THE BOOK--Playing The Percentages In Baseball

Here’s a similar study, using STATS ZR:

http://www.editgrid.com/user/cwyers/moving_between_positions

I’d throw out the CF to 1B numbers - it’s one of the smallest samples of the group, and the results conflict with everything else there.

And I do find that 2B is a more difficult defensive position than 3B, contrary to what your data says. It crops up in both the 2B to 3B data and the SS to 3B and SS to 2B data.

Good stuff.

Ok, you’ve got 1B as almost 4.5 plays (3.5 runs) away from the group of LF/RF/2B/3B, with little difference between LF/RF and 2B/3B. 

SS compared to 2B/3B is 2 runs gap.
2B is between SS/3B.
3B is 2 runs behind SS/2B.

CF compared to LF/RF is 2 runs gap.

So, trying to best-fit it real quick here, we get:
3 SS
1 2B
-1 3B

2 CF
0 LF/RF

-5 1B

This chart sticks to pretty much the findings in Colin’s chart.  If someone wants to try to best-fit it to see if they can get better numbers, feel free.

But, these numbers look way too tight.

You might want to control for aging.  Perhaps only look at players who move in their 20s?

The players in the sample had to play multiple positions on the same team in the same season. So I don’t know how much of an aging effect there’d be.

One thing I will note is that plays is being figured based upon the average ZR of players in the sample, not overall. So the ZR of the average second baseman (for the purposes of this chart) should be the sum of PM_1 / CH for POS_1 being 2B. Otherwise I was running into the problem of second base being the most difficult position on the field according to the chart.

Spreadsheet is updated - now there’s a second tab with similar data for RZR.

The players in the sample had to play multiple positions on the same team in the same season.

Wow, I think that would create severe potential selective sampling problems, not the least of which is that you are essentially excluding established players at their defensive position, like a Jeter.

It does, I guess, help with aging problems, as “established” players will probably only move (to the left in the spectrum) when they are too old and/or injured to play their established position. 

However, you are kind of limiting your sample to mostly players who are utility type players, I think.  They may do well at almost any position (they have that kind of skill set) and that is why they are utility players.

I’ll have to take a look at my data and see what I get. I am not sure that Tango has my latest UZR updates.  The aging problem can be dealt with a little bit by age adjusting all the numbers.

I think it’s a chicken-and-egg question when you get into age versus position adjustments. With a good set of positional adjustments, I think you could build a much better aging curve for fielding, because you substantially cut down on the number of players leaving your sample each year.

For outfielders I don’t think you have as much of a selective sampling issue.

To clarify - a player with one CH at another position technically qualifies for the study, with both of his plays made prorated out to one CH. So utility players do probably dominate the study, but there are chances for established position players to sneak in.

Right, I apply a bit of aging.  I also look at whether the move was from primary 2B to 3B or primary 3B to 2B.  There is an initial familiarity factor to account for, especially IF to OF.

I definitely use the whole 03-07, so that I don’t lose valuable data like say Erstad.

I take it you’re doing performance in Year Y to Year Y+1?

Using UZR data from 04-07, here is what I get:

Players had to played at least 10 games at any position for that position and data to be included in the sample.

No age adjustments.

I used the “delta method” (the only way to do it, I think), using he harmonic mean of the two “games played” for the weighting for that player.

Pairs of positions/total number of “harmonic mean games"/loss or gain from 1st to 2nd per 150 games

34 1001 1.7 (actually did better at second base)
35 2329 -4.8
36 683 -5.0
37 1788 -6.1
38 437 -7.6
39 1913 -9.9

45 2407 2.7
46 3424 -6.4
47 1299 8.7
48 835 -13.8
49 441 -.9

56 168 -4.4
57 349 3.3
58 136 -10.7
59 470 7.8

78 4724 -10.7
79 5158 1.2
89 1466 7.9

Doing a “rough best fit” of the OF positions, we have RF being 1.2 runs “easier” than LF, and CF being 9.3 runs harder than the average of LF and RF.  It makes sense that RF would be a little easier since you have to put your stronger arms there which limits the pool of players.  However, when we look at CF to LF or CF to RF, it looks like LF is easier than RF.  When we combine the combination effects, and call RF and LF equal, we get that CF is 9 runs harder than the corners.

In the IF, the “best fit” seems to be:

The “45” number suggests that third is 2.8 runs easier.  But the “46” and “56” data suggest that 2B is is 2 runs easier (we probably have the issue of “arm” which creates this discrepancy - you need a good arm to play SS and 3B, but not 2B).  The “34” and “35” data really screw things up, suggesting that 2B is much easier at least relative to 1B.

I think I’ll call 2B and 3B even as well (like Tango).  The “46” and “56” data suggest that SS is 5.4 runs harder than 2B or 3B.  And the “35” and “36” data (ignoring the weird “34” data) suggest that 1B is 5 runs easier than 2B, 3B, or SS.

The first base to OF data suggest that 1B is 8 runs easier than the corner outfield.  That suggests that corner outfielders are better than 2B and 3B, which really screws things up.

However, when 2B and 3B also play the corner outfield positions, the numbers suggest that the corner OF is 6 runs easier.  When 2B and 3B also play CF, they are 13 runs worse, which comports with the 2B and 3B to corner OF numbers.

So I will say that 2B and 3B are 5 runs harder than LF and RF.

So here is what I get (very roughly speaking, especially comparing the IF and OF), setting 2B and 3B at zero:

2B 0
3B 0
SS +.5
1B -1
CF +.5
LF/RF -.5

Pretty much same as Tango.

If I do the same thing with age adjustments, here is what I get:

For age adjustments, I assume a player peaks at 26 and gets worse or better by 2 runs a year (per 150) in CF and SS and 1 run per year at all other positions other than 1B.  For 1B, I assume peak at age 30 and 2 runs a year up or down otherwise. 

34 1001 3.1
35 2329 -2.0
36 683 1.4
37 1788 -3.9
38 437 -1.2
39 1913 -6.9

45 2407 2.7
46 3424 -4.0
47 1299 9.3
48 835 -13.1
49 441 -1.3

56 168 -2.8
57 349 2.6
58 136 -11.6
59 470 7.8

78 4724 -11.0
79 5158 1.1
89 1466 7.5

Pretty much the same numbers come out of this.

Tried duplicating MGL’s numbers as best I could. No minimum number of appearances. Using ZR data from 1987-2007:

1B 2B 4077 2.0
1B 3B 13795 15.8
1B CF 2772 -8.1
1B LF 12553 -5.9
1B RF 12019 -1.0
1B SS 2065 -9.8
2B 1B 1448 3.9
2B 3B 23011 15.2
2B CF 4946 4.1
2B LF 7309 -7.1
2B RF 3043 -0.4
2B SS 30997 -7.4
3B 1B 3696 -11.8
3B 2B 1910 -11.5
3B CF 900 -17.3
3B LF 2717 -22.0
3B RF 1714 -15.2
3B SS 4718 -28.9
CF 1B 999 10.6
CF 2B 818 11.3
CF 3B 449 37.0
CF LF 40412 -10.3
CF RF 37406 -6.1
CF SS 42 52.1
LF 1B 795 12.8
LF 2B 253 14.2
LF 3B 336 0.7
LF CF 3171 18.0
LF RF 15087 5.3
LF SS 27 162.1
RF 1B 1101 8.3
RF 3B 31 -45.7
RF CF 3322 6.9
RF LF 5348 -5.5
RF SS 29 71.3
SS 1B 367 6.6
SS 2B 7309 19.4
SS 3B 5142 20.9
SS CF 80 -36.3
SS LF 263 4.0
SS RF 399 42.3

First column is primary position in year one, second column is from year two. Third column is the harmonic mean of ZR chances. Fourth column is the difference in plays made over a full season.

Now, same data, but for players who played both positions in the same season:

1B 2B 5675 3.2
1B 3B 16440 14.2
1B CF 2597 -8.7
1B LF 15468 -6.1
1B RF 13437 0.2
1B SS 3015 1.5
2B 1B 15 -30.4
2B 3B 23900 7.6
2B CF 4345 -9.8
2B LF 5662 -12.3
2B RF 2596 1.1
2B SS 33635 -3.5
3B 1B 95 -11.1
3B 2B 203 -34.9
3B CF 610 -22.9
3B LF 1836 -21.6
3B RF 1067 -9.4
3B SS 5029 -22.7
CF 1B 2 296.0
CF LF 38164 -10.8
CF RF 35647 -4.0
CF SS 59 38.3
LF 1B 55 -5.0
LF CF 14 61.9
LF RF 14154 3.4
LF SS 182 9.9
RF 1B 40 -23.1
RF CF 159 38.4
RF LF 20 59.5
RF SS 44 29.7
SS 2B 242 16.1
SS 3B 267 -0.9
SS RF 4 -59.0

Colin: we actually don’t do year-to-year.  We consider the entire pool (03-07 for me, 04-07 for mgl) as one big clump.  You can apply some age adjustment, but for our case, as you can see, with so few years, it’s not really required.  That’s why for you, you can look at only performance in his 20s as one big clump.

2B 0
3B 0
SS +.5
1B -1
CF +.5
LF/RF -.5

Pretty much same as Tango.

Change “pretty much same” to “exactly”.

Those numbers are all approximated and rounded off (as are yours).  What I meant was that my raw numbers are (apparently) pretty much the same as yours…

oic.

Also note that for those people who simply can’t accept that the CF=SS, then the alternative that I posted at the top of this page, which I will repeat here:
+1.25 C (just forcing this one in)
+0.75 SS
+0.25 2B/3B/CF
-0.75 LF/RF
-1.25 1B

would likely be the limit to what you can do.  I basically dropped the OF/1B by 0.25 and upped the IF/C by 0.25.

These numbers might be more believable, and maybe if we had taken the original chart that we’ve each independently produced (using the same source data) and better addressed the selective sampling issue, perhaps that’s what we’d get.

But I think you have to be very careful.  Originally, the 2B/3B to 1B comp was 1 win, and now we have it at 1.5 wins.  Can we justify it any further than that?  We know that we can’t possibly bring the 1B and corner OF any closer than 0.5 wins.  Once you start to accept some of these things, you kind of are forced to go with these numbers.

I know Dan and Nate Silver have the SS above the catcher, and pretty far from 2B/3B.  I think that is really reaching and, to me, points more to an issue with their methodology than anything.

If we add up all salaries by primary position for all players since 2000, on per 90MM payroll basis, the CF earned 5.7MM and SS earned 5.3MM.  That would mean that the avg CF is, overall, 0.4MM better than SS, or 0.2 wins better than SS.

The average age of both positions is 29.0, so we can guess that they have the same service type of players.

If the avg CF is something like 0.7 wins better than the avg SS on offense, then the avg SS must be 0.5 wins better than the avg CF.  (We are always comparing our guys to say Willie Bloomquist, as to how he would perform at SS or CF.)

So, this gives support to the idea that the second modified chart I provided might make more sense.

3B get 6.0MM (age 29.9) and 2B get 4.2MM (age 29.7).  The 1.8MM gap would be say 0.9 win gap.  If the avg 3B is around 0.9 wins better as a hitter, it would imply that they are even as fielders.

Catchers made as much as SS.  So, if they are a bit worse as hitters, they should be a bit better as fielders.

Little correction: there were more primary SS than primary CF.  If we adjust for that, the implied difference in talent is that CF is +0.3 wins overall.  Doesn’t really change anything.

***

CF made as much as 3B.  They are typically even as hitters.  Maybe someone can double-check if that’s still the case for 2000-2007.  If so, they should be even as fielders.

Note though that 3B are older, meaning that the salaries are probably biased as more free agents or higher arb years.

In fact, the age of 3B is about even as the age of RF.  And RF made 2.0MM more, implying about +1 wins compared to 3B.  If the gap in their hitting is around 1 win, that would make them even as fielders, which certainly doesn’t sound right.

The original chart had them as 0.5 win difference in fielding, and the modified one as 1.0 win difference.

All of this may simply be a market inefficiency.

Finally, the avg OF made 2.0 MM more than the avg IF (2b,ss,3b).  The avg OF is a bit older (0.35 years) so we know there’s a service time issue bias in the salaries. 

I was using 2MM per win, but I should use 2.4MM per win (my base payroll is 90MM).  So, a 2.0MM (unbiased) gap in salary would imply 0.8 win gap between the two groups.

Hitting-wise the average OF is probably about 1.2 wins higher than the average IF?

In order for overall to be +0.8, the IF must be 0.4 wins better than the OF with the glove.  It should actually be a bit higher because the salary is biased against guys with low service time, and that’s more IF than OF.

The original chart said 0.3 wins and the modified chart said 0.8 wins.

I’m starting to think that the modified scale might be more appropriate.  But at this time, it’s still hard to say.

For 2000-07, center fielders created .197 runs/out; third basemen .195.

For the same time period, the infielders are -3.5 runs/650 PA and the outfielders are +8.1.

For what it’s worth.

Yowza, good guesses on my part.  Thanks for that.

Btw, this is what Dan R. gets with his methodology:
+1.1 SS
+0.9 C
+0.3 3B
+0.2 2B
+0.0 CF
-0.6 LF/RF
-1.2 1B

Fairly close to my modified chart.  He’s got 3B/2B/CF right around +0.2, give or take. 

Really, the big problem I have with his is the SS/C.  I don’t see how you can justify the SS to be +0.85 above 2B/3B.

Average free agent salary by position, 1995 - 2007:

1B 2,882,426
2B 1,587,405
3B 1,977,556
C 1,188,414
CF 2,637,642
DH 2,835,364
LF 2,541,120
P 2,025,191
RF 3,135,276
SS 1,865,065

Tango (and others), if we cannot figure out the relative values of the positions after spending hours poring over the data, why are you assuming that the salaries exactly reflect those values?

I think that is way too presumptuous.  What is it that teams know that we don’t? It is more likely that the salaries are an approximation of relative value PLUS all the stupid biases that teams have, such as “you must have defense up the middle, any offense your SS or C give you is a bonus,” etc.

You could make an argument that THEY ought to be scaling their salaries to what WE come up with and NOT vice versa.

I agree that they will come close (as will we), but I don’t think that they will do better than us necessarily.

I was just trying to see it from another angle.  Certainly they’ll have biases in their thinking, just as we have selection biases to deal with.  I’m trying to see how much can we reasonably expect the selection bias to be.  Can we push it to the point where the 3B’s glove is worth 2.0 wins more than the 1B’s glove (guys who play the same position would say that is way too far, and teams are not paying to that level).  So, I think we can reasonably come up with a cap here.

Regardless of how teams pay CF and the corners, I’m not budging on the +1.0 win difference with the glove.  So, I’m sticking hard on some things, and a bit softer where we have more selection bias issues.  And, we have certain boundaries that we’re not going to pass.

The problem is that we know the payroll system is biased. If we line a fielding aging curve up against a hitting aging curve, we see that a player should be hitting the downhill slope of his career as a fielder (if he hasn’t already) when he enters free agency; a player should be just entering or in his hitting peak years as he enters free agency.

This is why, in the salaries I listed, catchers are at the bottom and right fielders are at the top. Teams don’t buy defense in free agency because, by and large, defense isn’t for sale.

As for pre-free agency players, their compensation is largely subject to arbitration. I don’t get the impression that UZR is brought up nearly as often in arbitration hearings as, say, RBIs are.

As far the discrepancies in salaries for the various positions in #20, part of it is probably an age thing, as I assume that 1B, RF, LF, and DH tend to be older FA, who will command more money than younger ones given the same talent.  The other part, is I also assume that there is a tremendous bias towards power hitting 1B, DH, and corner outfielders, not withstanding their positional value.  IOW, teams routinely overpay for these positions (Carlos Lee, Konerko, etc.) because they do not fully understand positional value.  That has to be considered, if it is true.

I also assume that the pool of SS, C, and maybe CF hit a little worse than they could, as teams sort of overvalue defense at these positions (e.g., Ausmus gets to play full-time, but Castro of the Mets is a backup).

There are just too many biases and inefficiencies in the way teams value the various positions as well as the problem of trying to sort out the age factors, that I don’t think it is at all useful to look at salaries as any kind of gauge as to the true defensive positional values.

How do you take into account differences in position due to items not in ratings?

I dont think the zone ratings include the ability to turn the double play. That skill for a 2b has some value, that I dont think we are accounting for. If it is worth .2 runs (just making it up right now, I dont have an idea), should you add that to the 2b spot?

Likewise arm for RF - there is some value to the player’s arm in RF

there are going to be some OF who cant play RF because of his arm, but I dont think there are very many RFs who cant play LF. Take 30 guys and call them OF - 10 of the fastest play CF, the next 10 best arms play RF, the last 10 play LF.

Good question.

If you look at players who play both positions, you will find that the average LF arm is going to be around 2 runs worse than the RF arm.  But the range part of UZR is something like 1 run better for LF.  Basically, a wash.

For DP, I don’t have the UZR numbers. I can only guess that it would be something similar that the multi-positioners would also imply that the avg 2B would be +2 runs compared to SS/3B.

That might be enough to get the 2B out of the 3B class, and more in-tune with the CF class.