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Statistically Significant: UZR

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Defensive stats are a relatively new area of study, compared to offensive and pitching stats. Unfortunately, they're also some of the most complicated and unwieldy stats in the baseball toolbox, which leads to a lot of misconceptions and misunderstandings. But if used correctly, they can be incredibly powerful tools. In the fashion that I covered wOBA and FIP, I'd like to run through one of the most widely used defensive stats, Ultimate Zone Rating (UZR), a comprehensive statistic for both outfielders and infielders. This topic is a monster, so I'm only going to talk about the reasons for its creation and how to use it. If you're more curious, the creator, Mitchel Lichtman (co-author of The Book) has a very thorough and informative primer on the details here.

Before advanced defensive statistics were created, fielders were usually judged by eye, or if a number was needed, fielding percentage. Fielding percentage is simply the ratio of putouts and assists to total fielding chances, or in other words, it shows how frequently a fielder is able to successfully field a batted ball without making an error. The problem? It measures a fielder's reliability fairly well, but it says nothing about defensive range, which is a far more important factor. A shortstop who dives and tips the ball off of the end of his glove gets dinged with an error, but a weaker shortstop who dives and misses it entirely gets no error, and no bad mark on his fielding percentage. Another problem with analyzing defense is that more than anywhere else in baseball, our eyes often lie to us. An outfielder who makes a brilliant diving catch makes fans get up out of their seats, and yet, a better outfielder who makes the same catch without breaking his stride goes relatively unnoticed.

So how does it all work? UZR is expressed in the universal currency of all of baseball—runs. Zero is set at an average defensive performance for that position in the same year. A UZR of 6.0, for example, means that a particular fielder was six runs above average, or, in other words, he saved his team six runs more than the average fielder for his position that year. And, as you would expect, a UZR of -3.0 means that the fielder in question is three runs worse than average, meaning he has allowed three runs more than the average fielder at his position.

Now, it's important to note that these aren't actual runs. What I mean is that UZR doesn't count a run every time a fielder allows a baserunner that comes around to score. Instead, much like wOBA and FIP (among others), each play is given a fraction of a run based on its difficulty and importance, independent of any kind of game context. The engine behind UZR looks at a play and determines how much of a run that play was worth. Easy plays like soft groundballs or high outfield fly balls are almost never botched, so a successful putout gives a very small amount of positive credit to a fielder, while a failure to create an out results in a large negative hit. And as you'd expect, the opposite is true for very difficult plays, where failure results in a small negative tick and success is rewarded with a large UZR boost.

If you go to a site like Fangraphs and look up the current league leaders in UZR, you'll see a large and daunting spreadsheet full of all kinds of numbers. I'll do my best to explain them all in an easy and concise manner.

In the way Fangraphs is currently set up, UZR's section sits in the "Advanced" section of the fielding stat page (click here to follow along). All of the numbers in the columns to the right of the rightmost bold divider belong to UZR. These numbers are under columns titled "ARM", "DPR", "RngR", "ErrR", UZR", and "UZR/150". The first four columns are component stats that are all added up to create UZR. In order, they measure arm strength (for outfielders only, based on outfield assists), double play ability (for infielders only, based on the amount of double plays turned), range (for all fielders), and errors (also for all fielders, based on the amount of errors committed). These four stats are all summed up, and the results are in the fifth column, which gives the total amount of runs a fielder has given or taken away from his team. And finally, the last column, "UZR/150", calculates the UZR out to 150 defensive games, so fielders can be compared to each other on a level playing field.

A note about "defensive games": Even if two shortstops play the same amount of innings, it still may not be fair to compare their UZRs. A shortstop that played for a team with lots of groundball pitchers would get a lot more fielding chances than a shortstop that played behind pitchers who racked up strikeouts or otherwise kept the ball off of the ground. The concept of defensive games was introduced to adjust UZR so that every fielder had the same amount of fielding chances.

But the main downside of UZR? Like any other defensive stat, it's sample size. For batting stats, a full-time player gets somewhere north of 600 plate appearances. For defensive stats? Most of the plays that a defender makes are simple easy plays that most college fielders could execute every time. These plays tell us essentially nothing. The plays that separate great fielders from average ones only happen once or twice a week. Because of that, UZR requires around two and a half years to reach the same level of statistical reliability that one year of a batting stat like OPS has. Therefore, it's important to look at multiple years of UZR before making a decision on the quality of a fielder. One great season in a sea of average ones could just be a statistical blip, but several great seasons can pretty confidently show that a fielder is indeed a very good defender.

UZR really shows off its muscle if you go back and compare it to fielding percentage. For example, Derek Jeter almost never makes a mistake with batted balls he can reach. He regularly sets each season's high-water mark at shortstop in fielding percentage. And yet, his problem is that his range has deteriorated so much with age that he's a pretty poor fielder overall. And on the other side, Cliff Pennington is currently the sixth-worst shortstop in baseball by fielding percentage, but in actuality, he's extremely stout defensively. Pennington's huge range allows him to get to balls that many other shortstops would miss entirely. It also gives more chances for errors on difficult plays, but his extended range is definitely worth that price.

Oh, and if you add up Oakland's total UZR? Best defense in the American League, which currently stands over 40 runs above average. Trevor Cahill owes his defense a nice dinner.

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Athletics lead the series 1-0

Mon 09/13 WP: Bobby Cramer (1 - 0)
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Oakland Athletics
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Tuesday, Sep 14, 2010, 5:10 PM PDT
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Gio Gonzalez vs Zack Greinke

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