UZR, multiple positionsThe UZR of a player at multiple positions, 1999-2002© Tangotiger
UZR measures the runs saved relative to the average fielder at that position. However, the average CF is a much better fielder than the average LF. But, how much better?
Let's look at our 3 OF positions, and look at all players who played at multiple OF positions. The UZR of our sample player who played LF and CF was +10 and -4. That is, our player who plays LF was +10 better than the average LF, but 4 runs worse than the average CF. Conclusion? The average LF is 14 runs worse than the average CF. Comparing RF to CF, and we also find that the average CF is 14 runs better than the average RF. Comparing LF and RF, and the average LF is 3 runs better than the average RF. Listing this mathematically, and we have:
As you can see, it doesn't add up perfectly, but it's pretty close. The total number of games in the comparisons is over 8,000 among the three matched pairs. Trying to "force" a match, and realizing that the sample of LF-RF is twice that of the other two samples, and we can establish this mathematical equation:
In this case, this does add up.
Let's do the same between 2B, SS, 3B. The mathematical sample equations are:
Forcing in the true equations, and we get:
Again, not a perfect fit, but pretty close.
Now that we've established the adjustments among these similar positions, how about comparing the IF to the OF? Of the players who played CF-2B, CF-SS, and CF-3B, in each of the three cases, we determine that the average IF is about 3 better than the average CF (total games in the 3 matched pairs is about 500 games. That's not much of a sample.) Doing the same for IF-LF and IF-RF, and we get the following equations:
Again, performing more "forcing" and looking at the sample size of each matched pair, the mathematical equation comes out to:
Finally, let's look at 1B. In every matched pair of 1B to the other 6 positions, 1B came out worse (which we expected). We get the following sample equations:
Seeing that we have OF + 8 = IF, let's adjust our 1B equation to conform to that.
So, to recap, we have
Creating a neutral 3to9 position, and we have:
This looks alot like the fielding spectrum that we've come to know and love. I performed a much more convoluted process to try to minimize the differences between the matched pairs, using the sample size, and here are the results:
Now, what are the problems? Well, the matched pairs are only among those players that the managers have decided to try at multiple positions. Therefore, we have selective sampling issues to contend with. As well, I've made no attempt (yet) to adjust for Primary or Secondary positions. I'm a little bothered that 1B doesn't come out worse, but that may be a sample size issue as well. Or more likely, the really bad 1B will never get the chance to play in the OF and really drag down the averages alot more than the guys who are good enough to hold their own a little better at multiple positions. It's about exposing weaknesses and leveraging abilities.
What I should do next time is to break up UZR into a rate stat first. That is, UZR is a combination of runs above average per play times the number of plays. Since not all positions get the same number of plays, there is probably something happening in one variable that is not being captured very well. I didn't explain it well, but I'll try to elaborate next time.
Revised: added the following
I changed the process so that I look at "UZR runs / play", rather than UZR runs. From that standpoint, here are the adjustments:
In parenthesis are the "plays / game" that I used. If someone wants to provide more accurate figures, please post them here.
So, how do we use all this? Let's take a simple example (and most popular matched-pair), the 7-9. If you have a LF, let's call him Moises Alou, and he is -.003 runs / play relative to all LF, then how would he do at RF? Since the difference is .005 runs, he'd be +.002 runs / play at RF, relative to all RF. Giving him 3 x 162 plays in RF, that works out to 3 x 162 x .002 = +1 runs in this case.
Let's take an extreme example. Say you move Todd Zeile from 1B to SS, what happens? Let's say Zeile is +.02 runs / play at 1B better than the avg 1B. The conversion rate between 1B and SS is .036 runs / play. Zeile would then become -.016 runs / play at SS. So, at 1B he was worth .02 x 2 x 162 = +6 runs above the average 1B fielder. At SS, he is -.016 x 6 x 162 = -16 runs compared to the avg SS. (Works the same way if you do Jeter going the other way.)
Now, this was what I was trying to say. In the Zeile case, we see that the difference between the avg 1B and avg SS is 22 runs, and not the 16 runs I came up with, with my original process. This is due to splitting up the rate (quality) portion of performance, from the quantity portion of performance.
This will be even more apparent in the following example. Say you move Zeile from 1B to RF. That makes him +.020 runs / play at 1B and +.016 runs / play at RF. Working it out, and he is +6 runs at 1B and +8 runs at RF. Even though he is now being measured against a HIGHER quality of fielder (avg RF), he now comes out looking BETTER. This is because of the quality-quantity issue. It's about leveraging his abilities.
Practical Application
The following table summarizes the findings in an easy-to-use table. I take 7 players of varying fielding ability from horrible (-36 runs / 162 GP at a neutral position) to great (+36). Then, I take each player, and using the conversion rates, and opportunity to field, and determine how that player would do at each of the 7 fielding positions. For example, let's assume that an average overall fielder is named Hubie Raines (the "0" column). If he were to play 1B, how much value would be have relative to the average existing 1B ? My estimate is +8 runs. If Hubie were to play SS, he would be -11 runs, relative to the average SS.
We see that "Ozzie" would have the same value to himself regardless of the position he would play (though to the team the benefit is to put him at SS; more on that in a second). However, "Cecil" has no choice but to play 1B (or DH).
Let's say we have two OF, one named "Andruw" who is a "+24" neutral, and another named "Larry", who is a "0" neutral. We need to put them at LF and CF. What happens? Well, if you put the better one at CF, he'd be +22 relative to the average CF, and the other guy would be +8 relative to the average LF. Impact for the team? +30 runs. If we put Andruw at LF (+26) and Larry at CF (-3), the impact on the team is +23 runs. (Based on their neutral position fielding value, they total +24.)
This problem of trying to optimize your fielders among the positions is similar to the optimization of the batting order. It's all about leverage. Maximize the quality-quantity for the good players, and minimize the quality-quantity aspect for the bad players.
Yankees
Now, just for fun, let's do the Yankees. Let's assume the following "neutral position" values: Giambi -24, Soriano -12, Jeter 0, Ventura +12, Matsui +12, Bernie 0, Mondesi 0. (Let's ignore arm for this exercise.) Who should play where? These 7 fielders combined are -12 at neutral positions. At their current positions, they total -6 runs. How much can we optimize that? Well, how about we move Matsui to CF, Ventura to SS, Jeter to 3B, Bernie to 2B, and Soriano to LF? I get +9 runs for that, or a whopping increase of 15 runs by optimization.
There are problems, which should be apparent. The biggest one is that these conversion/optimization factors are based on average-type fielders. The fielding traits of a 3B is a little different than that of a SS. It just so happens that Ventura is able to... there's that word coming up... leverage his tools better at 3B than he could at SS. His weaknesses would be quickly exposed at SS, and he probably wouldn't be much of an improvement over Jeter. Moving the OF to IF, like Bernie, has other issues as well. All in all, this is an interesting exercise. If we can add more variables (like foot speed, arm strength, reflex, sure-handedness), we'd be in a much better position to construct a valid conversion table. What I've presented is only the first step.
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