UZR, 2000-2003, Adjusted by Difficulty of Position (December 21, 2003)
Positional-neutral UZR. (Preliminary.)
You'll notice that the top of the list is filled with SS,2B,3B,CF and Geoff Jenkins and Hidalgo. The bottom of the list is filled with 1B,LF,RF and Bernie Williams.
Added: Dec 22
Part 1
Using players who played multiple positions, but none of which would be considered primary (because of the rather evenness in which they split their time), here are the positional adjustment factors, for UZR Runs:
Pos Per Play Per 162 GP
3 (0.017) (8.3)
4 0.003 2.1
5 0.003 1.8
6 0.007 5.9
7 (0.001) (0.7)
8 0.004 2.8
9 (0.007) (3.6)
The "Per Play" column was determined as a best-fit to minimize the difference against the empirical data, weighted by how often each multiple position matchup occurred. For example, the most popular matchup was the 7-9, with 3277 games. The fielder, when in LF, was .013 runs below the LF average. When the exact same fielder was in RF, he was only .007 runs below the RF average. Since it's the same player in both positions, then we can say that the average MLB RF is .006 runs worse than the average MLB LF. The above table corresponds to this empirical data exactly.
The next most popular matchup was the 8-9 pair, and again, we get an exact match between our above best-fit table, and the empirical data. The third most popular was the 4-6, and again, a perfect match. The fifth most popular was the 4-5, and another perfect fit.
The fourth most popular was the 7-8 pair. The fielder, in LF, was at league average, but in CF he was .011 runs below average. Obviously, the average CF was much better, according to this set of data, than the average LF. However, in order to get a best-fit, the above table only shows a .005 run difference.
The largest source of error was the 4-7 pair, with 372 games. The above table shows a .004 run difference, while the empirical data shows a whopping .032 run difference.
Part 2
This time, I only looked at those players where the Primary Position was easy to determine. And, in this data set, we see an interesting effect, which I'll call the "Familiarity Factor". Let's look at the 4-6 and 6-4 switch. When a primarily SS plays 2B, this player goes from being +.001 above the MLB SS to -.005 relative to the MLB 2B. That's right, the average SS looks WORSE compared to the average 2B, by .006 runs per play.
But, what about the opposite? When a primarily 2B plays SS, this player goes from being +.011 relative to the average 2B (obviously only really good 2B are asked to play SS) to being -.012 relative to the average SS. That's not only a huge swing (.023 runs per play), but contrary to the 6-4 split.
What we have here, possibly, is the Familiarity Factor. If we look at the original table derived by players at non-Primary positions, we see that the avg SS has a .004 run advantage to the avg 2B. Using this, and looking at the 6 to 4 switch, we can give a Familiarity Factor of -.010 for this switch. That is, the SS gains +.004 for moving to 2B compared to the skill levels of the average 2B and SS, but loses .010 for his inexperience.
For the 4 to 6 switch, the Familiarity Factor is -.019. Again, the 2B loses .004 runs per play based on the level of talent at those positions, plus another .019 runs for not being familiar/experienced to play SS.
The biggest problem I have is with the CF. The 8 to 7 should have resulted in a +.005 gain, but it was actually +.022. So, here we have the reverse situation. The CF actually gains an extra +.017 runs compared to what we expected. The 7 to 8 should have resulted in -.005, but was actually -.013, or a Familiarity Factor of -.008. So, the 7 to 8 has a hard time doing the switch, but the 8 to 7 has an extremely easy go of it. The strange part is that the CF adapts far far better than the LF doesn't adapt. The numbers here suggest that you'd want to move your CF to LF and vice-versa. That's rather silly.
The same thing is repeated with CF/RF. The 8 to 9 should have resulted in a +.011 gain, but was actually +.030, or +.019 gain for switching. The 9 to 8 should have resulted in a -.011 change, but was actually -.054, or a whopping Familiarity Factor of -.043 runs.
Clearly, something is going on here, and it may simply be selective sampling. Or, the original table is not representative of all players. That is, the original table was determined by looking at players who were equally able to play CF and LF (according to their managers). However, when you look at players who are primarily LF and they are asked to play CF, perhaps they don't have the skillset to make that transition.
In fact, here is the best-fit table, looking at these Primary-Position players:
Pos Per Play Per 162 GP
3 (0.012) (5.9)
4 (0.011) (9.2)
5 (0.003) (1.8)
6 0.001 0.7
7 0.001 0.4
8 0.023 14.9
9 0.002 1.0
As you can see, this shows that, by far, the most talented fielders are found at CF. This shows a 14 run swing between a CF and the corner positions. The original table shows only a 5 run swing.
This entire table looks suspect. On a per play basis, the average 2B and 1B are even. The whole thing just looks wrong.
If we combine these two tables (which were made up of equal number of games), we get
Pos Per Play Per 162 GP
3 (0.015) (7.1)
4 (0.004) (3.5)
5 (0.000) (0.0)
6 0.004 3.3
7 (0.000) (0.1)
8 0.014 8.8
9 (0.003) (1.3)
I just don't like all this.
Revised: Dec 22
Putting all of my data together, without splitting by "Primary" position or not and trying to find the best-fit, here are the results:
Pos Per Play Per 162 GP
3 (0.018) (8.9)
4 0.003 2.4
5 0.002 1.1
6 0.008 6.5
7 (0.005) (2.5)
8 0.007 4.8
9 (0.007) (3.4)
These numbers are close to my original numbers in the article. The r between the empirical deltas, and this best-fit is .54. So, I propose the following (for the moment):
+7: SS
+5: CF
+2: 2B
+1: 3B
-3: LF,RF
-9: 1B
Cool stuff! How much do you think it would likely change, after whatever refinements can be made are made?
Posted 7:33 p.m.,
December 21, 2003
(#2) -
Charles Saeger(e-mail)
Looks like Jeter is somewhere below a third baseman.
Posted 7:55 p.m.,
December 21, 2003
(#3) -
MGL
Good stuff! The idea of a position-neutral UZR is still rattling around in my head like a pinball on speed. Can you explain a little bit what a chart like that means and how it can be "used" (when you get the time, of course)?
Posted 8:28 p.m.,
December 21, 2003
(#4) -
tangotiger
I don't think it'll change much, but we'll see.
As for its implications, for the most part, you do have the best fielders at the top needing to play in one of the 4 top fielding positions.
There might be some oddball players where they have such a specific skillset, that they can't leverage those skills.
To whoever followins Jenkins: please give us a scouting report.
Posted 9:00 p.m.,
December 21, 2003
(#5) -
MGL
As for its implications, for the most part, you do have the best fielders at the top needing to play in one of the 4 top fielding positions.
That is exaclty what I was saying to DS on the other thread - that when a player is x amount of UZR runs above or below average at his position, where x is some large number, you MUST consider moving him to another position. I could not explain to DS why this is so. Is it because it is easier (and cheaper) to replace a player at an easier defensive position?
Posted 9:04 p.m.,
December 21, 2003
(#6) -
MGL
Does this mean that Rolen, Polanco, and Bell should be considered for SS? Jenkins and Hidalgo should be playing center?
Should all the guys near the bottom who are playing one of the top 4 positions (Bernie, Jeter, et al.) be moved?
Again, unless we have evidence of some special skill set....
Posted 10:10 p.m.,
December 21, 2003
(#7) -
tangotiger
There's only a 4 or 5 run advantage between SS and 2b/3b. However, there is a familiarity disadvantage of moving a 2b to SS, and so you might not make up for all that.
There's also this thing about leveraging skills. If the 2b just doesn't have the arm, the conversion rate would be worse from 2b to ss. That is, if the only difference if the arm, and that's the reason for the 4 run difference, a 2b with a really bad arm might have an 8 run difference, and a 2b with a great arm would have no difference.
Certainly, Jenkins should be considered for CF, but, you'd really have to know how fast he is. Maybe the LF/CF need a quick first step, but the CF needs to be extra fast as well.
Posted 11:12 p.m.,
December 21, 2003
(#8) -
MGL
Tango, say you have a very good CF'er, and you move him to left field and then his UZR numbers are extrmemely high (maybe this is the case with Jenkins - we don't know). How do you explain that he SHOULD be in CF and not LF (assuming that is true), when it appears that wherever you put him the team has the same overall offensive and defensive runs, assuming a replacement player in the position you don't put the fielder?
After all, the flip side of the argument that you MUST comsider moving an extememly gifted defender at one position is that if he were already at that position, you would not move him to the easier position. IOW, if Jenkins is indeed a CF'er in disguise (his UZR in left STRONGLY suggests that he is), you would not even think of moving him to LF. That would be like moving Cameron or Erstad to LF.
The reason I say that a player must be WAY WAY above average (like Jenkins) before you consider moving him, and that then you MUST consider moving him as opposed to just WAY (one "way") above average, like L-Gon or O'Leary, is that if a player is THAT far above average, that is already a VERY STRONG indication that he is playing the wrong position!
Posted 3:51 a.m.,
December 22, 2003
(#9) -
AED
Tango, on the other thread about position difficulties you ended up using UZR runs per play, rather than total UZR runs. I think it would be more useful for players in this table to be shown in UZR runs per play instead of per 162 games; otherwise good shortstops and bad first basemen are overrated, while bad shortstops and good first basemen are underrated. I think this is what caused MGL's confusion -- an above-average player should be at a position that gets more plays to leverage his superior skills.
Posted 4:53 a.m.,
December 22, 2003
(#10) -
MGL
AED, very provocative point! I am interested in Tango's response!
Posted 4:54 a.m.,
December 22, 2003
(#11) -
MGL
Actually, the only problem with that point is that all the OF positions get around the same number of plays (per game)...
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Posted 8:08 a.m.,
December 22, 2003
(#13) -
tangotiger
AED,
Actually, I only work on UZR runs per play. I agree that the chart is a little confusing when you look at it. I'll update it a little later, as well as a step-by-step so that you can see what and why I'm doing what I'm doing.
I'm also working on better positional adjustments, rather than those off-the-cuff ones I'm using.
MGL,
Read the other article I brought forward on multiple positions. I gave a perfect example of moving Andruw Jones to LF and Chipper Jones to CF, and the effect that would have.
Posted 9:46 a.m.,
December 22, 2003
(#14) -
David Smyth
Yes, Andrew and Chipper. I did mention about the leverage factor in my back-and-forth with MGL. Now that I see an example of how much of a difference it would make in the OF, the main remaining questions are, for Jenkins (say), 1) Why was he not a CFer all along (IOW, is there something about his skills/speed), and 2) what is the cost of his having to adapt to a new position, both in defensive runs and possibly in offense (if his effort to adapt distracts him at the plate).
Posted 11:15 a.m.,
December 22, 2003
(#15) -
tangotiger
I added a whole new section in my comments. Please go to the top of this page.
Posted 11:43 a.m.,
December 22, 2003
(#16) -
David Smyth
---"I just don't like all this."
Well, I like it because it (should) get us step closer to understanding the position questions. It's probably just a matter of figuring out why the results are what they are, assuming it's not just selective sampling (or rather, that the sampling component is small).
Very Good work, Tango.
Posted 12:50 p.m.,
December 22, 2003
(#17) -
tangotiger
I guess I don't like it, because there's alot of work left to do!
I added another revision. Go to top of page, and look for it.
Posted 12:54 p.m.,
December 22, 2003
(#18) -
Anonymous
.
Posted 3:03 p.m.,
December 22, 2003
(#19) -
David Smyth
Those numbers show the same thing for CF, as being higher in the def spectrum, as I recall some old DPA numbers did. And yet, CFs seem to be avg or close to it in the OPA. So, CFs "should" be worse hitters than they are? Or, I guess maybe, considering both O and D, CFers are the best baseball players? If you think about it, that does make some sense.
Posted 4:50 p.m.,
December 22, 2003
(#20) -
tangotiger
I have this lying around:
Pos LWTS
ss -13
c -10
2b -6
cf -1
3b 0
lf 7
rf 9
1b 17
Off LWTS by position, both leagues, 1989-2001.
Adding the fielding chart I just put up:
+7: SS+5: CF+2: 2B+1: 3B-3: LF,RF-9: 1B
and we get, overall OFF+DEF:
Pos LWTS
ss -6
2b -4
3b +1
cf +4
lf +4
rf +4
1b +8
(Doesn't add up because of catching.)
Posted 11:40 p.m.,
December 22, 2003
(#21) -
tangotiger
(homepage)
The above homepage link contains the Excel workbook that goes through in step-by-step detail as to how I did all this. (Numbers will be different, as I changed things slightly.)
I used Erstad as the example. Fields in green are given by MGL. Fields in red are set by me. I've tried to make it easy to follow. Let me know if there are any questions.
Posted 11:26 a.m.,
December 23, 2003
(#22) -
tangotiger
The year-to-year r for players with at least 300 BIP was .54 (average of 510 BIP).
My initial regression towards the mean equation for UZR is:
Step 1: rr = 430/BIP
Step 2: regression towards the mean = rr / (1+rr)
So, if the fielder has 510 BIP, rr=.84, and regression = .46
For a fielder with 1500 BIP, the regression would be 22% towards the mean. So, if Erstad is showing +40, he's probably actually +31.
Posted 12:54 p.m.,
December 23, 2003
(#23) -
ColinM
Tango,
OK, that regression seems reasonable. So Erstad probably has a "true" UZR of +31. But what's intersting to me is, how much more should UZR be regressed before you can combine it with an offensive measure to get a total value stat?
What I mean is, in a situation where you want to combine UZR and an offensive rating, shouldn't there be a further regression applied to UZR in order to account for the amount of confidence we have that UZR is actually measuring the right thing?
In another thread you provided a comparison between UZR and David Pinto's method. Both methods seem great, but there are still some pretty big differences there. The r you found was .69. What would the r be between RC and BaseRuns or XR or EQR, etc...? I would guess it would be quite a bit higher, .9 or more? So if you do adjust UZR to account for confidence in the method, how much extra would you regress?
Posted 1:09 p.m.,
December 23, 2003
(#24) -
tangotiger
The r would be at .95 or .99 for those hitting measures. That's because they are really measuring it the same way (the differences only affect a handful of players, like Bonds.)
I'm not sure what should happen if you regress say Off LWTS by 20%, and UZR by 50% and add it up. That is, what's the new confidence interval?
Posted 1:18 p.m.,
December 23, 2003
(#25) -
Charles Saeger(e-mail)
One thing to keep in mind is that the value of a play saved in the outfield is greater than in the infield, since outfielders are responsible for preventing extra-base hits.
Posted 1:32 p.m.,
December 23, 2003
(#26) -
tangotiger
Charlie, this is true. However, the effect is probably on the order of .05 runs or so.
That is, if a single/out is worth around .75 runs, and the double/out is worth 1.05 runs, let's say the following:
of hits saved by IF: 90% are singles
of hits saved by OF: 70% are singles
So, the weighted average comes in at .81 for the IF and .84 for the OF.
Posted 2:04 p.m.,
December 23, 2003
(#27) -
Charles Saeger(e-mail)
Are you sure those proportions are correct? Since UZR doesn't have a flyball component for infielders (unless I am mistaken), more than 90% of all infield outs would be singles. Very few extra base hits come from groundballs.
Posted 2:08 p.m.,
December 23, 2003
(#28) -
tangotiger
Charlie, no, those numbers were just for illustration. I'm just pointing out that the impact is rather contained. Perhaps we are talking about .10 runs per play, or 5 runs difference over a season between the IF and OF.
If I had the more granular data, I would definitely do as you suggest.
Posted 2:30 p.m.,
December 23, 2003
(#29) -
Chris Dial
(homepage)
I don't have more granular data, but when I developed my defensive system off raw ZR numbers (not pbp), I discussed the weightings with Dale Stephenson, and I have those weightings:
SS/2B: (0.9895*plays made*0.75) + (0.0105*pm*1.06)
1B: (0.86*pm*0.75)+(0.125*pm*1.06)+(0.015*pm*1.37)
3B: (0.84*pm*0.75)+(0.158*pm*1.06)+(0.002*pm*1.37)
LF: [(0.76*pm*0.75)+(0.213*pm*1.06)+(0.026*pm*1.37)]*pitf + A*0.59
CF: [(0.76*pm*0.75)+(0.183*pm*1.06)+(0.057*pm*1.37)]*pitf + A*0.59
RF: [(0.76*pm*0.76)+(0.18*pm*1.06)+(0.06*pm*1.37)]*pitf + A*0.59
This comes from the defensive average/defensive runs by Sherri Nichols and the Baseball Workshop.
Tango's off-the-cuff guess of 90% and 70% is correct with respect to the difference - ~20%. It's actually 98.7 versus 76%
Try your analysis with these breakdowns.
Posted 5:16 p.m.,
December 23, 2003
(#30) -
Charles Saeger(e-mail)
Using Chris's numbers: 2b/ss 0.753, cf 0.842. That's about 0.09, and that can add up over the course of a year; an SS who is +50 plays versus a CF who is +50 plays has a difference of 4.5 runs.
Posted 6:14 p.m.,
December 23, 2003
(#31) -
MGL
Colin, Tango's regresson formula for UZR IS the exact amount of regression you want to use before combining it with offense (after regressing the sample offensive lwts) in order to come up with a total player "value," where "value" is an estimate of "true" value...
Posted 11:41 a.m.,
December 24, 2003
(#32) -
ColinM
No MGL, I don't agree with that. In Tango's example he says that after regression, Erstad's "true" UZR value is +31. I'm not arguing that. I'm sure that this is the best guess for Erstad's true UZR. What I'm arguing is that UZR itself is not as good an estimate of a players REAL defensive value as most offensive measurements are of a players REAL offensive value.
Now I'm not trying to critisize UZR here. You do an unbelievable job with it and it is the best thing I've seen for defense. However, as I've already pointed out, all of the many offensive measurements out there correlate extremely well with each other. Tango says this is mainly beacuse they are measuring the same thing. But the reason they are measuring the same thing is because we are really damn sure that this is the best way to measure offensive production!
UZR on the other hand, does not correlate nearly as well to other defensive systems like Pinto's. There just can't be as much confidence that UZR measures real defensive value as well as LWTS measures real offensive value. And you can't just add together two numbers that you have differing levels of confidence in if you want to have the most accurate rankings. You have to further regress UZR. How much further? Well, that's what I was hoping to find an answer for here...
Posted 12:04 p.m.,
December 24, 2003
(#33) -
tangotiger
I don't think you can further regress.
If Erstad is +31, with a 95% interval of +/- 6 runs on fielding, and he's -5, with a 95% interval of +/- 2 runs on hitting, he now becomes +26 with a 95% interval of ???? runs overall.
Assuming the his BIP is 1500 on fielding, and his PAs are 2500 on hitting, maybe it's a simple matter of weighting the interval like that, so you get: 1500*6 + 2500*2 / 4000 = 3.5 runs.
So, maybe ???? is +/- 3.5?
I'll leave this to the stats-savvy to comment on.
Posted 12:39 p.m.,
December 24, 2003
(#34) -
ColinM
Tango,
I'm probably not writing very clearly because you've missed my point entirely. We're talking about two completely different measures of confidence. When you give the 95% CI this is a statistical measure estimated (I think) using UZR's year to year correlation with itsself. What I'm tallking about is confidence that UZR makes a usefull measurement, which is a totally separate thing.
Look, here's a silly example. I created a stat called Defensive Runs Prevented. I calculate this stat by taking the amount of letters in a player's last name and subtracting 7. Erstad had -1 DPR last year. This stat has a 100% year to year correlation, so I'm 100% confident that Erstad's "true" DPR is -1. It needs no regression to the mean! But how much extra should I regress it before I combine it with Off LWTS? Why 100% of course, since I've got no confidence at all that it actually measures defensive value.
See what I mean?
Posted 2:11 p.m.,
December 24, 2003
(#35) -
MGL
Colin M., I understand exaclty what you are saying. I'll have to think about what the answer is in terms of UZR and other components of a player's value. Of course you are talking about the classic difference between "reliability" and "accuracy" in experimental science, where reliability is correlation from one measurement to the other (for the same element), i.e., year to year UZR correaltion, and accuracy is how well the measurement reflects the true value, i.e., how well UZR describes actual fielding talent or value. For example, fielding percentage probably has a high degreee of reliability, but a poor degree of accuracy in terms of defining overall fielding skill (not just error rate).
The more stat-savvy Primates will probably have to chime in on this one. If they do, hopefully they will respond in English rather than stat-ese, which I hate to say it, is the main reason why I hesitate to ask for their help...