Big League Stew - MLB

The world of advanced baseball statistics can be an intimidating place for those of us who slept our way through advanced algebra or haven't been a follower of the Bill James revolution from the beginning. 

Still, that doesn't mean that we should feel left out when it comes to another way of understanding and appreciating the game we all love. With that in mind, BLS stat doctor Alex Remington will explore a new advanced statistic each week during the offseason, providing a simple primer for the uninitiated.

Today's statistic: UZR

What does it stand for?: Ultimate Zone Rating. Devised by baseball statistician Mitchel Lichtman, it's based on Zone Rating, a defensive stat kept by STATS, Inc. that measures a fielder's success at getting to balls determined to be in his "zone" of the playing field.

How to calculate UZR: The baseball field is divided into 78 zones, 64 of which are used in UZR calculation. (As Lichtman explains, infield line drives, infield pop flies, and outfield foul balls are ignored. Pitchers and catchers are not included.)

Here's what is calculated for each zone: the out rate and the percentage of balls in that zone that turn into outs. The league average out rate is then subtracted from the player's out rate — if this number is negative, it means the player is worse than league average. If it's positive, it means he's better than league average.

That rate is then multiplied by the number of balls that hit in that player's zone. This yields a Zone Rating. To obtain the run value, it's multiplied by the Zone Ratings that are calculated for each zone the fielder covers, and then summed. This sum is a simple, unadjusted UZR. It is then further adjusted for park factors, batted ball speed, which side of the plate the batter was hitting from, the pitcher's groundball/flyball ratio and the number of baserunners and outs at the time. The adjustments are made because each of these variables can significantly affect the average out rate in a particular zone. Using run expectancy charts, these rates can be converted to runs.

Got all that? Yes, it's rather complicated.

What UZR is good for: This part is easy. UZR attempts to measure how good or bad a fielder is, as compared to the league average. There are serious sample size problems and UZR often has major fluctuations from month to month and even year to year. Because of that many people prefer to look at three-year UZRs in order to have stable data.

But if you keep the sample size caveats in mind, UZR is an excellent way to eyeball a player's defensive impact on his team in terms of the runs he personally prevents. Because UZR is stated in terms of runs, it can be compared to the number of runs a player personally puts on the board for his team. (On FanGraphs, those batting runs are often expressed in terms of Runs Above Average, calculated from wOBA.) These comparisons can be eye-opening — sometimes the best sluggers are such poor fielders that they literally give back with the glove everything that they add with the bat. For example, in 2008 and 2009, according to FanGraphs, Adam Dunn(notes) had 61.9 batting runs and -64.3 fielding runs. Because UZR is parallel to batting run measures, they can also be incorporated into a more general all-purpose stat like WAR.

When UZR doesn't work: As with batting average, there are frequent, serious sample size problems associated with UZR. (These sample size problems mean that FanGraphs' UZR/150, a pro-rated version of UZR that prorates performance to a 150-game season, should be used at one's peril. It's useful to have a standardized number to compare across players, to compare their defensive impact across the exact same number of outs — but 150 defensive games is not generally a sufficient sample size for UZR.)

A player's one-year UZR is not a good measure of his true talent level as a fielder, nor is it a good predictor of future performance. UZR also frequently conflicts — or at least it doesn't perfectly align — with the other major defensive stat in use, John Dewan's Plus/Minus, which is published in The Fielding Bible and on Bill James Online.

These differences can often be significant. While Adam Dunn had -64.3 fielding runs by UZR in 2008 and 2009, by Plus/Minus he was only at -45 — still appallingly bad, but 20 runs is a major difference.

Lichtman discusses the contrasts between his stat and Dewan's stat here. Both ultimately make use of a lot of the same data, which is determined by humans watching video of every play and assigning numerical values to what happened. They use different methodologies, but both are predicated on the same concept, trying to determine how many balls a fielder got to at a particular place on the field that other fielders would not have gotten to. Lichtman clearly prefers his own, but rather than discarding either, it's probably best to just keep both in mind when assessing how good a fielder is, rather than trying to get by on UZR alone.

Also, as The Sports Ph.D. has written, "UZR has one large minus: It is almost completely inaccessible to any but the most devoted sabermetric fan. Casual fans can understand it and look it up on sites that list it, but they don't have access to the data necessary to calculate it easily." We're simply not at a point where defense can be measured both accurately and precisely without a very large sample size.

Why we care about UZR: It's a very easy to use stat — provided, of course, that you can just look it up. While it's not the ideal defensive stat, because it conflicts with Plus/Minus and requires a large sample size, it's infinitely better than what we had before, which was essentially fielding percentage, the dubious list of past Gold Glove winners, and nothing else.

A lot of the innovations in defensive statistics are being done by the teams themselves, who have hired some of the most prominent sabermetricians in the business — including Bill James, Mitchel Lichtman, and Tom Tango — to do proprietary work for them. So the bleeding edge of defensive stats isn't widely available. But for ease of use, wide availability, and improvement over what we had before, it's hard to beat UZR.

Next week's lesson: Bill James' Hall of Fame predictors (Black Ink, Grey Ink, Hall of Fame Standards, and Hall of Fame Monitor)

Previous lessons: BABIP, OPS+, FIP, wOBA, WPA, WAR

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