## Sunday, August 22, 2010

### Rudimentary Team Fielding Metrics

If you divide baseball into offense, pitching, and fielding, there's no question that fielding is the one I spend the least amount of time on as a sabermetrician. Just look at the labels on the side of the page; as of this writing I have 61 posts labeled "Offense", 24 labeled "Pitching", and just 3 labeled "Fielding". This even understates it a little, since none of the fielding posts include any new ideas put forth by me, and because a lot of what is classified as "Offense", like run estimators, is equally applicable to the defense, but as a whole.

It's not that I don't think fielding is important to winning ballgames. It's not that I think sabermetrics has got fielding all figured out. It's just not a topic that I have ever had much to contribute towards.

One of the major reasons for this is the same reason that I don't do any work with Pitch F/x data--I don't really understand it well enough to come up with anything useful. I love algebra and probability and statistics and most calculus; I hate geometry and trigonometry and those calculus problems in which you try to figure out the volume of a cylinder rotated around the y-axis. Have a problem which requires use of the quadratic equation, the binomial distribution, or partial differentiation? Sign me up. But the minute you start tossing around polar coordinates or angles, I'm just as math-averse as the average old-school sportswriter.

This limitation can be quite an inhibition when it comes to being on the cutting-edge of fielding or pitch analysis, so I stick with the topics in which one can safely avoid any angles or sines. I was reading an article the other day in which "3-space" was mentioned, and it was the first time in reading a sabermetric piece that I could relate to the guy who says "I like baseball, not math."

None of that is intended to in anyway suggest that the research being done in those areas is less important than the things I write about. It's more of an apology for the rudimentary nature of the team fielding metrics that follow.

The impetus for this post is that I wanted to add a couple of team fielding metrics to my end-of-season stats, just to make it clear that I realize fielding is part of the game. The philosophy with those stats has always been to stick to either official categories or things that are easy enough to find otherwise (like doubles and triples allowed, or inherited runners). So any of the advanced fielding metrics are already disqualified from inclusion, and even if they weren't it would be pointless because I would just be copying someone else's work so to speak.

So, limiting the scope of categories available just to the official and semi-official categories, what can one do about team fielding? Obviously there's Defensive Efficiency Record, which is very important even in the PBP fielding age. There's team Fielding Average, which is not particularly useful but is still widely cited in the mainstream. You could do something with double plays, passed balls, or stolen base percentage and after that the pickings are fairly slim. I've passed on double plays because they are highly correlated with the groundball tendencies of the pitching staff, and to look at them without that context would be misleading at best.

As a result, I'm including just three categories: DER, a modified fielding average, and a rate of wild pitches and passed balls:

(1) Battery Mishap Rate (BMR)

It is hardly a novel idea to combine wild pitches and passed balls; while I was working on this post, by chance I stumbled upon Bill James describing the distinction between WP and PB as the "silliest distinction in the records" in 1988. I agree with him, so BMR is simply the ratio of WP and PB to baserunners, multiplied by 100:

BMR = (WP + PB)/(H + W - HR)*100

A battery mishap can occur without a baserunner (a mishandled third strike that allows the batter to reach) but baserunners make more sense as the opportunity factor than anything else. The highest team BMR of the last twenty years (1990-2009) was 6.0, by the 1993 Marlins (a wonderful combination of a knuckleballer with an expansion team); next is the 1990 Yankees (5.8, without any such easy excuse). The lowest rate was 1.5 by the '92 Padres, and the average was 3.4 overall and in 2009. The lowest BMR was 2.0 (BAL); the highest was 5.4 (KC).

(2) Modified Fielding Average (mFA)

Fielding Average has many issues, foremost of which is that it is built on the silly distinction between a hit and an error. Still, it's not going anywhere and it won't hurt anything to list it on a spreadsheet.

A really easy alteration to traditional FA is to remove strikeouts, since they are generally easy putouts with little opportunity for errors. In fact, the most common mishap on a strikeout is a wild pitch or a passed ball, and thus not scored as an error at all. So we can define kFA (strikeout-adjusted FA) for a team as (PO + A - K)/(PO + A - K + E).

I think there's another modification that's simple but justified, and I wouldn't be surprised if someone has already proposed it, although I couldn't find anything in a quick search. Consider this theoretical inning:

1. 6-3
2. E5
3. 6-4 fielder's choice
4. 5-4 fielder's choice

Three putouts, one error, three assists = .857 FA

And this one:

1. fly to 8
2. fly to 9
3. E4
4. 6 unassisted fielder's choice

Three putouts, one error, no assists = .750 FA

Team A is credited with a better FA (ostensibly a lower error rate) than Team B, but does this really make sense? Each team recorded three outs and made one error. In the first case, plays were completed by assists, while in the second all plays were made unassisted.

It's possible to make the case that plays involving assists take more skill, generally, than those that don't. But even someone taking that position would have to admit that there are many cases in which there is no meaningful distinction (such as the fielder's choices with and without assists). In some cases, like a first baseman with bad knees flipping to the pitcher, or a rundown involving more players than necessary, the assist is actually indicative of a poorer fielding outfit.

The practice of including assists in fielding average appears to me to be a reflexive application of the same formula that one would use for individuals. There's no reason why the same formula must be used for teams as well. Considering the number of players that handle the ball obscures the fact that the goal of a team in the field with respect to errors (which isn't really the goal at all) is to make as few errors as possible while recording outs, not collecting chances.

So I offer a modified FA for teams:

mFA = (PO - K)/(PO - K + E)

One thing I should note is that there's a decent case to be made for looking at the complement of FA--making errors the numerator rather than putouts. Since all the numbers are clustered in a small range in the upper .900s, they look better on paper clustered in a small range less than .050.

For most teams, using mFA makes very little difference. For 1990-2009, the correlation between kFA and mFA is +.994. Over that period, the average team has a ratio of .51 assists per (PO - K), ranging from .43 ('02 MIN) to .59 ('03 LA). mFA correlates better with DER, but not significantly so. The teams with high ratios would generally have been teams that got more groundballs, and as a driving factor for why kFA and mFA diverge, there is a messy and intertangled relationship between mFA, DER, and overall team defense (including pitching).

Even if one believes that plays involving assists should be given extra weight, do you really think the appropriate weight on assists is one, double-weighting those plays in establishing the opportunity factor for errors? mFA weights them at zero; perhaps it would make more sense to use, say, .3, but one seems excessive in any event.

One might ask why BIP is not the denominator. The drawback to using BIP is that a team's error rate would be reduced by allowing a hit. It makes more sense to combine errors and hits as failures and compare them to BIP--which is exactly what DER does.

The average mFA over the period and in 2009 was .967. The highest mFA was .981 by Seattle in 2003; they ranked third in standard FA. The top nine teams in FA rank are also the top nine in mFA, although in different order. The lowest mFA was .951 by the 1992 Dodgers--that's what happens when Jose Offerman plays short and makes 42 errors. That Dodgers team was second-to-last in traditional FA; the opposite combination is true for the 2009 Nationals.

The team whose ranking improves the most by using mFA is the 1992 Tigers (.981 FA, .969 mFA). They recorded just 693 strikeouts, the fewest of any team in the period in a non-strike season. The team with the biggest drop in ranking is the 2003 Cubs (.983 FA, .965 mFA), and they struck out more batters than any team in the period. Strikeouts pad the putout total and obscure the true error rates of fielders when they are included in fielding average.

Here are the 2009 team figures, with ML rank in FA and mFA, sorted by difference in ranks. Positive differences indicate teams that rank higher in mFA than in FA:

(3) Defensive Efficiency Record (DER)

Given that Bill James' DER is the most-widely used measure of team fielding, you'd think his original formula would be easy to find online, or in one of the STATS or Baseball Info Solutions publications James contributed to. You'd be wrong. I'm sure it's out there somewhere, but it's not easy to find, so I saved time by rummaging through the closet to dig out my one of my Abstract copies.

DER is the percentage of balls in play that are converted into outs, and James used two estimates to establish the numerator of plays made. One used putouts as its starting point; the other begins with plate appearances. The second is now used by most analysts, as the data is more accessible and it is also for all intents and purposes the complement of BABIP, the metric whose behavior is at the heart of DIPS theory.

I'll use that second estimate exclusively as well, but for completeness, the first formula is:

PM1 = PO - K - DP - 2TP - CS - ofA

This estimate assumes that a putout occurs on a batted ball unless it's a strikeout, or multiple outs are recorded on the same play (DP, TP), or it is a baserunning out (CS, ofA).

PM2 = PA - K - H - W - HB - .71E

The second estimate assumes that every batter is out on a ball in play unless he reaches safely (H, W, HB) or on an error (ROE is estimated to be 71% of total errors), or he strikes out.

PM is then figured as the average of PM1 and PM2, and DER follows:

DER = PM/(PM + H - HR + .71E)

I have gone with the PA form, as many others have--it takes a lot more effort to run down team outfield assists, and the two estimates are always very close.

For 1990-2009, here are the correlations between each of these metrics, plus Run Average, Unearned Run Average, and W%. I'm not offering this table up as being analytically important, and some of the correlations are silly--BMR with DER, for instance. The computer spits them all out, though, so I might as well list them:

As always, you have to be careful when interpreting correlations of this sort, and not putting too much stock in them. mFA and kFA have weaker correlations with W% and RA than FA, but that is not unexpected and tells us next to nothing about their performance as measures of fielding. Removing strikeouts isolates fielding results, but removes valuable information about how good the team was at defense overall (defense defined as pitching + fielding).