different expected winning percentage if they play in a 9 RPG environment than if they play in a 10 RPG environment. Metrics like ERA+ and OPS+ do not translate relative runs into relative wins, but presumably the users of such metrics are ultimately interested in what they tell us about player contribution to wins.<br /><br />There are two key points that should be acknowledged upfront. One is that the difference in win value based on scoring level is usually quite small. If it wasn’t, winning percentage estimators that don’t take scoring level into account would not be able to accurately estimate W% across the spectrum of major league teams. While methods that do consider scoring level are more accurate estimators of W% than similar methods that don’t, a method like fixed exponent Pythagorean can still produce useful estimates despite maintaining a fixed relationship between runs and wins.<br /><br />The second is that players are not teams. The natural temptation (and one I will knowingly succumb to in what follows) is to simply plug the player’s run ratio into the formula and convert to a W%. This approach ignores the fact that an individual player’s run rate does not lead directly to wins, as the performance of his teammates must be included as well. Pitchers are close, because while they are in the game they are the team (more accurately, their runs allowed figures reflect the totality of the defense, which includes contributions from the fielders), but even ignoring fielding, non-complete games include innings pitched by teammates as well.<br /><br />For the moment I will set that aside and instead pretend (in the tradition of Bill James’ Offensive Winning %) that a player or pitcher’s run ratio can or should be converted directly to wins, without weighting the rest of the team. This makes the figures that follow something of a freak show stat, but the approach could be applied directly to team run ratios as well. Individuals are generally more interesting and obviously more extreme, which means that the impact of considering run environment will be overstated.<br /><br />I will focus on pitchers for this example and will use Bob Gibson’s 1968 season as an example. Gibson allowed 49 runs in 304.2 innings, which works out to a run average of 1.45 (there will be some rounding discrepancies in the figures). In 1968 the NL average RA was 3.42, so Gibson’s adjusted RA (aRA for the sake of this post) is RA/LgRA = .423 (ideally you would park-adjust as well, but I am ignoring park factors for this post). As an aside, please resist the temptation to instead cite his RA+ of 236 instead. <a href="http://www.hardballtimes.com/of-pluses-and-minuses/">Please</a>.<br /><br />.423 is a run ratio; Gibson allowed runs at 42.3% of the league average. Since wins are the ultimate unit of measurement, it is tempting to convert this run ratio to a win ratio. We could simply square it, which reflects a Pythagorean relationship. Ideally, though, we should consider the run environment. The 1968 NL was an extremely low scoring league. Pythagenpat suggests that the ideal exponent is around 1.746. Let’s define the Pythagenpat exponent to use as:<br /><br />x = (2*LgRA)^.29<br /><br />Note that this simply uses the league scoring level to convert to wins; it does not take into account Gibson’s own performance. That would be an additional enhancement, but it would also strongly increase the distortion that comes from viewing a player as his own team, albeit less so for pitchers and especially those who basically were pitching nine innings/start as in the case of Gibson.<br /><br />So we could calculate a loss ratio as aRA^x, or .223 for Gibson. This means that a team with Gibson’s aRA in this environment would be expected to have .223 losses for every win (basic ratio transformations apply; the reciprocal would be the win ratio, the loss ratio divided by (1 + itself) would be a losing %, the complement of that W%, etc.)<br /><br />At this point, many people would like to convert it to a W% and stop there, but I’d like to preserve the scale of a run average while reflecting the win impact. In order to do so, I need to select a Pythagorean exponent corresponding to a reference run environment to convert Gibson’s loss ratio back to an equivalent aRA for that run environment. For 1901-2015, the major league average RA was 4.427, which I’ll use as the reference environment, which corresponds to a 1.882 Pythagenpat exponent (there are actually 8.94 IP/G over this span, so the actual RPG is 8.937 which would be a 1.887 exponent--I'll stick with RA rather than RPG for this example since we are already using it to calculate aRA).<br /><br />If we call that 1.882 exponent r, then the loss ratio can be converted back to an equivalent aRA by raising it to the (1/r) power. Of course, the loss ratio is just an interim step, and this is equivalent to:<br /><br />aRA^(x*(1/r)) = aRA^(x/r) = waRA<br /><br />waRA (excuse the acronyms, which I don’t intend to survive beyond this post) is win-Adjusted Run Average. For Gibson, it works out to .450, which illustrates how small the impact is. Pitching in one of the most extreme run environments in history, Gibsons aRA is only 6.4% higher after adjusting for win impact. <br /><br />In 1994, Greg Maddux allowed 44 runs in 202 innings for a run average of 1.96. Pitching in a league with a RA of 4.65, his aRA was .421, basically equal to Gibson. But his waRA was better, at .416, since the same run ratio leads to more wins in a higher scoring environment.<br /><br />It is my guess that consumers of sabermetrics will generally find this result unsatisfactory. There seems to be a commonly-held belief that it is easier to achieve a high ERA+ in a higher run scoring environment, but the result of this approach is the opposite--as RPG increases, the win impact of the same aRA increases as well. Of course, this approach says nothing about how “easy” it is to achieve a given aRA--it converts aRA to an win-value equivalent aRA in a reference run environment. It is possible that it could be simultaneously “easier” to achieve a low aRA in a higher scoring environment and that the value of a low aRA be enhanced in a higher scoring environment. I am making no claim regarding the impressiveness or aesthetic value, etc. of any pitcher’s performance, only attempting to frame it in terms of win value.<br /><br />Of course, the comparison between Gibson and Maddux need not stop there. I do believe that waRA shows us that Maddux’ rate of allowing runs was more valuable in context than Gibson’s, but there is more to value than the rate of allowing runs. Of course we could calculate a baselined metric like WAR to value the two seasons, but even if we limit ourselves to looking at rates, there is an additional consideration that can be added.<br /><br />So far, I’ve simply used the league average to represent the run environment, but a pitcher has a large impact on the run environment through his own performance. If we want to take this into account, it would be inappropriate to simply use LgRA + pitcher’s RA as the new RPG to plug into Pythagenpat; we definitely need to consider the extent to which the pitcher’s teammates influence the run environment, since ultimately Gibson’s performance was converted into wins in the context of games played by the Cardinals, not a hypothetical all-Gibson team. So I will calculate a new RPG instead by assuming that the 18 innings in a game (to be more precise for a given context, two times the league average IP/G) is filled in by the pitcher’s RA for his IP/G, and the league’s RA for the remainder.<br /><br />In the 1968 NL, the average IP/G was 9.03 and Gibson’s 304.2 IP were over 34 appearances (8.96 IP/G), so the new RPG is 8.96*1.45/9 + (2*9.03 - 8.96)* 3.42/9 = 4.90 (rather than 6.84 previously). This converts to a Pythagenpat exponent of 1.59, and an pwaRA (personal win-Adjusted Run Average?) of .485. To spell that all out in a formula:<br /><br />px = ((IP/G)*RA/9 + (2*Lg(IP/G) - IP/G)*LgRA/9) ^ .29<br />pwaRA = aRA^(px/r)<br /><br />Note that adjusting for the pitcher’s impact on the scoring context reduces the win impact of effective pitchers, because as discussed earlier, lowering the RPG lowers the Pythagenpat exponent and makes the same run ratio convert to fewer wins. In fact, considering the pitcher’s effect on the run environment in which he operates actually brings most starting pitchers’ pwaRA closer to league average than their aRA is. <br /><br />pwaRA is divorced from any real sort of baseball meaning, though, because pitchers aren’t by themselves a team. Suppose we calculated pwaRA for two teammates in a 4.5 RA league. The starter pitches 6 innings and allows 2 runs; the reliever pitches 3 innings and allows 1. Both pitchers have a RA of 3.00, and thus identical aRA (.667) or waRA (.665). Furthermore, their team also has a RA of 3.00 for this game, and whether figured as a whole or as the weighted average of the two individuals, the team also has the same aRA and waRA.<br /><br />However, if we calculate the starter’s pwaRA, we get .675, while the reliever is at .667. Meanwhile, the team has a pwaRA of .679, which makes this all seem quite counterintuitive. But since all three entities have the same RA, the lower the run environment, the less win value it has on a per inning basis. <br /><br />I hope this post serves as a demonstration of the difficulty of divorcing a pitcher’s value from the number of innings he pitched. Of course, the effects discussed here are very small, much smaller than the impact of other related differences, like the inherent statistical advantage of pitchers over shorter stints, attempts to model differences in replacement level between starters and relievers, and attempts to detect/value any beneficial side effects of starters working deep into games.<br /><br />One of my long-standing interests has been the proper rate stat to use to express a batter’s run contribution (I have been promising myself for almost as long as this blog has been existence that I will write a series of posts explaining the various options for such a metric and the rationale for each, yet have failed to do so). I’ve never had the same pull to the question for pitchers, in part because the building block seems obvious: runs/out (which depending on how one defines terms can manifest itself as RA, ERA, component ERA, FIP-type metrics, etc.)<br /><br />But while there are a few adjustments that can theoretically made between a hitter’s overall performance expressed as a rate and a final value metric (like WAR), the adjustments (such as the hitter’s impact on his team’s run scoring beyond what the metric captures itself, and the secondary effect that follows on the run/win conversion) are quite minor in scale compared to similar adjustments for pitchers. While the pitcher (along with his fielders) can be thought as embodying the entire team while he is the game, that also means that said unit’s impact on the run/win conversion is significant. And while there are certainly cases of batters whose rates may be deceiving because of how they are deployed by their managers (particularly platooning), the additional playing time over which a rate is spread increases value in a WAR-like metric without any special adjustment. Pitchers’ roles and secondary effects thereof (like any potential value generated by “eating” innings) have a more significant (and more difficult to model) impact on value than the comparable effects for position players.phttp://www.blogger.com/profile/18057215403741682609noreply@blogger.com0tag:blogger.com,1999:blog-12133335.post-26287845358202567992017-02-13T17:58:00.000-05:002017-02-13T17:58:52.196-05:00Rebuilding a Strip Mall"Rebuilding", as commonly thrown around in sports discussions, is an interesting term. It inherently implies that something had been built on the same spot previously. It does not, however, give an indication whether what was built there was a blanket fort or the Taj Mahal, a strip mall or the Sears Tower. If one rebuilds on the site of a strip mall, does "re-" imply they are building another strip mall, or might they be building something else? <br /><br />The baseball program that Greg Beals has presided over for six seasons at The Ohio State University has been much more of a strip mall than a Sears Tower. After his most successful season, which saw OSU tie for third in the Big Ten regular season, win the Big Ten Tournament, and qualify for their first NCAA regional since 2009, Beals is now faced with a rebuilding project in the classic sports sense. Of the nine players with the most PA in 2016, OSU must replace seven, so it would be fair to say that there will be seven new regulars. OSU must also replace two of its three weekend starters; the bullpen is the only area of the roster not decimated by graduation and the draft.<br /><br />Note: The discussion of potential player roles that follows is my own opinion, informed by my own knowledge of the players and close watching of the program and information released by the SID, particularly the season preview posted <a href="http://www.ohiostatebuckeyes.com/sports/m-basebl/spec-rel/020817aaf.html">here</a>.<br /><br />Sophomore Jacob Barnwell will almost certainly be the primary catcher; he played sparingly last season (just 29 PA). This is one of the few open positions not due to loss, but rather to a position switch which will be discussed in a moment. Classmate Andrew Fishel (8 PA) will serve as his backup.<br /><br />First base/DH will be shared by senior Zach Ratcliff, who has flashed power at times during his career but has never earned consistent playing time, and Boo Coolen, a junior Hawaii native who played at Cypress CC in California. Junior Noah McGowan, a transfer from McLennan CC in Texas, would appear to have the inside track at the keystone; his JUCO numbers are impressive but come with obvious caveats. Sophomore Brady Cherry, who got off to a torrid start in 2016 but then cooled precipitously (final line .218/.307/.411 in 143 PA) is likely to play third and bat in the middle of the order. At shortstop, senior captain Jalen Washington moves out from behind the plate to captain the infield; he spent his first two years as a Buckeye as a utility infielder, so it was the move to catcher, not to shortstop that really stands out. Unfortunately, Washington didn’t offer much with the bat as a junior (.249/.331/.343 in 261 PA). Other infield contenders include true freshman shortstop Noah West, redshirt freshman middle infielder Casey Demko, true freshman Conor Pohl at the corners, and redshirt sophomore Nate Romans and redshirt freshman Matt Carpenter in utility roles.<br /><br />The one thing that appears clear in the outfielder is that junior Tre’ Gantt will take over as center fielder; he struggled offensively last season (.255/.311/.314 in 158 PA). True freshman Dominic Canzone may step in right away in right field, while left field/DH might be split between a pair of transfers. Tyler Cowles, a junior Columbus native who hit well at Sinclair CC in Georgia will attempt to join Coolen and satisfy the Beals’ desperate need for bats with experience and power. Other outfielders include senior former pitcher Shea Murray and little-used redshirt sophomore Ridge Winand.<br /><br />The pitching staff is slightly more intact, but not much so. Redshirt junior captain Adam Niemeyer will likely be the #1 starter as the only returning weekend starter; his 2016 campaign can be fairly described as average. Sophomore Ryan Feltner was the #4 starter last year and so is a safe bet to pitch on the weekend; his 5.67 eRA was not encouraging but 8 K/3.9 W suggest some raw, harness-able ability. The third spot will apparently go to an erstwhile reliever. Junior Yianni Pavlopoulos was a surprising choice as closer last year, but pitched very well (10.3 K/3.3 W, 3.72 eRA), while senior Jake Post returns from a season wiped out by injury. Neither pitcher has been the picture of health throughout their careers, but Pavlopoulos seems the more likely choice to start. Junior Austin Woodby (7.75 eRA in 39 innings) and sophomore lefty Connor Curlis (six relief innings) will jockey for weekday assignments along with junior JUCO transfer Reece Calvert (a teammate of McGowan) and three true freshmen: lefty Michael McDonough and righties Collin Lollar and Gavin Lyon.<br /><br />The bullpen will be well-stocked, even assuming Pavlopoulos takes a spot in the rotation. Junior sidearmer Seth Kinker was a workhorse (team-high 38 appearances) and behind departed ace Tanner Tully was arguably Ohio’s most valuable pitcher in 2016. Senior Jake Post will return from a season lost to injury looking to return to a setup role, and junior sidearmer Kyle Michalik pitched well in middle relief last season. These four form a formidable bullpen that will almost certainly be augmented by a lefty specialist, a favorite of Beals. He’ll choose from senior Joe Stoll (twelve unsuccessful appearances), true freshman Andrew Magno, and the favorite in my book is Curlis should be not best Woodby for a starting spot. It appears that sophomore JUCO transfer Thomas Waning (also a sidearmer; one of the few positives about Beals as a coach is his affinity for sidearmers). Other right-handed options for the pen will include junior Dustin Jourdan (a third JUCO transfer from McLennan), sophomore Kent Axcell (making the jump from the club team), and true freshman Jake Vance.<br /><br />The non-conference schedule is again rather unambitious. The season opens the weekend of February 17 in central Florida with neutral site games against Kansas State (two), Delaware, and Pitt. Two games each against Utah and Oregon State in Arizona will follow as part of the Big Ten/Pac 12 challenge. The Bucks will then play true road series in successive weekends against Campbell and Florida Gulf Coast, then play midweek neutral site games in Port Charlotte, FL against Lehigh and Bucknell. The home schedule opens March 17 with a weekend series against Xavier (the Sunday finale being played in at XU), and the next two weekends see the Buckeyes open Big Ten play by hosting Minnesota and Purdue.<br /><br />Subsequent weekend series are at Penn State, at Michigan State, home against UNC-Greensboro, home against Nebraska, at the forces of evil, at Iowa, and home against Indiana. Midweek opponents are Youngstown State, OU, Kent State, Cincinnati, Eastern Michigan, Northern Kentucky, Texas Tech (two), Bowling Green, Ball State, and Toledo, all at home, giving OSU 28 scheduled home dates.<br /><br />Should OSU finish in the top eight in the Big Ten, the Big Ten Tournament is shifting from the recent minor league/MLB/CWS venues (including Huntington Park in Columbus, Target Field, and TD Ameritrade Park in Omaha) to campus sites, although scheduled in advance instead of at the home park of the regular season champ as was the case for many years in the past. This year’s tournament will be in Bloomington, and it speaks to both the volume of players lost and Beals’ uninspiring record that participation in this event should not be taken for granted.<br /><br /><br />phttp://www.blogger.com/profile/18057215403741682609noreply@blogger.com0tag:blogger.com,1999:blog-12133335.post-25658568319880827582017-02-09T18:49:00.000-05:002017-02-09T22:42:40.712-05:00Simple Extra Inning Game Length ProbabilitiesWith the recent news that MLB will be testing starting an extra inning with a runner on second in the low minors, it might be worthwhile to crunch some numbers and estimate the impact on the average length of extra innings game under various base/out situations to start innings. I used empirical data on the probability of scoring X runs in an inning given the base/out situation based on a nifty calculator <a href="https://gregstoll.dyndns.org/~gregstoll/baseball/runsperinning.html#about">created by Greg Stoll</a>. Stoll’s description says it is based on MLB games from 1957-2015, including postseason. <br /><br />Obviously using empirical data doesn’t allow you to vary the run environment…the expected runs for the rest of the inning with no outs, bases empty is .466 so the average R/G here is around 4.2. It also doesn’t account for any behavioral changes due to game situation, as strategy can obviously differ when it is an extra innings situation as opposed to a more mundane point in the game. Plus any quirks in the data are not smoothed over. Still, I think it is a fun exercise to quickly estimate the outcome of various extra inning setups.<br /><br />These results will be presented in terms of average number of extra innings and probability of Y extra innings assuming that the rule takes effect in the tenth inning (i.e. each extra inning is played under the same rules).<br /><br />If you know the probability of scoring X runs, assume the two teams are of equal quality, and assume independence between their runs scored (all significant assumptions), then it is very simple to calculate the probabilities of various outcomes in extra innings. If Pa(x) is the probability that team A scores x runs in an inning, and Pb(x) is the probability that team B scores x runs in an inning, then the probability that team A outscores team B in the inning (i.e. wins the game this inning) is:<br /><br />P(A > B) = Pa(1)*Pb(0) + Pa(2)*[Pb(0) + Pb(1)] + Pa(3)*[Pb(0) + Pb(1) + Pb(2)] + ….<br /><br />Since we’ve assumed the teams are of equal quality, the probability for team B is the same, just switching the Pas and Pbs. We can calculate the probability of them scoring the same number of runs (i.e. the probability the game extends an additional inning) by taking 1 – P(A > B) – P(B > A) = 1 – 2*P(A >B) since the teams are even, or directly as:<br /><br />P(A = B) = Pa(0)*Pb(0) + Pa(1)*Pb(1) + Pa(2)*Pb(2) + … = Pa(0)^2 + Pa(1)^2 + Pa(2)^2 + … since the teams are even<br /><br />I called this P. The probability that game continues past the tenth is equal to P. The probability that the game terminates after the tenth is 1-P. The probability that the game continues past the eleventh is P^2; the probability that the game terminates after the eleventh is P*(1 – P). Continue recursively from here. The average length of the game is 10*P(terminates after 10) + 11*P(terminates after 11) + …<br /><br />I used Stoll’s data to estimate a few probabilities of game length for a rule that would start each extra innings with the teams in each of the 24 base/out situations. For a given inning-initial base/out situation, P(10) is the probability that the game is over after 10 innings, P(11) the probability it is over after 11 or fewer extra innings, etc. “average” is the average number of innings in an extra inning game played under that rule, and R/I is the average scored in the remainder of the inning from Stoll’s data for teams in that base/out situation.<br /><br />It will come as no surprise that generally the higher the R/I, the lower the probability of the game continuing is. In a low scoring environment, the teams are more likely to each score zero or one run; as the scoring environment increases, so does the variance (I should have calculated the variance of runs per inning from Stoll’s data to really drive this point home, but I didn’t think of it until after I’d made the tables), and differences in inning run totals between the two teams are what ends extra inning games.<br /><br />The highlighted roles are bases empty, nobody out (i.e. the status quo); runner at second, nobody out (the proposed MLB rule); runners at first and second, nobody out (the international rule, starting from the eleventh inning; this chart assumes all innings starting with the tenth are played under the same rules, so it doesn’t let you compare these two rules directly); and bases loaded, nobody out, which maximizes the run environment and minimizes the duration of extra innings (making games beyond 12 innings as theoretically rare as games beyond 15 innings are under traditional rules). Of course, these higher scoring innings would take longer to play, so simply looking at the duration of game doesn’t fully address the alleged problems that tinkering with the rules would be intended to solve. <br /><br />I did separately calculate these probabilities for the international rule--play the tenth inning under standard rules, then start subsequent innings with runners on first and second. It produces longer games than starting with a runner at second in the tenth, which is not surprising.<br /><br /><a href="https://3.bp.blogspot.com/-nlFkDuHBuFI/WJz_YJuLuFI/AAAAAAAACXg/tNN4znGcg-Urrt2htmqRgOYKbM1DUixFQCLcB/s1600/extrainnprob.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://3.bp.blogspot.com/-nlFkDuHBuFI/WJz_YJuLuFI/AAAAAAAACXg/tNN4znGcg-Urrt2htmqRgOYKbM1DUixFQCLcB/s400/extrainnprob.jpg" width="400" height="261" /></a><br /><br /><a href="https://2.bp.blogspot.com/-ykslq2yWoQ4/WJz_cs9vWLI/AAAAAAAACXk/sBfxx4ZKvywE-wsn38-NQHwwQrbD5WubwCLcB/s1600/extrainnwbcprob.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://2.bp.blogspot.com/-ykslq2yWoQ4/WJz_cs9vWLI/AAAAAAAACXk/sBfxx4ZKvywE-wsn38-NQHwwQrbD5WubwCLcB/s400/extrainnwbcprob.jpg" width="400" height="22" /></a>phttp://www.blogger.com/profile/18057215403741682609noreply@blogger.com0tag:blogger.com,1999:blog-12133335.post-67475038795339924882017-01-30T09:49:00.000-05:002017-01-30T09:49:08.424-05:00Run Distribution and W%, 2016Every year I state that by the time this post rolls around next year, I hope to have a fully functional Enby distribution to allow the metrics herein to be more flexible (e.g. not based solely on empirical data, able to handle park effects, etc.) And every year during the year I fail to do so. “Wait ‘til next year”...the Indians taking over the longest World Series title drought in spectacular fashion has now given me an excuse to apply this to any baseball-related shortcoming on my part. This time, it really should be next year; what kept me from finishing up over the last twelve months was only partly distraction but largely perfectionism on a minor portion of the Enby methodology that I think I now have convinced myself is folly.<br /><br />Anyway, there are some elements of Enby in this post, as I’ve written enough about the model to feel comfortable using bits and pieces. But I’d like to overhaul the calculation of gOW% and gDW% that are used at the end based on Enby, and I’m not ready to do that just yet given the deficiency of the material I’ve published on Enby.<br /><br />Self-indulgence, aggrandizement, and deprecation aside, I need to caveat that this post in no way accounts for park effects. But that won’t come in to play as I first look at team record in blowouts and non-blowouts, with a blowout defined as 5+ runs. Obviously some five run games are not truly blowouts, and some are; one could probably use WPA to make a better definition of blowout based on some sort of average win probability, or the win probability at a given moment or moments in the game. I should also note that Baseball-Reference uses this same definition of blowout. I am not sure when they started publishing it; they may well have pre-dated by usage of five runs as the delineator. However, I did not adopt that as my standard because of Baseball-Reference, I adopted it because it made the most sense to me being unaware of any B-R standard.<br /><br />73.0% of major league games in 2015 were non-blowouts (of course 27.0% were). The leading records in non-blowouts:<br /><br /><a href="https://4.bp.blogspot.com/-ZSgAUfnwS00/WIzdl5JsVhI/AAAAAAAACWw/N1vmeYtq5lMYU5vUzubloUuhNiJHSanvQCLcB/s1600/rd16a.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://4.bp.blogspot.com/-ZSgAUfnwS00/WIzdl5JsVhI/AAAAAAAACWw/N1vmeYtq5lMYU5vUzubloUuhNiJHSanvQCLcB/s400/rd16a.jpg" width="134" height="400" /></a><br /><br />Texas was much the best in close-ish games; their extraordinary record in one-run games which of course are a subset of non-blowouts was well documented. The Blue Jays have made it to consecutive ALCS, but their non-blowout regular season record in 2015-16 is just 116-115. Also, if you audit this you may note that the total comes to 1771-1773, which is obviously wrong. I used <a href="http://www.baseballprospectus.com/sortable/index.php?cid=1819116">Baseball Prospectus' data</a>.<br /><br />Records in blowouts:<br /><br /><a href="https://4.bp.blogspot.com/-cFItaQ5n6AQ/WIzdqjtD_MI/AAAAAAAACW0/RdZGZu1opGYZJ44so-uXuornCNExJb6nACLcB/s1600/rd16b.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://4.bp.blogspot.com/-cFItaQ5n6AQ/WIzdqjtD_MI/AAAAAAAACW0/RdZGZu1opGYZJ44so-uXuornCNExJb6nACLcB/s400/rd16b.jpg" width="134" height="400" /></a><br /><br />It should be no surprise that the Cubs were the best in blowouts. Toronto was nearly as good last year, 37-12, for a two-year blowout record of 66-27 (.710). <br /><br />The largest differences (blowout - non-blowout W%) and percentage of blowouts and non-blowouts for each team:<br /><br /><a href="https://1.bp.blogspot.com/-roAGb5GmGF4/WIzdumZCaLI/AAAAAAAACW4/Sbj4-j49POEfOB9CBWy7ln_7sUFqHQIOgCLcB/s1600/rd16c.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://1.bp.blogspot.com/-roAGb5GmGF4/WIzdumZCaLI/AAAAAAAACW4/Sbj4-j49POEfOB9CBWy7ln_7sUFqHQIOgCLcB/s400/rd16c.jpg" width="133" height="400" /></a><br /><br />It is rare to see a playoff team with such a large negative differential as Texas had. Colorado played the highest percentage of blowouts and San Diego the lowest, which shouldn’t come as a surprise given that scoring environment has a large influence. Outside of Colorado, though, the Cubs and the Indians played the highest percentage of blowout games, with the latter not sporting as a high of a W% but having the second most blowout wins.<br /><br />A more interesting way to consider game-level results is to look at how teams perform when scoring or allowing a given number of runs. For the majors as a whole, here are the counts of games in which teams scored X runs:<br /><br /><a href="https://4.bp.blogspot.com/-UJgIvw3VBeo/WIzd6YJ_WjI/AAAAAAAACW8/6qWa_DqaL3EIOn_3B-l6orl_2_vBYIVJgCLcB/s1600/rd16d.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://4.bp.blogspot.com/-UJgIvw3VBeo/WIzd6YJ_WjI/AAAAAAAACW8/6qWa_DqaL3EIOn_3B-l6orl_2_vBYIVJgCLcB/s400/rd16d.jpg" width="400" height="272" /></a><br /><br />The “marg” column shows the marginal W% for each additional run scored. In 2015, the third run was both the run with the greatest marginal impact on the chance of winning, while it took a fifth run to make a team more likely to win than lose. 2016 was the first time since 2008 that teams scoring four runs had a losing record, a product of the resurgence in run scoring levels.<br /><br />I use these figures to calculate a measure I call game Offensive W% (or Defensive W% as the case may be), which was suggested by Bill James in an old Abstract. It is a crude way to use each team’s actual runs per game distribution to estimate what their W% should have been by using the overall empirical W% by runs scored for the majors in the particular season. <br /><br />The theoretical distribution from Enby discussed earlier would be much preferable to the empirical distribution for this exercise, but I’ve defaulted to the 2016 empirical data. Some of the drawbacks of this approach are:<br /><br />1. The empirical distribution is subject to sample size fluctuations. In 2016, all 58 times that a team scored twelve runs in a game, they won; meanwhile, teams that scored thirteen runs were 46-1. Does that mean that scoring 12 runs is preferable to scoring 13 runs? Of course not--it's a quirk in the data. Additionally, the marginal values don’t necessary make sense even when W% increases from one runs scored level to another (In figuring the gEW% family of measures below, I lumped games with 12+ runs together, which smoothes any illogical jumps in the win function, but leaves the inconsistent marginal values unaddressed and fails to make any differentiation between scoring in that range. The values actually used are displayed in the “use” column, and the invuse” column is the complements of these figures--i.e. those used to credit wins to the defense.)<br /><br />2. Using the empirical distribution forces one to use integer values for runs scored per game. Obviously the number of runs a team scores in a game is restricted to integer values, but not allowing theoretical fractional runs makes it very difficult to apply any sort of park adjustment to the team frequency of runs scored.<br /><br />3. Related to #2 (really its root cause, although the park issue is important enough from the standpoint of using the results to evaluate teams that I wanted to single it out), when using the empirical data there is always a tradeoff that must be made between increasing the sample size and losing context. One could use multiple years of data to generate a smoother curve of marginal win probabilities, but in doing so one would lose centering at the season’s actual run scoring rate. On the other hand, one could split the data into AL and NL and more closely match context, but you would lose sample size and introduce more quirks into the data.<br /><br />I keep promising that I will use Enby to replace the empirical approach, but for now I will use Enby for a couple graphs but nothing more.<br /><br />First, a comparison of the actual distribution of runs per game in the majors to that predicted by the Enby distribution for the 2016 major league average of 4.479 runs per game (Enby distribution parameters are B = 1.1052, r = 4.082, z = .0545):<br /><br /><a href="https://1.bp.blogspot.com/-rfOvKAk1X8U/WIzeAcucDoI/AAAAAAAACXA/hBeNKXqFlpUdmJqQssDC8270gl0mgw-RQCLcB/s1600/rd16e.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://1.bp.blogspot.com/-rfOvKAk1X8U/WIzeAcucDoI/AAAAAAAACXA/hBeNKXqFlpUdmJqQssDC8270gl0mgw-RQCLcB/s400/rd16e.jpg" width="400" height="263" /></a><br /><br />This is pretty typical of the kind of fit you will see from Enby for a given season: a few important points where there’s a noticeable difference (in this case even tallies two, four, six on the high side and 1 and 7 on the low side), but generally acquitting itself as a decent model of the run distribution.<br /><br />I will not go into the full details of how gOW%, gDW%, and gEW% (which combines both into one measure of team quality) are calculated in this post, but full details were provided <a href="http://walksaber.blogspot.com/2009/01/perfunctory-look-at-run-distribution.html">here</a> and the paragraph below gives a quick explanation. The “use” column here is the coefficient applied to each game to calculate gOW% while the “invuse” is the coefficient used for gDW%. For comparison, I have looked at OW%, DW%, and EW% (Pythagenpat record) for each team; none of these have been adjusted for park to maintain consistency with the g-family of measures which are not park-adjusted.<br /><br />A team’s gOW% is the sumproduct of their frequency of scoring x runs, where x runs from 0 to 22, and the empirical W% of teams in 2015 when they scored x runs. For example, Philadelphia was shutout 11 times; they would not be expected to win any of those games (nor would they, we can be certain). They scored one run 23 times; an average team in 2016 had a .089 W% when scoring one run, so they could have been expected to win 2.04of the 23 games given average defense. They scored two runs 22 times; an average team had a .228 W% when scoring two, so they could have been expected to win 5.02 of those games given average defense. Sum up the estimated wins for each value of x and divide by the team’s total number of games and you have gOW%.<br /><br />It is thus an estimate of what W% a team with the given team’s empirical distribution of runs scored and a league average defense would have. It is analogous to James’ original construct of OW% except looking at the empirical distribution of runs scored rather than the average runs scored per game. (To avoid any confusion, James in 1986 also proposed constructing an OW% in the manner in which I calculate gOW%).<br /><br />For most teams, gOW% and OW% are very similar. Teams whose gOW% is higher than OW% distributed their runs more efficiently (at least to the extent that the methodology captures reality); the reverse is true for teams with gOW% lower than OW%. The teams that had differences of +/- 2 wins between the two metrics were (all of these are the g-type less the regular estimate):<br /><br />Positive: MIA, PHI, ATL, KC<br />Negative: LA, SEA<br /><br />The Marlins offense had the largest difference (3.55) between their corresponding g-type W% and their OW%/DW%, so I like to include a run distribution chart to hopefully ease in understanding what this means. Miami scored 4.167 R/G, so their Enby parameters (r = 3.923, B = 1.0706, z = .0649) produce these estimated frequencies:<br /><br /><a href="https://1.bp.blogspot.com/-cvIBFY6ofC0/WIzeF8_zQCI/AAAAAAAACXE/lNOA9-HdeV0CHaTFH4Hj-9pDOLm5EuXLgCLcB/s1600/rd16f.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://1.bp.blogspot.com/-cvIBFY6ofC0/WIzeF8_zQCI/AAAAAAAACXE/lNOA9-HdeV0CHaTFH4Hj-9pDOLm5EuXLgCLcB/s400/rd16f.jpg" width="400" height="263" /></a><br /><br />Miami scored 0-3 runs in 47.8% of their games compared to an expected 47.9%. But by scoring 0-2 runs 3% less often then expected and scoring three 3% more often, they had 1.3 more expected wins from such games than Enby expected. They added an additional 1.2 wins from 4-6 runs, and lost 1.1 from 7+ runs. (Note that the total doesn’t add up to the difference between their gOW% and OW%, nor should it--the comparisons I was making were between what the empirical 2016 major league W%s for each x runs scored predicted using their actual run distribution and their Enby run distribution. If I had my act together and was using Enby to estimate the expected W% at each x runs scored, then we would expect a comparison like the preceding to be fairly consistent with a comparison of gOW% to OW%).<br /><br />Teams with differences of +/- 2 wins between gDW% and standard DW%:<br /><br />Positive: CIN, COL, ARI<br />Negative: NYN, MIL, MIA, TB, NYA<br /><br />The Marlins were the only team to appear on both the offense and defense list, their defense giving back 2.75 wins when looking at their run distribution rather than run average. <br /><br />Teams with differences of +/- 2 wins between gEW% and standard EW%:<br /><br />Positive: PHI, TEX, CIN, KC<br />Negative: LA, SEA, NYN, MIL, NYA, BOS<br /><br />The Royals finally showed up on these lists, but turning a .475 EW% into a .488 gEW% is not enough pixie dust to make the playoffs. <br /><br />Below is a full chart with the various actual and estimated W%s:<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-OlPaAw--tlE/WIzeKU72fqI/AAAAAAAACXM/_Nwm13g6FvAw-xjs6DaXhn_eFcUEyI21ACLcB/s1600/rd16g.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://2.bp.blogspot.com/-OlPaAw--tlE/WIzeKU72fqI/AAAAAAAACXM/_Nwm13g6FvAw-xjs6DaXhn_eFcUEyI21ACLcB/s400/rd16g.jpg" width="328" height="400" /></a></div>phttp://www.blogger.com/profile/18057215403741682609noreply@blogger.com0