THE BOOK--Playing The Percentages In Baseball

Some more interesting data:

1B and DH both had an RPI per 700PA of 165, which is about 11 runs above average.  As players aged an average of over 31, we obviously have more free agents in this group.  They earned 164% of league average, or an average of 9.8MM, which is 3.8MM above the 6MM average.  But, as noted, because they are older, that figure is a bit inflated.  Anyway, if we divide by 2.25MM per win, that means they are paid for 1.7 wins above average.  This figure is inflated, and so, probably closer to 1.2 or so, which means that MLB provided NO discount for position.  Ugh.  1B are severely overpaid.

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For LF/RF, LF are a bit older, which means they get the benefit of the free agent salary.  And even then, RF are paid much more: 138% of league average compared to 116% of league average.

LF are just crap. 

Anyway, the RPI per 700 is only +3 for the RF over LF, which must mean they have a goodly amount of fielding+positional value over the LF.

The difference between 138% and 116% is 1.32MM$, which is roughly 0.6 wins, or 6 runs.  So, it seems that MLB teams are paying RF on the basis that they are 3 runs better than LF on offense and 3 runs better than LF on fielding.  Perhaps more, because as I said, LF are more likely to have been free agents.

The Fans Scouting Report were very very down on LF in 2008, and have always been down on them, anyway.  I would not be surprised if the true difference in the fielding of LF is 5 runs below that of RF.  The problem is that the interpositional comps don’t agree with that assessment.

What we have here is that MLB teams and Fans agreeing that RF are much better fielders than LF, but UZR not agreeing.

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SS are paid about 1MM more than 2B (implying about generating 4-5 more runs than 2B), and they produced about 3 runs less than 2B with the bat.  This would make the SS contribution with the glove about 7-8 runs more than 2B, based on how MLB are paying them.

I’ve been allocated 5 runs, but maybe that’s a bit low.

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There are alot more catchers than any other position. If we look at gross totals (not per player), we see that teams paid as much for all their catchers as they did for all their SS.

Per 700 PA, catchers generated 7 fewer runs of offense than SS.  It seems therefore that we need to put catchers at 7 runs ahead of SS with the glove.  I’ve been using 5 runs, which may be a bit low.

When I look at 1985-1995 (which of course includes collusion years, but let’s presuppose that there isn’t any positional bias here):

3B is +9 offense over 2B

Salary difference is only 6% of the league average (92% to 98%), or 0.36MM$, which implies less than 0.2 wins (or 2 runs) difference.  This would further imply that the fielding+positional impact of 2B, as paid by MLB, was some 7 runs higher than 3B.

We have seen an enormous shift in fielding talent over these last 10 years, and MLB teams have responded to it.

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SS were paid an identical amount as 2B (though they were 1.1 years younger).

2B offense was +5 ahead of SS, implying SS fielding must be 5 ahead of 2B.  Actually a bit more, because of the service time bias.

If someone wants to jump from a 5 runs to a 7.5 run gap between SS and 2B/3B, you may be very-well justified.

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RF was paid 116% of league average and LF 107%.  This would imply a difference of a bit over 2 runs.  Their ages are also similar (bit younger for RF, so maybe the difference is really 3 runs, according to MLB teams).

Their offense was 3 runs ahead for RF, so that makes their fielding identical.

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CF earned a tiny bit less than RF, but if you account for the age difference (0.7 years), let’s call it even.

RF were 6 runs ahead of CF, meaning that CF were 6 runs ahead with the glove, maybe a smidge more.

It’s possible that there’s been a bit of a shift toward more glove men in CF this last decade, compared to the 85-95 time period.

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Catcher salary was a bit more than SS (implying 0.2 more wins for catchers), but they are also 1.6 years older, so they are probably paid the same.  Offense, SS were 3 runs behind C, so C are probably 3 runs ahead of SS.

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1B continued their outrageous salaries.  They were 1 run ahead of RF on offense, but they were paid 149% (!) of the league average.

It is totally insane, and implies that 1B were paid more for their fielding than RF.

It is surprising that MLB teams fell in line so strongly to what my independent model would have suggested for all the other positions, and are so completely out-of-whack with 1B.

Tango:  Any chance the 1Bmen are older than RF, so you’re comparing FA salaries to arb salaries?  If not, does seem insane....

Ages from 1985-95:
DH 32.6
1B 29.6
LF 29.4
RF 29.0

From 1996-2008:
DH 32.8
1B 31.0
LF 30.3
RF 29.6

So, I can believe that the 96-08 is unduly influenced by free agents, but not 85-95.

Guy, I’ve run those numbers before by free-agency class:

http://www.insidethebook.com/ee/index.php/site/comments/average_payroll_per_position/

Still have a bias between pre-arb and arb-eligible in there, but that’s actual FA salary by position.

Could LF/RF be as simple as a selection bias? Do they just put the better of their two corner OF in RF to help massage the star’s ego?

Or it could be something as obvious as the average RF arm is three runs better than the average LF

One thing that could skew the 1B results (or any other position) would be a few catastrophically bad performance declines.  Just scanning the 1985-95 1Bmen, it looks like there were a number of these, guys like Alvin Davis or Greg Walker.  I don’t know how much they were paid in their last few seasons, but presumably too much.  An extreme example is Nick Esasky, who the Braves paid top dollar for several seasons while he didn’t play at all (vertigo).  Albert Belle’s $12M “DL” seasons could have the same impact in the later period at LF or RF (depending on where you have him slotted).  An eleven-year sample seems pretty big, but I’d guess a couple of extreme outliers could skew these results.

Of course, if there’s some reason to think 1Bmen are systemically more likely to sustain career-ending injuries or dramatic performance declines, then it would be fair to include that.  But seems unlikely....

Bumping to coincide with other thread…

With talk of Teahen moving to 2B, I did a defensive comparison of players that have played 2B and 3B.

Using the data from FanGraphs I looked at players that had at least 100 innings at each position over the last 3 years. Here are the results

Total players: 43
Innings at 2B: 25410
Innings at 3B: 23656
UZR/150 at 2B: -2.24
UZR/150 at 3B: -0.34

Grouped players that had more innings at 2B vice 3B:
Innings at 2B: 16008
Innings at 3B: 5438
UZR/150 at 2B: -2.21
UZR/150 at 3B: 0.89

Grouped players that had more innings at 3B vice 2B:
Innings at 2B: 6415
Innings at 3B: 15879
UZR/150 at 2B: -2.40
UZR/150 at 3B: -0.93

Looks like 2B is harder to play (about 2-3 runs of UZR/150) than 3B when comparing players that have played them both.

Jeff, good job.

Note that you limited your sample to three years and with a minimum number of innings.  That may be good or not good.  I don’t know.

You also did not say whether your did an equal sample in each pool.  That is, if one guy has 100 innings at 2B and 1000 at 3B, did you prorate the higher innings to 100?  You’d have to somehow make them equal, otherwise you have a heavy bias.

When I looked at it:
http://www.insidethebook.com/ee/index.php/site/article/dual_positions_using_buzr/

This is what I said, using 2002-08 data:

Finally, 2B/3B: 203 players, totalling 5915 games, -0.8 at 2B, -1.1 at 3B.  Even!  I don’t think we have an age-bias to contend with, but we may have a talent-bias.  Not necessarily in terms of quality of talent, but perhaps in breadth of skills.

In my case, that gives me 53,000 innings.  And I have them almost dead-even.

So, be careful with any conclusion at this point, if you base it on a smaller sample than mine.

#11

The main problem I was having is the total lack of data (only last 3 years at time can be downloaded from Fangraphs).  I did want to see have players that played significant time at each position, while still having a large group.

for the totals I added UZR and innings for each category and then divided then created UZR/150 by:

Total UZR/(Total Innings/G/150)

Is this not the correct method?

Jeff, suppose you have the following:

Figgins:
1000 innings at 3B, +10 runs total
100 innings at 2B, 0 runs

Punto:
100 innings at 3B, -10 runs
1000 innings at 2B, 0 runs

You figure… oh well, 1100 innings at 3B, 1100 at 2B, 0 total at 3B, 0 at 2B… even!

But, that first +10 was done in 1000 innings, which means it’s +1 in 100 innings.  Figgins goes from +1 in 100 innings to 0 in 100 innings.

Punto goes from -10 in 100 innings to 0 in 100 innings.

That sound the same to you?

You need to equally weight the players in both pools.

Read this for further info:
http://tangotiger.net/aging.html

If I do equally weight them, people like Ryan Freel (37.7 uzr per 150 games) really begin to dominate.

Tom, your method seem to be like averaging all the players batting averages on a team to get the team’s total batting average.

Averaging the UZR/150 for the players I get:

Average UZR/150 at 2B: -1.23
Average UZR/150 at 3B: -1.83

Grouped players that had more innings at 2B vice 3B:

Average UZR/150 at 2B: -2.11
Average UZR/150 at 3B: -2.97

Grouped players that had more innings at 3B vice 2B:

Average UZR/150 at 2B: -0.21
Average UZR/150 at 3B: -0.52

Jeff… ahh, but I would weight the UZR/150 by the lesser of his two innings.

Averaging the UZR/150 (Weighting UZR/150 to lesser innings) for the players I get:

Average UZR/150 at 2B: -1.93
Average UZR/150 at 3B: -0.18

Grouped players that had more innings at 2B vice 3B:

Average UZR/150 at 2B: -1.71
Average UZR/150 at 3B: 0.41

Grouped players that had more innings at 3B vice 2B:

Average UZR/150 at 2B: -2.35
Average UZR/150 at 3B: -0.94

I think next I will look at when the list is expanded and contracted what the values do.

I am not exactly sure of the mathematical justification for weighting by the lesser of the two sets of innings, and I don’t exactly know what would happen if you didn’t, but intuitively, in doing so, you prevent a fluke number in one half of each pair from carrying a lot of weight if the other half happens to have a lot of innings.

For example, let’s say that Teahan has 1000 innings at 3B with a UZR of +5 per 150 games, and 10 innings at 2B with a UZR of +40 per 150 games.  Well, we know that the +40 is a sample size fluke and not really indicative of anything.  However, if we weight that data pair by the average of the two innings (505), we get a difference if +35 (40-5) weighted by 505 innings for that one player.  That can’t be right.  We intuitively know that the difference for that player (+35 runs) is almost meaningless since the time at 2B is only 10 innings.  So the best way to practically ignore that player is to weight that difference by 10 innings.  (If another player has 500 innings at 2B and another 500 innings at 3B, we intuitively know that their UZR at each position is somewhat reliable, so we are comfortable weighting the difference by 500 innings, which is 50 times the weight of the other player). 

I think that the exact mathematical way to do the weightings is to use the harmonic mean of 10 and 1000, which is close to the 10 anyway (1/(1/10+1/100)).

The weight should probably be the harmonic mean, so:
2/(1/10 + 1/1000) = 20

You “need” the 2 there, so that if you had 1/10 + 1/10, you want the answer to be 10, not 5.

Obviously, you don’t “need” it, since it’s a constant that will apply to everyone anyway, which is why you don’t see the “2” in there to begin with.

I just did a quick little look at it using STATS ZR. I took all players who played both 2B and 3B between 2001 and 2008. I placed an age limit of 28 - so all seasons age 29+ were excluded. I ran a weighted average of ZR by lowest number of total chances.

3B were -2.6 plays per 500 CH, 2B were -7.9 per 500 CH. Average 2B has 591 CH per 162 games, average 3B has 502 CH per 162 games.

Convert to runs, and per 162 games:

2B -7.02, 3B -2.12

Interesting work, Colin.  Do you have any DP data for these players?  My suspicion is that a lot of 3Bmen couldn’t handle the pivot at 2B well, even if they can handle GBs fairly well at 2B.

Colin, you are saying that players at 2B were -7 runs and those same players at 3B were -2?

Can you report the number of matching CH, and how many full-time equivalent seasons that is?

Did you also only match based on in-season moves, or for the 2001-08 as a total?

Right. 2B were -7/591 and 3B were -2/502. (That’s using a value of 0.754 runs per play at 2B and 0.800 runs per play at 3B - those are Chris Dial’s values.)

I used the sum of each player’s PM/CH for the in-sample period; I capped the age at 28 to avoid having any aging bias.

2B had 27,245 CH in 75,612.3337 innings; 3B had 15,695 CH in 51,861.333 innings. So we have a total of 46 full seasons worth of 2B play by chances or 51 by innings; 31 seasons worth of 3B play by CH or 35 seasons by innings.

I don’t have that DP data, Guy. I think Rally has a dataset like that.

I should probably answer the question asked. The sum of matching chances (by which I presume you mean the smallest number of chances per player) is 7,029, or about 13 seasons worth if you split the difference between 2B and 3B chances (or 546.5 chances per season).

"2B were -7/591 and 3B were -2/502”

Why the different denominators, if you did a matched set?

Because that’s a season’s worth of chances per position. If I go with per 550 CH (splitting the difference between the two and rounding a bit), I get -6.5 for 2B and -2.3 for 3B.

Okay, I redid the study, with some differences. I expanded the range of years, so now it’s 1994-2008. And I set a hard cap per player of 150 chances. All figures per 500 CH.

POS_1 POS_2 PM_1 PM_2 DIFF_500 WCH
2B SS -2.822695 -7.96824 5.145545 13654
2B 3B -7.95299 -2.856445 -5.096545 10489
3B SS -3.12411 -8.20412 5.08001 7314

Here’s where I get stuck:

* There seems to be a five-run gap between SS and 2B.
* There seems to be a five-run gap between SS and 3B.
* There seems to be a five-run gap between 2B and 3B.

All three of those things can’t be true.

And this is where I have my largest sample size, outside of LF/CF/RF. (And that’s pretty well in agreement, no matter how I slice the data - LF/RF are even, 8-run gap between CF and LF/RF.)

Now for all years, 1987-2008

POS_1 POS_2 PM_1 PM_2 DIFF_500 WCH
2B 3B -6.56862 -1.99289 -4.57573 20207
2B SS -3.04356 -6.375355 3.331795 27631
3B SS -2.43989 -6.09991 3.66002 14557

This problem doesn’t seem to resolve itself simply by throwing more data at it. The 3B-SS pair seems to consistently be the least common transition among IF players in sample.

"All three of those things can’t be true.”

That’s only the case if fielding is a single, unitary skill.  But if you make the model just a little more complex, this result is definitely possible.  Let’s say there are two skills, range and arm, and here’s the skill level for average player by position compared to a generic average player (Range, Arm)
2bmen: +5/-3
SSs: +7/+5
3Bmen: 0/+5
Presumably, the proportional value of the skills varies by position.  Let’s say (#s all made up, of course) it works this way:
2B: 80% range, 20% arm
SS: 70% range, 30% arm
3B: 50% range, 50% arm

Given those values, here are ratings for each talent when playing at 2B:
2B: 3.4
SS: 6.8
3B: 0.5

At SS
2B: 2.6
SS: 6.4
3B: 1.5

At 3B:
2b: 1.0
SS: 6.0
3B: 2.5

Shortstops are the best at every position.  But 2Bmen are better than 3B when playing at 2B, yet worse than 3Bmen when playing at 3B.  You could easily tweak these variables and get results like those you report.

I’m not arguing these are the right values, or only skills, but it’s probably a better approximation of reality than assuming a single “fielding skill”. 

Guy is right that you do need to be careful, because you are not leveraging the same skills.

This becomes even more apparent when comparing OF and IF to 1B.  You don’t get the gap you expect, if all other things are equal.

I should add that I think this complexity mainly applies to the IF (and catcher, of course).  I agree with Tango that we can treat OFs as a single talent pool.  Much as people like to talk about RF arms, the ability to “catch ball before it hits the ground” really trumps everything else.

Colin:  it might be interesting, sample size permitting, to explore subgroups of these position transitions.  For example: 
*How do above-avg-2B do at 3B, compared to below-average-2B? And vice-versa?
*What do the numbers look like for players who start at 2B and move “down” to 3B, vs. those who start at 3B and move “up” to 2B? (and are there even players who clearly belong in those categories?)

Uncapped, 1994-2008, with POS_1 representing the primary position determined by number of chances:

POS_1 POS_2 PM_1 PM_2 DIFF_500 WCH
2B 3B -7.47578 -7.228875 -0.246905 8770
2B SS 1.108845 -9.472585 10.58143 7676
3B 2B 8.22996 -3.72155 11.95151 4761
3B SS 3.66577 -6.965865 10.631635 2654
SS 2B -3.75966 -2.914165 -0.845495 10629
SS 3B -6.17916 -4.388455 -1.790705 5878

So, fer instance, a 2B moving to 3B typically stays the same; a 3B moving to 2B normally loses 10 runs.

It’s odd - the SS to 2B transition has a difference of 0, which is unusual at best. Hrm.

Could age be a complicating factor in some of these, such as SS to 2B? (older IFs would tend to be worse fielders)

This is complicated....

I don’t think so, Guy - I specifically capped the age at 28 for the purposes of the study, so any aging should be slight. I just ran average ages for all of these transitions, and they seem practically identical.

Think of it in terms of the “familiarity factor” (look for those two words on my blog, as we’ve discussed this in the past).

Take the SS/3B: primary SS moving to 3B gain only +1.8 runs (using the data above),while primary 3B moving to SS lose 10.6 runs.

What if, there is a 4.4 runs because of familiarity?  That is, no matter what, moving to an unfamiliar position will cost you 4.4 runs. 

So, the primary SS, moving to 3B, will start off in the hole -4.4 runs.  Instead, he actually gained +1.8 runs.  So, this shows the extra talent at SS is +6.2 runs compared to 3B.

And the primary 3B, moving to SS, will start off -4.4 runs.  Instead, he was actually -10.6 runs.  That makes the true difference at 6.2 runs.

So, the data gets resolved that there is a 6.2 difference between SS/3B, and an extra 4.4 runs if you move them out-of-position.

An alternative explanation—or in addition to familiarity—is that positions leverage different skills. 
* Perhaps a 2B moving to 3B doesn’t gain anything, because his relative advantage (range) is poorly leveraged at 3B, while a 3B going to 2B declines because his limited range is exposed while his arm is less valuable. 
* A SS moving to 2B doesn’t gain much because his main superiority over a 2Bman--better arm--is poorly leveraged there.  But a 2B moving to SS gets killed because his weaker arm is exposed.
* A SS moving to 3B doesn’t gain much because his main superiority--range--is poorly leveraged there.  But a 3B moving to SS gets killed because his limited range is exposed.

That works, I think. It seems to hold up for the OF as well:

POS_1 POS_2 PM_1 PM_2 DIFF_500 WCH
CF LF 0.405985 5.536635 -5.13065 12654
CF RF -1.8441 1.695455 -3.539555 11403
LF CF 9.5791 -7.099155 16.678255 7449
LF RF 3.7015 -1.527775 5.229275 10606
RF CF 6.87444 -6.209935 13.084375 8128
RF LF -0.394745 -4.493025 4.09828 11134

If that model holds up, then what we have is a 5-play gap between SS-3B, a 5-run play between SS-2B, and… a 5-play gap between 2B-3B.

In that case, you can make an arguement for both a 0-play and a 5-play gap between the positions, based upon relative value. I’m very unsure of how to determine which is correct.

I guess I’m a bit skeptical about familiarity as the main explanation.  For one thing, I believe Pos1 and Pos2 are based on playing time, not chronology.  And we don’t know what these guys played in the minors or before.  So it won’t always be true that Pos2 is “unfamiliar.”

One pattern I see here is that the switcher who play predominantly at a more demanding position (SS/2b, SS/3b, 2b/3b, CF/CR) show modest improvement of 0-5 runs at the easier position.  But when a player is asked to play a more demanding position than their dominant position (CR/CF, 2b/SS, 3b/SS, 3b/2b) they invariably collapse:  about -11 runs in IF, -14 in OF. 

The LF-RF players are both better at their dominant position.  That could reflect familiarity, or simply that managers have tended to correctly identify the position for which their specific skills are marginally better suited.

I agree with Guy as well, on the issue of leverage, which is exactly why you see the gap not so wide with 1B.

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Colin: while ZR is good, I don’t see how it’s better than UZR.  ZR is a subset of UZR, so if you have access to UZR (Fangraphs is nice enough to go back to 2002 with it), then part of the solution to your problem is to see what UZR says.

And since I already did that work…