Meanderings

Sorry, I've been doing this a lot lately. I've had more mini-posts I want to write, and more things I need to vent (I'm turning crotchety, I guess), and so you've been getting meanderings instead of substantive posts. It's either this or start Twittering, and I'd like to avoid that at all costs.

* Why do people wring their hands about an athlete's "legacy"? We are told that Brett Favre is ruining his legacy by un-retiring. But how many retired athletes can you name whose legacy was truly ruined (whatever a legacy actually is--it's a pretty nebulous term)? Steve Carlton bounced around pitching ineffectively, but he's still seen as Steve Carlton, Phillies Ace. Willie Mays is celebrated as one of the greatest players of all-time despite bumbling around with the Mets.

I also don't understand why people are so emotionally invested in athletes retiring. If they still want to play, and a team still wants to employ them, I have no problem with it. I understand frustration at media coverage ("Oh look, there's Favre getting off the plane!"), but try to separate general ESPN disgust from the athletes themselves. I can also see why Packers fans would be annoyed that their icon is going to play for a division rival. But outside of that, the reaction to Favre puzzles me.

* It never ceases to amaze me how the billionaires who own pro sports franchises have managed to convince the public that the (relatively) uneducated millionaires that they employ (and their agents, of course) are screwing them over. It is a remarkable phenomenon.

I need to issue the disclaimer that I'm not saying that the owners are wrong simply because they are billionaires, and that the lesser income group must be getting the shaft. That's not what I'm saying at all. I think that both the owners and the players are right about some things and wrong about others (and of course neither group is homogeneous in their motivation and desires). It's just that the public as a whole seems to always side with the owners. Here are just a handful of situations in which this manifests itself:

1. The owners have apparently managed to convince the public that increased salaries drive ticket price increases, rather than the opposite--more revenue to teams means more potential value added by players (of course, labor costs could change the profit-maximizing ticket price, but it's folly to think that ticket prices would be dramatically lower if salaries were lower).

2. Players are derided by many fans for trying to exert some control over which organization they begin their careers with (even if they can only do it by making vague pre-draft bonus demands). But the system that assigns players to organizations with no choice, and rewards failure (at least in theory) is an accepted part of every sport.

3. You have the strange concept of "loyalty", which is a one-way street meaning that players are loyal to their teams, whatever that even means. Trades are accepted as part of the game, but if a player dares to leave via free agency, he is a scoundrel. Players who display what seems to qualify as loyalty (and thus worthy of admiration) are sometimes derided as losers (as seen when Jake Peavy initially rejected his trade to the White Sox). Players who are jerked around by their teams in service time maneuvers are expected to show loyalty. Players are expected to show loyalty to whichever team they happen to play for currently, even if they have a different hometown team they'd ideally like to play for.

4. Players are often criticized for chasing an extra million dollars or two--"Why isn't $12 million enough? Why do you need $15 million?" Of course, this same question is never asked of the owner--"Why do you need to make $20 million in profit? Isn't $17 million enough?"

5. Owners' claims of poverty are generally accepted. We are supposed to believe that these billionaires have absolutely no business sense when it comes to sports and are losing money left and right, necessitating public stadium financing, contraction, or some other scheme that is against the best interest of fans as a whole--despite the fact that different billionaires keep shelling out hundreds of millions of dollars to buy into the industry.

Incidentally, my position on all of this is that both sides should be expected to seek what is in their economic self-interest, and that neither side is wrong for doing so. It's just that the public sides with sports management to a much greater extent (as far as I can tell) then they do in other industries.

* We're getting to that time of year when everyone is all atwitter about the BBWAA awards. As I've said before, I try not to pay too much attention to those--just enough to get a good laugh but not pop a blood vessel when Ryan Howard finishes second in the NL MVP vote or what have you. The Internet Baseball Awards and certain individual's own hypothetical ballots are worthy of more attention in my eyes.

However, my efforts sometimes fail, and I find it irresistible to comment in one way or another. I had a discussion with Sky of Beyond the Box Score recently, and in the course of it I noticed that Roy Halladay has never received a single MVP vote in his career. Not even one measly tenth-place vote. Halladay won the AL Cy Young in 2003 but did not receive a vote for MVP, while Carlos Lee (830 OPS) did and Shannon Stewart (823 OPS) finished fourth.

Halladay is an unusual case--it seems from a perfunctory look at recent voting that the top Cy Young contenders usually manager to get a nod somewhere on a few ballots. But certainly not the extent that I think they deserve to (or advanced metrics think they deserve to).

I realize he pitched well...

but I didn't realize he could make Mariners disappear.

My Personal Path to Sabermetrics

This post is quite self-indulgent, and I don't really expect it to be of any interest to anyone. I was writing a post about a related topic and this wound up being a lengthy digression, so I took it out to use as a stand-alone post.

In the aforementioned post, which I may or may not ever get around to publishing, I offer up definitions for three generations of sabermetric practitioners and disciples (for lack of a better word). Pioneers (folks like Pete Palmer and Bill James just to name a couple), second wave (those who were brought into sabermetrics through the work of the pioneers), and the internet generation. Which group one falls into (to the extent that such classifications are valid and worthwhile, which is questionable) is not so much a question of age but of when his interest in sabermetrics was germinated.

I fall right on the bubble between the second wave and internet generation, and in case I ever do publish that post, you might want to understand where I am coming from based on my own experiences.

I was not much of a baseball fan as a kid (nine years old and under). I never played any sport at any level above friendly neighborhood games (no athletic ability--see, I meet the stereotype for a stat nerd already), and we mostly played football and basketball at that age. My general impression of baseball was that it was boring. I remember my dad watching the World Series one time, and I couldn't sit there and watch it for more than one or two innings despite being able to watch entire football games contentedly.

The first major league game I attended was in 1993; it was the fourth-last game played at old Municipal Stadium, Brewers v. Indians. The Indians won 6-4, but I couldn't have told you that if I hadn't looked it up on Retrosheet. It was a chilly fall Sunday, and the Browns were playing in Indianapolis, and a lot of the people there were listening to the game on the radio, and there was a guy with a little portable TV that people were huddled around. The Browns lost--that much I remember. This experience did nothing to lure me into baseball fandom. Looking at the box score, I feel remorseful about this, as a young Jim Thome went deep and Bill Wertz pitched in relief for the Indians, something that would make me incredibly excited were it to happen today.

The Opening Day game at Jacobs Field in 1994, despite the fact that I only experienced it through the radio, made me a baseball fan. By that time I was listening to sports talk radio, mostly to here football talk, but the opening of the Jake and the cautious optimism surrounding the Indians' 1994 campaign was a popular topic. And I certainly had a sense of history, so when I got home from school I listened to the end of the game, which the Indians won in extra innings after Randy Johnson had taken a no-no fairly deep into the game. That alone got me hooked, but it might not have stuck had the Indians not continued to play well. Fortunately, they did, and by the time summer came around I was a born-again baseball nut. Even the strike did nothing to deter me, and I the next spring I was happily listening to Joe Slusarski, Joe Biasucci, Eric Yelding, and the other Indian replacement players on the radio.

To really get into sabermetrics, you need to possess two traits. First and foremost is a deep interest in baseball, but second is the desire to quantify things and to understand them. I may have been woefully lacking in the first department, but I already possessed the latter trait. As long as I can remember I was always interested in learning facts and reading. My favorite book when I was in the second grade was the World Almanac. When I was in kindergarten or first grade, I kept notecards with data about the planets on them--distance from the sun, length of day and year, diameter, etc.--even though I was obviously too young to really understand what it meant.

So it was only natural that when I did catch the baseball spark, it was only a matter of time until I was interested in records and statistics. And since I was predisposed to like that sort of thing, the wealth of records and statistics in baseball only strengthened my interest in the game. I did take a short detour into the world of baseball cards, but that only lasted through the spring of 1995, and I was always reading the numbers on the back.

By 1995, I was filling up sheets and sheets of notebook paper with lists of the World Series winners, home run leaders, team nickname histories--basically, all of the information that you get in an average sports almanac. Fortunately, I was aware of two offensive stats called On Base Average and Slugging Average, and wanted to include lists of those in my folders, and to collect the lifetime stats for all of the great players.

The yearly SLG leaders were easy enough to find, but lifetime stats and OBA leaders were harder to find in conventional sources. I needed a specialized reference, a baseball encyclopedia, to answer my questions. And it just so happened that I had an older friend in the neighborhood who had a copy of Total Baseball II, and he leant it to me.

So I got the data I needed, but I also saw a whole world of new categories, and naturally I wanted to understand those. So I read the glossary, and when I saw The Hidden Game of Baseball at the library, I checked it out. And from there, it was pretty much over. I was into sabermetrics. Bill James followed and that was all she wrote, by the summer of 1996.

Based on my generational definitions, that account falls solidly as second wave. However, while we didn't have the internet in our house yet, I had friends who did. When school started in the fall, I told one of my friends who was also a baseball fan about sabermetrics, and he googled it (actually, he didn't, as Google didn't exist yet), and printed out some stuff for me, mostly from Keith Woolner's site (which was not yet called Stathead.com--it was still called Baseball Engineering). Anyway, I distinctly remember the article on Marginal Lineup Value being one of the things he gave me.

So while I came to sabermetrics primarily through the work of the pioneers, and not the internet (which is my definition of second wave, more or less), it was only a short matter of time until I was getting sabermetric content from the internet. Furthermore, I had only been a baseball fan for about a year and a half before I got into sabermetrics. That means I had very little time to be indoctrinated into the conventional wisdom and the conventional statistics, and I was very open to persuasion by sabermetric arguments as they didn't challenge any long-held beliefs. That is a trait that I generally associate with the internet generation of sabermetric devotees.

If I pride myself on anything about my formative sabermetric experience, it's that I didn't get sucked into Bill James' anti-linear weights stance expressed in the Historical Baseball Abstract. I always kept an open mind between the two positions and tried to see how they could be reconciled (by some rudimentary "+1"-type analysis of Runs Created). It wasn't until much later that I fully understood the full range of benefits of linear weights, but at least I never reflexively rejected them. Perhaps it was fortunate that I read The Hidden Game before I read the Historical Abstract.

Anyway, if I ever get around to publishing that post, it is somewhat critical of certain elements of the internet generation while showing a bit of a bias towards pioneers and second wavers. Hopefully, this account admitting my own biases and my straddling of the fence between the second wave and internet generation will enable my comments to be taken in the constructive nature in which they are intended, rather than viewed as self-aggrandizing.

Meanderings

* I think I need to give up my Indians fandom, limited as it may be. It's incredibly frustrating to go through the same thing year after year. Every year on July 31, you know exactly what to expect. Unless the team is in the thick of the race, a group of veteran players eligible for free agency or close to it will be traded away for prospects. And all you can do is shake your head and wonder, "Don't these people get it?"

I speak of course not of Mark Shapiro and the Indians front office, but about the mainstream "fan view" that you see on message boards and on talk radio.

Please recognize that I am not saying that I am enamored with the return the Tribe got in their trades, nor am I criticizing those who analyze the moves on a player-by-player basis and find them lacking. The return for Lee seems underwhelming, the return for Martinez seems a little bit underwhelming, but reasonable, the returns for Betancourt and DeRosa seem eminently fair, and the return for Garko seems more than generous. I don't suspect that the Cliff Lee trade will go down in history as a coup, but I'm also not foolish enough to write it off as a failure a week after it was made.

My real frustration with fan-think is that it doesn't matter who the Indians got in the trades. They could have got the Phillies and Red Sox top prospects, and the vox populi would still be howling. There was a similar outcry in Cleveland over the Colon trade, which of course turned out to be a massive coup. But there is nary little recognition that Lee himself was acquired in the very same type of trade he was dispatched in. Again, I'm not saying that this specific trade will work out as well as the Colon trade did. The Colon trade came under special circumstances and cannot be used alone as a precedent, and looked a lot better on paper at the time.

The outcry over the Pirates' moves is even more puzzling. The way some commentators have talked about Freddy Sanchez, Jack Wilson, and Nyjer Morgan, you would think they are stars. Again, I have no issue with questions about whether the return will do any good, but the idea that Freddy Sanchez was an integral future piece for the Pirates is absurd.

* More broadly, why is it that the baseball fan public at large has such a hard time grasping some very simply truths about baseball economics? I can't tell you how many people I've encountered with business sense and a solid understanding of economics (I'm not exactly Milton Friedman myself, mind you) that just can't apply it to baseball at all.

Here are just a few simple principles about trades that seem to be missed by a large portion of casual fans. There is some overlap between them, and I'm certainly not claiming that you didn't already think this way:

1. You are not trading for a player; you are trading for his contract too.

This is of course the key tenant of the type of trade analysis that is popular at sabermetic sites. People act as if you are trading Cliff Lee's entire future, but in fact what you are trading is 1 1/2 years of Cliff Lee's services. Of course, in Lee's case he is paid less than his free agent value, but in many other cases players are paid about what they would get on the free agent market, and in others they are paid more.

2. When a player is eligible for free agency, you are probably going to have to pay him is market value. In some cases there might be a hometown discount, or a security discount if you sign an extension in advance, but for the most part you pay market value.

Just because Cliff Lee is an Indian doesn't mean that he's going to stay an Indian. Would you expect the Indians to reach a free agent agreement with a pitcher of similar quality? No? Then you probably shouldn't expect them to reach a contract extension with him either.

Circling back to #1, trading Lee just means you give up 1 1/2 years of his service, not his whole future career. You can't trade what you never owned to begin with.

3. Even if a player's contract is a decent value, that doesn't mean he's the best possible fit for your organization.

Nyjer Morgan is not a bad player, but if he can handle center field well and your top prospect plays that position as well, then maybe you're better off trading him to a team with a gaping whole in center field in exchange for some other pieces. Simple, right? But how many hand-wringing comments about the Morgan trade ignored the presence of McCutchen and the possibility that Morgan's value is not maximized by playing left for the Pittsburgh?

4. Teams have to think about long-term implications

This is self-evident and shouldn't have to be stated at all, but the knee-jerk reaction often overlooks it regardless. The Indians recently traded Carl Pavano to Minnesota, and some fans balked because he was just about the most reliable starter left on the team (sad but true). But he was only going to be an Indian for two more months, and it doesn't make any difference how the Indians perform over the next two months.

Of course, the Indians got essentially nothing in return and just saved whatever was left on his contract, so it's not as if they would have lost out on some great opportunity had they held onto him. But still there were fans who reacted with an eye only on how it would affect the end of the Indians' lost season, and not the fact that it opened up a rotation spot for Justin Masterson (and maybe Carlos Carrasco or Hector Rondon or someone in September) or the dollar savings, etc.

* I am glad to see that strikeouts per PA (as an alternative to K/IP for pitchers) is gaining more widespread use in the sabermetric community. K/PA is something I've agitated for in the past--I don't know that I've ever done it here, but I could dig up some embarrassingly intemperate FanHome threads to prove it.

I don't mean to suggest that K/IP is worthless, but it doesn't measure what the casual fan seems to think it does. Innings Pitched has widely been accepted as our standard for how much someone pitched, but in fact it is the number of outs they recorded divided by three. So K/IP can actually be thought of as the percentage of outs that are recorded by strikeouts.

K/PA is the percentage of batter struck out, so it takes a binary approach--a strikeout is a "success" and any non-strikeout is a "failure". Of course, there are other ways you could break it down as well--some people exclude walks, for instance. It all depends on what you are seeking to measure.

But to me, K/PA answers the most relevant question. A pitcher with truly "unhittable" stuff would be able to strike batters out at will (ridiculous extreme, granted). Excluding walks ignores the tradeoff that often has to take place between attempting to avoid contact and throwing strikes. K/IP is still useful, IMO, as you could look at is measuring how often a pitcher takes care of a batter himself and how often his fielders are involved. And of course there is a strong correlation between K/PA and K/IP--you're not going to go too wrong either way and conclude that Nolan Ryan was a master of pitching to contact and that Nate Cornejo was a flamethrower.

Before you send me any angry emails about referring to PA rather than Batters Faced, one of my pet peeves is the use of different names for the same statistic based on whether it is for a hitter or a pitcher. It just causes unnecessary confusion.

* Out of the four major North American pro team sports, my order of preference is baseball (big gap), football (big gap), basketball, hockey. I was recently thinking about this and it occurred to me that my preferences correspond very well to the continuum of possession fluidity. The more fluid possessions are, the less I like the sport.

I am not saying that is the one and only explanation for my preferences--it is a kind of after the fact analysis. But I do like the increased order of each sport.

In baseball, there really isn't possession in the same sense as other sports, as of course the ball is not advanced towards a goal. But there is a very rigid process of changing sides, which occurs if and only if three outs are made or the game ends. Unlike in other sports, the offense and defense are kept completely separate, and there is never any incentive formed out of a goal of winning the game to do anything other than attempt to score or prevent the opponent from scoring. (Of course, there are times in which it makes sense to try to score one or two runs rather than attempting to maximize your runs. But there is never any win-based reason to eschew scoring at all, or severely curtail it, as there are in the other sports).

Football's possessions are fairly well-defined. Possession changes on a score, on the orderly concept of downs, or when one team voluntarily decides to surrender position, usually by punting. The only disorderly change of possession occurs on turnovers, and on about half of plays (running plays), the ball is physically in the possession of an offensive player at all times.

Basketball has much less rigidity. Possession changes on certain fouls and infractions, on certain scores, and on the shot clock. That list does not include turnovers, which are much more frequent than in football and understandably so, as the ball can only be cradled for a brief period of times. The rules of the game dictate that the ball almost always be accessible to thievery by the defense, and passing is a necessity done in close quarters rather than downfield as in football.

I would argue that hockey has the most possession fluidity of any of the sports, as possessions are not formally defined (there is no shot clock, no downs, and certainly no innings change). The puck must always be on the ice where it is up for grabs, and while hockey players have amazing control over the puck with their sticks (I tried to write this five different ways and none of them sounded good), it's hard to say that it is a safer way to secure the ball/puck than holding it with your hands.

If you thought this was going somewhere, sorry, it's not.

Silly OPS Tricks

I'm not really sure why I'm writing this post, since it uses a metric that I don't particularly wish to propagate and doesn't offer any serious analytical application.

Nonetheless, herein is a (relatively) simple and reasonably accurate way to predict a team's win-loss record from its OPS and OPS Allowed. It combines two simple rules of thumb (one relating OPS to runs, and one relating runs to wins) into a single OPS to wins conversion. And that is the reason I am sharing it here despite my antipathy towards OPS--the two rules of thumb both take the same form, and so their combination is fairly elegant. I guess what I'm trying to say is that it is "neat", even if I don't think you should use it.

This will be a metric of the type that I call predicted winning percentage, which is based on component statistics, as opposed to expected winning percentage, which is based on actual runs scored and allowed.

The first rule of thumb is the conversion between OPS and runs. OPS has, roughly, a 2:1 relationship with runs scored. If a team has an OPS 5% better than league average, then we expect them to score about 10% more runs than league average. I have noted this relationship before, but of course it is well-known.

Above and in the linked post, I used this in relation to the league average, but it can be applied to a team and its opponents as well. So we can estimate a team's run ratio (R/RA) as:

RR = 2*OPS/OPS Allowed - 1

Run Ratio can be related to wins in any number of ways, some more accurate than others--the most notable application is the Pythagorean formula. A linearization of the Pythagorean formula for the normal range of run scoring is what Bill James called "Double the Edge"--a team that scores 5% more runs than its opponents should win about 10% more games. So we can estimate a team's win ratio (W/L) as:

WR = 2*RR - 1

We can substitute the OPS relationship in, and get:

WR = 2*(2*OPS/OPS Allowed - 1) - 1

which simplifies to:

WR = 4*OPS/OPS Allowed - 3

As you can see, this is a steep function, and is a consequence of combining the pair of 2:1 functions. A team with an OPS 5% better than its opponents figures to have a W/L ratio of 4*1.05 - 3 = 1.2.

Win Ratio can be converted to a more familiar form, W%, very simply, as WR/(WR + 1). If we substitute the OPS relationship into that equation, we get this formula that takes us directly from OPS and OPS Allowed to W%:

W% = (4*OPS/OPS Allowed - 3)/(4*OPS/OPS Allowed - 2)

How well does this work? Not too shabby...over the past two seasons (not the largest sample size in the world, but nothing in this post is meant to be rigorous in any way, shape, or form) it has a RMSE in predicting actual W% of 5.64. My PW% estimate using Base Runs and Pythagenpat has a similar RMSE over the same period (5.52). Using it to estimate expected W% (Pythagenpat record, based on actual runs scored and allowed), the OPS knockoff has a RMSE of 4.06, while PW% has a RMSE of 3.46.

When you estimate W% from component statistics (in other words, without the benefit of R and RA), you have three areas where errors can occur:

1. error in predicting runs scored
2. error in predicting runs allowed
3. error in converting between runs and wins

If you estimate W% from runs and runs allowed, you obviously only have to worry about the third type of error. But with so much going on in figuring PW% (as I have defined it), it doesn't really matter whether you use "state of the art" methods (BsR + Pythagenpat), or use chicken scratchings based on OPS. You're going to have some fairly significant error either way. The theoretical superiority of the "state of the art" approach is hinted at by its better tracking of EW%.

Anyway, there are still a number of weaknesses with the OPS method (I'll give it a name just for convenience--let's call it the Reynolds estimate, since we all know Harold loves his OPS). These include, but are not necessarily limited to:

1. The simple fact that it's based on OPS. OPS has a lot of problems, but they don't manifest themselves too much when you deal with real teams in the normal performance range, so it's not too much of a concern here.

2. It can't be used with OPS+. OPS+ is no great shakes either, but given it's prominence in the Total Baseball and later the ESPN Encyclopedia and Baseball-Reference, it gets used just as much in the sabermetric community as ordinary OPS. The Reynolds estimate is incompatible with OPS+, as OPS+ does not have a 2:1 relationship with runs (it has a 1:1 relationship--the misunderstanding of the OPS and OPS+ relationships with runs is a never-ending frustration of mine). This is a selling point for OPS+, but it means it doesn't work here (you can of course work out a PW% estimate based on OPS+, but that's besides the point).

3. It breaks down at the extremes. The OPS to runs relationship, particularly when using outs, will cause you all sorts of problems if you attempt to use it to estimate how many runs Babe Ruth created in 1920. The double the edge estimate of W% is fine in the normal performance range, but you don't want to use it to figure individual Offensive W% or anything. Combining those two issues, you don't want to figure a pitcher's estimated W% or a hitter's OW% with this method.

4. It does not have the property of reciprocity between a team and its opponents. For example, the 2007 Red Sox had an OPS of 806 and allowed an OPS of 705. That gives them a Reynolds estimate of .611.

But if you plug in the Red Sox opponents (a team with an OPS of 705 and an OPS Allowed of 806), you get a Reynolds estimate of .333. In order for this to make theoretical sense (unless you know something about run distributions that the rest of us don't), the Red Sox and their opponents need to add up to 1.

Why does this happen? Well, for one thing I played fast and loose by equating OPS Allowed with League OPS when plugged into the regression equation. In fact, this is a shortcut that works fine for average teams but will cause problems at extremes. Let me reintroduce an equation for estimating runs from OPS and outs:

Runs = (.496*OPS - .182)*(AB - H)

The Red Sox OPS of 806 means they should score about .218 runs/out, and their OPS Allowed of 705 means they should allow about .168 runs/out, for a run ratio of 1.299. Our shortcut (2*OPS/OPS Allowed - 1) yields an estimated run ratio of 1.287. Not a huge difference, but a small source of error, and due entirely to a shortcut.

It's worse for the Red Sox opponents, who should be estimated with a run ratio of .77 (.168/.218). But the shortcut estimates a run ratio of .749. To make matters worse, the shortcut estimates a 1.287 run ratio for the Red Sox, which has a reciprocal of .779. But the use of the shortcut eliminates reciprocity between the run ratio of a team and its opponents.

To state it again, the reason this happens is that 2*OPS/LgOPS - 1 relates to runs scored by a team, and is centered around LgOPS. It really should be applied separately to estimate runs scored from OPS and runs allowed from OPS Allowed.

An even bigger reciprocity problem arises from the use of WR = 2*RR - 1. This is why analysts who have worked with that equation (like Bill Kross) have used a different formula for teams whose run ratio < 1. We could invert OPS and OPS Allowed and subtract from one:

W% = 1 - (4*OPS Allowed/OPS - 2)/(4*OPS Allowed/OPS - 3)

Which can be simplified to:

W% = 1/(4*OPS Allowed/OPS - 2)

Doing it this way, with separate equations, the RMSE against actual W% drops to 5.40, which is actually a tad better than the Base Run/Pythagenpat estimate (remember, this is only a small sample of sixty teams, and I'm not using the most accurate BsR formula available). The entire approach is a shortcut itself, and so I'm not advocating using separate formulas; that would defeat the purpose of a quick and dirty estimate. If you want something deeper than a quick and dirty estimate, you shouldn't be using OPS at all.

Anyway, the reason I got to thinking about this at all was that in the Bill James Gold Mine, the statistical summary for each team includes OPS and OPS Allowed. I certainly don't go out of my way to look up team OPS. Then it dawned on me that it was a neat coincidence that the conversion could be made by combining the pair of 2:1 functions, and that it would at least look nice. But make no mistake--like anything involving OPS, it's an "accident" that it works out so nicely. The 2:1 relationship between runs and wins is well documented, and it is the basis for a few W% estimators (including Pythagorean). But OPS is not a meaningful, real-life baseball number; it's a made-up statistic that happens to relate to runs on the team level at 2:1.

To end on a *truly* frivolous note, the inclusion of OPS and OPS Allowed in the Gold Mine caused me to notice something I hadn't before--that a team's raw run total over 162 games is relatively close to its OPS without the decimal place (in mathematical terms, OPS*1000). For 2008-2009, the RMSE of this direct estimate (looking at OPS-->Runs and OPS Allowed-->Runs Allowed) is 43.94. Of course, a real estimate based on OPS will have a much lower RMSE, somewhere in the general vicinity of 26 runs. But that involves applying a formula like:

Runs = (.496*OPS - .182)*(AB - H)

Just looking at a team's OPS over the course of a 162 game season, without any sort of mathematical manipulation, gives you an estimate of team runs that is in the same accuracy ballpark as running a regression for runs based on batting average. This is not any great shakes, of course, and you'd be a fool to estimate that because the Rangers allowed a 817 OPS last year, they should have allowed 817 runs (they actually allowed 967). But in many other cases, it will put you in the right ballpark, although you will be stuck in the nosebleed seats.

The reason this "works" can be seen by looking at the regression equation. The average team will make about 4080 outs (AB-H) per season (25.2 outs/game * 162 games). Substituting 4080 into the equation for outs, you can simplify it to roughly:

Runs = 2*OPS - 743

Over the past two years, the average major league team has scored 765 runs and compiled a 753 OPS. So for an average team, there isn't much difference between figuring 2*OPS - 743 or just taking OPS, since their OPS is pretty close to 743 as it is. As you move away from the average, this "formula's" accuracy will take a nose dive (exemplified by the Rangers example above).

This is the part where I set off the secret beacon in the Statue of Liberty and perform a mind-wipe, and you forget everything you just read and never, ever actually use the Reynolds estimate, okay?