Tango on Baseball Archives

UZR, multiple positions (July 7, 2003)

Doing a matched-pair study of players who played at multiple positions, using UZR.
--posted by TangoTiger at 04:51 PM EDT

Posted 5:19 p.m., July 7, 2003 (#1) - David Smyth
Nice work, Tango. I encourage and appreciate all of the effort possible with this method (the DPA). But in the end, I don't think it will ever equal the OPA (given sufficient sample size for both).

Posted 6:25 p.m., July 7, 2003 (#2) - MAH
Tango, very interesting. As a practical matter, the selective sampling issue might not be very important. No one would ever consider putting Frank Thomas at third or left, so the fact that his absence from the sample causes the first base rating to seem a little high is not important. What the study suggests is that among the subgroup of players that it would not be crazy to shift around, the likely impact of shifting them around should be what you found. In a sense, the "selective" sample is the relevant sample.

Posted 6:41 p.m., July 7, 2003 (#3) - ADP
This is terrific work. It also suggests a better way of comparing players at diffrent positions. If the average SS contributes 19 more runs with his glovethan the average RF, we can use this amount to perform position adjustments.

This is better than the usual approach of using the average offensive performance at each position, which is based on the assumption that the average SS and the average RF are equally valuable.

The "equal value assumption" has always troubled me, both because it is an a priori assumption based on computational convenience and not hard evidence, and because it is clearly not true in other sports or even in other levels of baseball (the average high school SS is much more valuable than the average right fielder).

Posted 9:10 p.m., July 7, 2003 (#4) - tangotiger
ADP, you comment about high-school SS, or other sports (say like an avg NFL QB v avg NFL OT) are bang-on, and something that I've been talking about at fanhome for the longest time.

It's a given that the avg HS SS is better than the avg HS player at almost any other position (except for probably pitcher). So, if we were to expand MLB to 3000 teams, I think we can say the same thing. What if we only had 6 MLB teams? (The NHL had 6 teams for the longest time.) Well, I think we can see how maybe the avg LF or the avg SS in MLB might be better than at other positions. So, somewhere between 6 and 3000 teams, there's a balance where the avg player at each position is equivalent.

There's no reason that balance has to be at 26 or 30 teams. And really, we shouldn't even look for it. We also shouldn't expect that if you do find that the balance should exist for 30 teams that this should exist EVERY YEAR. Sometimes, the avg SS overall is better than average, or the avg 1B overall is better. Why balance to every year?

I think we can maybe accept that over a 25-year period, there would be a balance, but that's only to make our life easier. That trying to balance it to the last 2 or 3 runs might be not worth our while. And maybe that's true. But, to use a 1-year adjustment is just plain wrong.

Posted 7:24 a.m., July 8, 2003 (#5) - David Smyth
According to those numbers, the 3B DPA is at +5 (meaning 5 runs better than avg). Assuming that his OPA is at zero for the sake of argument, this means (I think) that the 3Bman is essentially about 5 runs/162G better than his adj. Slwts/162G. So if a 3Bman and somebody at another position both have +25 adj Slwts/162, the 3Bman is actually better, or more valuable. So an avg 3Bman is an above avg player overall, I guess. But since every team has to field a player at each position, it's not apparent what advantage this could confer. I guess it might be useful in MVP discussions.

Posted 9:13 a.m., July 8, 2003 (#6) - tangotiger
David, you are probably right that the avg 3B is probably better than the avg player overall (since I believe as a hitter, he is lg average).

I don't buy the "someone has to play that position", because you can make that argument about HS baseball too, or NFL. The avg QB gets paid far more than the avg at other positions. The avg HS SS is far better than the avg HS at most other positions. Every team needs a QB or SS.

This is useful not only for MVP discussion, but for how much to pay the player. The avg 3B, if the above analysis is correct (above average fielder, average hitter) should be paid more than the average player overall.

Posted 10:33 a.m., July 8, 2003 (#7) - tangotiger
I have revised my process. Please see article above, and page down to the "Revised" section.

Posted 3:08 p.m., July 8, 2003 (#8) - tangotiger
I revised the article again. In addition to the "Revised" section, look for the "Practical Application" section.

Posted 10:14 a.m., July 9, 2003 (#9) - David Smyth
The Yankees thing is pretty cool. Obviously, if they made that change today, including Bernie at 2nd (healthy, of course) and Ventura at SS, they would not gain 15 runs. They would lose runs, I think. And once you inlclude all of the other variables in the conversion, you probably end up where they are now.

Tango, how much confidence do you have in those UZR conversion values, compared with the OPA values? And you did not elaborate on the process you used to generate your "final" values.

Posted 10:29 a.m., July 9, 2003 (#10) - tangotiger
Well, it is only based on 4 years of data, so just generally confidant. If you want to bump some position up or down .003 runs / play (about 2 runs / 162 GP), I wouldn't disagree with you.

I'm a little annoyed about the LF-RF thing not being closer. But with the largest matched-pair being LF-RF, of all the matchups, that's the one that we should have the most confidence in. As well, position-wise, there's really very little difference in playing LF or RF (though I suppose if you wanted to add a trait like "what's his UZR against LH/RH while in LF/RF, that would be a good thing).

Generally speaking, the values I presented are in-line with the fielding spectrum.

As for the Yankees comment, putting Bernie at LF and Matsui in CF should be done immediately. Switching say Jeter for Ventura is probably a net loss, knowing the traits of these 2 players specifically. Generally, you want your better fielder at SS and worse at 3B, but when one guy is 27 and the other is 35 (or whatever), speed becomes critical. Putting say Soriano at LF and Bernie at 2B I think might also be a positive (after some time).

As for the process, what I did was take UZR / 162 GP and turned that into UZR / play. (using 4 plays per game for 3b, 3 plays for lf,rf, etc...). That gives you this list that I published
6 +.011 (6)
4 +.009 (5)
5 +.007 (4)
8 +.005 (4)
7 -.016 (3)
9 -.021 (3)
3 -.025 (2)

Then, that final table was generated using only the above figures (difference in runs / play, and number of total plays / 162 GP). If you look at the Hubie column, those would be the neutral "posistional adjustments".

Posted 5:14 p.m., July 9, 2003 (#11) - tangotiger
I'm looking at the LF-RF mulitple positioning, and I split it up into "Primary LF", "Primary RF", "Neutral LF/RF", with the split being that the primary position is at least 50% more games than the secondary position. In each matchup, there was between 1100 and 1700 games, which is pretty good.

Anyway, when the player whose position was a primary LF got moved to RF, this was the change:
- 7 runs to +2 runs.

So, right away, we know that the guy who moves from LF to RF is a below-average LF, and he becomes above average at RF.

What about the primary RF who moves to LF? He was +1 run at RF and +2 runs in LF. So, an average RF gets moved to LF, and he continues to be around average. In fact, he looks slightly better.

And what about the players with no primary positions? They were -2 runs in LF and -4 runs in RF, meaning that there was tougher competion in RF (and that the guys with no primary position were below average).

It seems that the next breakdown I should do would be based on:
primary LF - above average
primary LF - average
primary LF - below average
... how does each do when moved to RF?

Repeat for primary RF moving to LF, and non-primaries.

Not sure when I'll get to it, but I also want to repeat this for the 2b/ss, the other natural comparison point.

Posted 10:11 a.m., July 10, 2003 (#12) - tangotiger
Breaking down by Primary, Seconday and Neutral positions adds an interesting layer.

Let's look at the IF, starting with SS as the primary position. I will present the UZR runs / play at each position, relative to the league average of that position.

SS/2B (823): 0.000, -.004
SS/3B (647): +.001, +.008

So, what does this mean? In the 823 games where our player played at SS and 2B, with SS being the primary position of the player, he performed at league average level at SS, and slightly BELOW league average at 2B. Since we "know" that the average 2B is a worse fielder than the avg SS, we would have expected that our SS would have performed better at 2B. He didn't. Sample size is an issue. The other factor would be experience, that there's a natural dropoff in performance when playing at a secondary position. On the other hand, looking at SS/3B, we get pretty much what we expected. We have essentially an average SS performing very well at 3B.

Let's look at the 2B as the primary position
2B/3B (689): +.002, +.001
2B/SS (710); +.013, +.001

We see that the guys who shift from 2B to 3B are slightly above average fielders as 2B. They pretty much maintain that same level of performance at 3B.

The next line is the very interesting one. Of the players whose primary position is 2B, and they were asked to play SS, they were the cream of the crop, with a very very above average +.013 runs / play at 2B (the equivalent of +11 runs / 162 GP). When they played at SS, they performed essentially as the equivalent of a league average SS.

Finally, with 3B as the primary position:
3B/2B (638): +.022, -.008
3B/SS (513): +.017, +.007

The 3B to 2B shift is only done with very good 3B, and they end up performing below average at 2B. Interestingly, the same level of 3B also gets moved to SS, but he performs at an above average level at SS. That is, there is more of a dropoff going to 2B than to SS, even though the base talent level he is being compared to is higher at SS than 2B.

Wheh! That's alot of inconsistencies on the surface. With a sample of 670 games, at 5 plays per game, and .8 runs / play, one standard deviation is .006 runs. Essentially, I really don't have the sample size here to say anything with confidence. So, what I'm about to say in the rest of the article, I'm saying it without the numbers actually supporting me.

The SS to 3B move indicates that the avg SS is .007 runs / play better than the avg 3B. The 3B to SS move indicates a .010 runs advantage for the SS. Splitting the difference, and it works out to a .009 advantage. We can even say that the difference between the .009 and .007 is the "experience/familiarity/similarity" factor.

Doing the same process for SS to 2B (.004 advantage to 2B) and 2B to SS (.012 advantage to the SS), and we can say that the SS gets a .004 advantage (with that whopping .008 difference being the familiarity factor).

The 2B to 3B (.001 advantage to 3B) and 3B to 2B (.030 advantage to 2B) implies a whopping .015 advantage to the 2B, with the largest familiarity factor of the bunch as well. Essentially, it's tough to ask the players to switch between 2B and 3B.

Listing this mathematically, and we have:
3B + .009 = SS
2B + .004 = SS
3B + .015 = 2B

Trying to force a best-fit equation gives us the following spectrum among these three players:
SS: +.004
2B: +.004
3B: -.008

I think what this exercise shows is two important points:
1 - Sample size, sample size, sample size
2 - That the primary/secondary component is critical, since the familiarity/tools aspect comes into play. Specifically, the 2B/3B tools are different enough, such that the experience level to leverage those tools conspire to bring the whole house down.

Anyway, I don't think I can do much more without a large enough sample.

Posted 10:14 a.m., July 10, 2003 (#13) - tangotiger
By the way, based on the level of talent that is moved around, this supports what we already knew: the fielding spectrum is SS/2B/3B. Going from SS to 2B to 3B, the talent level is much less than going from 3B to 2B to SS.

Posted 1:07 p.m., July 10, 2003 (#14) - tangotiger
I had this laying around, so I thought it would be interesting to look at too.

Off LWTS by position, both leagues, 1989-2001.

Pos LWTS
ss -13
c -10
2b -6
cf -1
3b 0
lf 7
rf 9
1b 17

This looks pretty similar to the "Hubie" column. Let me put them up, side-by-side:

Pos...OffLWTS...FieldingAdj (Hubie column)
ss... -13 -11
c... -10 ???
2b... -6 -7
cf... -1 -3
3b... 0 -2
lf... 7 7
rf... 9 10
1b... 17 6

The first column is the actual Offensive value. The second column is how Hubie Raines would play, relative to lg average, at each position.

As you can see, the big difference is at 1B. I mentioned in the article that there's only so much damage a fielder can do at 1B, since the opportunities for damage are less. (Even more so at DH, where the fielding value of Hubie, relative to an average fielder at DH is ZERO.)

If you take col 1 and subtract col 2, you get the overall value at that position. The 1B has a sizeable advantage in this regard (i.e., we put too much penalty on the 1B fielding value.) In pretty much all other cases, it seems that the managers have properly balanced the fielding to their hitting.

Posted 5:49 p.m., July 11, 2003 (#15) - David Smyth
The endpoint of this process is the ability to compare a player to an avg player at an avg position. You can get there, in principle, by doing what Tango is doing here--trying to create a satisfactory DPA (defensive positional adjustment). But as he states, his UZR DPA values are only a first step. And these steps are not easy or straightforward. Another approach might be to simply devise an additional adjustment to the OPA (offensive positional adjustment, used in the Slwts method). The OPA is much more inclusive and complete, compared to the DPA. The only problem is that it doesn't go far enough, and essentially assumes that every position has an equal talent level. The examples used to "disprove" this (high school SS, QBs vs linemen, etc.) are fine, but we "know" that any similar discrepancies in ML ball are on a much smaller scale. Still, it is entirely possible that there are minor differences in positional talenet levels. Can these be detected and adjusted for?

I think the answer is yes, at least in principle. For example, let's say that we expect that the current SS group is an above avg set of players, due to the emergence of ARod et al at around the same time. So the "avg" SS is a better player than the "avg" LF (let's surmise). But the "average" is just a math construct. Where would the actual SS advantage lie? At the star level? At the avg starter level? At the backup/replacement level? All of the above? My theory is that the backup/replacement level should be about the same (in terms of absolute talent) for all the positions. The reason is that it is essentially capped at both ends. At this level, there is a large group of available players, which caps it on the low end. And on the high end, if you are above a certain point, you will be a regular. So there is no reason that I can think of why a backup SS should be a better player than a backup LFer, despite the ARods and Nomars.

How to quantify this? If the marginal player at an avg position is worth -25 Slwts runs/162G, then maybe the marginal SS is worth -29 runs, because of ARod et al. That difference of 4 runs should be added to the adj Slwts/162 for SS, as a secondary adjustment. Of course, I just picked SS as an example to explain--I have no idea, despite ARod and Nomar, whether SS is actually an above avg position. The "range" of this type of adjustment should be much less than the OPA itself--maybe from -4 to +4 runs?

I am not the guy to figure out how to technically compare the low level talent at each position. Maybe use a "percentile" method, over some reasonable sample size of seasons. Tango???? And if there should turn out to be essentially no difference among the positions, then maybe we shouldn't worry too much about the "theoretical" problems with the OPA...

Posted 10:28 p.m., July 11, 2003 (#16) - tangotiger
Excellent post David! I pretty much agree with the sentiment.

I also think the key is to look at the replacement level to help us out. However, I think this applies far more in NFL than MLB. What does the best QB and the best tackle not in the NFL have in common? They are both worth exactly 0 dollars to the NFL team. AND they (pretty much) have no other position to play except QB and tackle, respectively. Therefore, for the NFL, I have no problem setting a player's worth compared to this best player at his position not in the bigs.

In baseball, CF/LF/RF are very much related, as are SS/2B/3B. And the pool to draw from 1B is the largest. C might be a unique position. P is. (And guys who can't make it as an SS/2B/3B can still make it as OF.)

Therefore, I think it's hard to find that replacement level by position. Which is why the multiple-position player analysis comes in handy. It's a built-in conversion factor between positions that you can chain for the whole spectrum. But, as we've found, going from a primary position to a less difficult secondary position is not always advantageous. This is because it's not THAT easy to make the switch (at least insofar as 2b/ss/3b is concerned).

I agree that what I think we will find is that if we use a long-term offensive-based positional adjustment (OPA), we'll be better off. 10 or 20 years or something.

I would NOT do like some people do and use a 1-year OPA.

Posted 11:08 a.m., July 30, 2003 (#17) - tangotiger
Someone sent me an email regarding figuring out position-neutral UZR. Here is my response:

===============================
For example, if you go to the bottom of [the above article], you'll see my hypothetical neutral fielder called Hubie Raines. This fielder, at SS, would be 11 runs below the MLB avg SS. Put him in RF, and he's be 10 runs above the MLB avg RF, etc, etc.

So, in terms of trying to get his neutral fielder rating, and assuming all you know is that he's 11 runs below the MLB avg SS, this translates to "0" relative to ALL fielders.

Trying to look for a best-fit equation, I would then say that
UZR(neutral) = UZR(SS) x 0.667 + 8.

So, Jeter, if we think that he's really a -18 UZR at SS would come out as -4 as a fielder at a neutral position.

Doing the same for 1B: UZR(neutral) = UZR(1B) * 2 - 16

So, if you've got a top 1B who is +10 UZR relative to the avg 1B, he'd come in at +4 as a fielder at a neutral position.

We can of course can't take it to this extreme. There are certain tools of a 1B that just won't translate to SS, and vice-versa. Zeile could be a +10, or more at 1B, but the tools that he can hide at 1B would be exposed at SS. And what he can leverage at 1B might not be exploited at SS.

It is better to think of "what would an average fielder do at this and that position". From this standpoint, now you can compare Jeter's -18 to Hubie's -11. (Jeter is 7 worse). And you can compare Zeile's +10 to Hubie's +8. Zeile is 2 better.

You've given them the same comparsion baseline player, without getting involved with actually figuring out how to move Zeile or Jeter around.

It allows you to do these neutral positional comparisons, without losing the argument (which you would) about moving Zeile to SS or Jeter to 1B.

Posted 3:20 p.m., August 4, 2003 (#18) - tangotiger
Having said what I said above, and all that still holds, for those who wish to compute a UZR(neutral) for all positions, here's the best-fit equations:

Pos...slope... intercept
3 2.0 -16
4 0.8 6
5 1.0 5
6 0.65 8
7 1.3 -10
8 1.0 3
9 1.3 -13

So, for seconbase, it would look like this:
UZR(neutral) = UZR(2B) * 0.8 + 6

A 2B who has a -7.5 UZR as a secondbaseman would be considered an "average" fielder overall.

Again, I'll repeat it. This does not mean that all 2B who are -7.5 would be average at a neutral position. It's just a neat little way to say that an average fielder at a neutral position would be a -7.5 if he played 2B.

You'll end up with weird numbers, if say your 1B was +15 runs above the avg 1B. By this process, this 1B would end up as +14 relative to an average fielder at a neutral position. Hard to believe you can have a 1B that good. But, in reality, what I'm saying is that an average fielder at a neutral position would be +8 as a 1B. So, if you do have a 1B who was +15, then he must have really really leveraged his skills that added an extra 7 runs. What kind of skill? Maybe his height or his scooping or his charging the plate or whatever... things that you essentially not come into play anywhere near as much at a neutral position. And he was able to hide his lack of speed maybe, a skill that would be quickly exposed at a neutral position.

Hope all that was clear...

Posted 7:28 p.m., December 18, 2003 (#19) - tangotiger
I'm going to make this thread "Required Reading of the Week". The article has pertinent information in trying to compare fielders at different positions. Please read the article and all posts herein, prior to commenting.

Posted 10:10 p.m., December 18, 2003 (#20) - MGL
This is good stuff. I will have to re-read before I put out my Super-lwts again...

Posted 10:59 p.m., December 18, 2003 (#21) - tangotiger
I had forgotten that I did work on the primary/secondary position thing (post #12). It's definitely a critical component. As soon as I get my hands on the 2003 UZR, I'll update all this.