There's a Stat for That: UZR

UZR or Ultimate Zone Rating is becoing a standard defensive metric, but I worry a little that it's popularity stems mostly from being readily available at FanGraphs.com. So I was excited a couple of months ago to stumble across and interview with the developer of UZR, Mitchel Lichtman at BaseballDailyDigest.com, conducted by Joel Hamrahi. I can't find it on that site anymore, but what follows is a synopsis of how it works.

UZR starts with a map of the field that divides it into 22 slices and then divides those up into distances of 30-35 feet. (Just so you can picture it, I threw together the dreadful little drawing on the left.) For each of those spots it has been computed from historical data what percentage of the time a ball is turned into outs.

In addition, each of those probabilities are broken down into more granular probabilities based on further conditions. Those other conditions are important, so Lichtman specified them. They are:

(The most notable exception in my mind? There is nothing on the type of hit (line drive, fly ball, etc) or on the speed at which the ball got to that zone, which I would think would be fairly important in determining how likely it was to be fielded.)

So, basically you have a huge table that has location and the rest of these conditions as columns, and for every possible combination of those, it has the percentage of time a ball is turned into an out by each fielder. Based on those percentages, a fielder gets or loses varying amounts of credit for their performance. For instance, if Jermaine Dye catches a ball that 90% of right fielders catch, he gets credit for 10% of an out. If he misses a ball that 60% of right fielders catch, he loses 60% of an out.

Then UZR turns those plays into runs using a very high level metric. It counts an out as .28 runs, an infield hit as .5 runs and an outfield hit as .6 runs. Since every ball is one or the other, I'm assuming that a play by an infielder credits or subrtracts .78 runs, and an outfielders play counts as .88 runs. So I think that if we go back to our outfielder who got credit for 10% of a catch, he gains .088 runs for that catch.

Lichtman goes into more detail, and I think a few of them are important. First, he rightly points out that in his system "fielder positioning is inherent in the results." He also only tracks flyballs to outfielders and groundballs to infielders, so an outfielder who misplays ground balls isn't penalized. He also adjusts the final numbers based on the outfielders throws. He adjusts for park factors. And finally, an outfielder is never penalized if a gap hit is caught by another outfielder, but is if it is a hit.

One can make a case that he is penalized by this system in at least a few ways.

1. Those probabilities aren't park specific. So if a ball hit 350 feet down the right field line is caught XX% of the time, Cuddyer is going to be penalized that XX% every time - because the wall is only 328 feet from home plate. It isn't clear just how big a difference that is, but consider that in the spacious left field of the Metrodome, Denard Span's UZR looks fantastic, but in right field it look's terrible. Does that make any sense? Of course not - excpet that there is a lot more room in left field to make plays that might look good compared to other parks.

2. If Cuddyer holds a runner to a single by playing a ball off the wall cleanly, he gets no extra credit for it. Run are determined by multiplying a number by the outs/hits the outfielder made. That's it. Thus, it also doesn't matter if the outfielder misses the ball because it drop in front of him or if it gets over his head and rolls to the wall.

So, we know UZR isn't perfect, but neither is any stat really. I'm sure when batting average was introduced it was pointed out that some batters were facing tougher pitchers than other batters, or that a single didn't mean as much with two outs in a five-run game as it did leading off a tie game. That didn't stop it from being valuable.

In case you're intersted, you can find the Twins current UZR's here.