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Encyclopedia Brown: Kevin Kouzmanoff & The Case Of The Fluctuating UZR

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The question of Kevin Kouzmanoff's 2011 defense is an important one because it affects how well the A's young ground ball pitchers can be expected to perform. Significant regression on Kouzmanoff's part would not be a "victimless crime" -- rather it would affect Trevor Cahill and Brett Anderson, among others, because any dropoff in the quality of defensive play at 3B will impact the pitchers who rely greatly on their infield defense in order to thrive.

One of the arguments I've made this off-season is that if he is at least as healthy as he was in 2010, I don't expect Kouzmanoff's defense to regress much. I expect his UZR rating to come down, but for his actual performance to remain about the same. This post explains why.

The first thing to note about UZR is that pretty wild year-to-year fluctuations are not uncommon. UZR takes about 3 years of data to stabilize, meaning that in the relatively small sample of one season it is likely to deviate considerably from the "true talent level" but over three seasons it is likely to regress pretty close to the mean (the "true talent level") when you average out the three seasons.

Before looking at Kouzmanoff's UZR data, let me use the concept of coin flips to explain samples, fluctuations, and the difference between the player (or coin) regressing and simply the data regressing. We can all agree (hopefully -- if not, please seek psychiatric help) that a coin's "true level" of ability to come up heads is 50%, and that if we flip a coin 10 times its "true talent level" is 5, and that if we conduct three "seasons" of "10 coin flips" the "true talent level" is 5 each season, and that regardless of what happens in those three seasons if we conduct an exciting fourth season of "let's flip a coin 10 times," the coin's "true talent level" will again be 5.

The thing about flipping a coin 10 times is that it is not at ALL unusual for it to come up heads 7 times, or 3 times. It is so unremarkable that when it happens you should not wonder if the coin is defective. In fact, each occurrence happens 11.7% of the time, meaning that one or the other will happen nearly 1/4 of the time.

So if you conduct three "seasons" of "let's flip a coin 10 times," and your results are 3, 5, 7, your coin is fine, you know that variations happen in small samples. In fact over three seasons, and an overall sample of 30 flips, your coin has come up heads an average of 50% of the time -- which is also the "true talent level" you should expect that coin to have next "season."

In contrast, were you to flip a coin 100 times each "season" it is far less likely that it would come up heads 30 times or 70 times (the odds of each are only .0023%). You'd likely get numbers closer to 50% in each sample, like perhaps 52, 47, 53, and each "season" the results would look more similar to one another.

It's in smaller samples that fluctuations are larger, and these are fluctuations that do not "regress" because they are related to the data itself, not to the coin. In other words, the coin that came up heads 3 times out of 10, then 5 times, then 7 times, did not come up 7 times in order to balance out the data. It's just that as the data grew, eventually the "overs" and the "unders" started balancing each other out, because the odds of being higher than 5 (the "true talent level") and being lower than 5 were equal each time, and eventually it was bound to even out.

Here are Kevin Kouzmanoff's UZR/150 numbers over the last three seasons:

2008: +2.6
2009: +9.9
2010: +17.5

Now it's possible that Kouzmanoff has significantly improved on defense every year, but I don't believe this is the case. It's also possible that Kouzmanoff had a "career year" on defense in 2010 and is bound to significantly regress in 2011, but I don't believe this is the case either. Remember that in a one-season sample, UZR is more like flipping a coin 10 times and that over a three season average it is more like flipping a coin enough times to get a reliable "true talent" baseline.

My belief is that Kouzmanoff has been consistently playing about +10.0 defense throughout his late 20s. In 2008, in a small (only one-year) sample UZR got it way too low. In 2009, in a small (only one-year) sample UZR nailed it. In 2010, in a small (only one-year) sample UZR got it way too high.

And over the three-year average (10.0), UZR totally nailed it. Does this remind you of the coin that came up heads 3, then 5, then 7 times out of 10? That coin enters its 4th "season" with the same ability as it had last season and should be predicted to actually perform at the exact same "ability to come up heads" level it has performed before.

And so will Kouzmanoff who has, by most eyeball accounts, been playing a "very good but not spectacular" 3B all along. Which is consistent with around a +10.0 rating, not a +2.6 (meh) or a +17.5 (ZOMG!). He played "very good but not spectacular" defense last year (great to his right, decent to his left, great charging the ball, inconsistent throwing), and figures to do so again this year. The data will regress and find its mean, but Kouzmanoff will just continue to play +10.0 defense, while UZR fluctuates pretty wildly around that number but averages it in the end.

And if you accept that the data's regression does not reflect any change in what the player is actually doing, and that the regression will take place on the spreadsheet but not on the actual diamond, that's good news for Cahill, good news for Anderson, good news for us.