THE BOOK--Playing The Percentages In Baseball

Here it is since 1992:
Sal Prim
42.8% P
8.5% 1B
6.4% RF
6.3% 3B
5.7% LF
5.7% C
5.5% OF
5.5% SS
5.1% 2B
4.7% CF
3.6% DH

The three OF position are at 16.7% and the three IF positions are at 16.9%.  So, it is possible that I should set the spectrum such that the total offense at the OF position minus the IF position be the negative on the fielding side.

If Patriot or someone has the totals since 1992, please post them.  Otherwise, I can take a look at it a bit later.

1B+DH are getting 12.2%, for occupying 1.5 positions.  So, they are still getting paid more than their peers, and therefore, we shouldn’t expect that the avg 1B, overall, be = avg OF overall.  Unless of course the 1B is biased with free agents (which may certainly be the case).

Catchers are 5.7%, and 16.7 or 16.9 divided by 3 is 5.6%.  The overall value of the catcher, off+def, should be the same as the average in the IF or OF.

Interestingly, the pitcher got 42.83% of the salary.  I give out three-sevenths of all WARs to the pitcher, and 3/7 is 42.86%.

Catchers and shortstops are low on the list, very low. (So are center fielders.) If defense peaks in the early twenties, it stands to reason that most of your prime defensive positions are being filled by pre-free-agency players, driving down their salary commitments. I’ll try to look at this when I get home tonight.

Ideally, you would weight the players based on their service years.  So, a guy with 6+ service years would have say 180% of league average salary, a guy with 3 years of service would have 70% of league average salary.

You would average the “years of service” based on the above scale, to figure out how biased each position is based on years of service.  So, we might say expect that 1B has more 6+ years of service players, and therefore, the average salary expectation for 1B might be 120% of the average position, and SS might be 80%.  So, if the average position is say 7%, then maybe the comparison point would be 8.4% for 1B and 5.6% for SS.  That if the true payroll rate are those numbers, then teams are paying fairly.

All numbers for illustration only.

***

I just noticed that I had “OF” as a position in post 1.  I’ll have to fix that up.  Treat the numbers in post 1 as unreliable until I fix that.

This means nothing, but I’m curious: what does the 3B% look like if you reduce A-Rod’s salary to the next highest figure (or something like $16M)? Just want to see how much one player can affect a number.

For 1992-2007, I have 2B/3B/SS as -6.8 runs per 650 PA, and OF as +4.7 (compared to non-pitchers only).  If some other expression would be more useful, I can give you anything based on PA or outs.

Pre-1996, Lahman DB reports position in the OF only as OF.  So, we need to add the 4 columns of data (LF, CF, RF, OF) to get the total OF.  That’s 22.3%.  The infield is 16.9%.  (As you can see, these numbers are fairly similar to the 2003-07 data.) On a 90MM payroll, the difference between 22.3 and 16.9% is 4.9MM.  That would imply a gap in wins of 2.0 wins between the 3 OF and 3 IF positions.

Good stuff Patriot.  He’s reporting the gap in offense as 11.5 runs per 650 PA.  Per 2100 PA, that’s 37 run gap, or about 3.5 wins.

So, we have that the payroll gap (implying off+def) is 2.0 wins, while the offensive gap is 3.5 wins.  This means that the fielding gap between IF and OF is 1.5 wins.

If you have this kind of spectrum:
+0.6 SS
+0.4 CF
+0.1 2B/3B
-0.6 LF/RF

You get a 1.6 win gap (+0.8 wins for your IF, and -0.8 wins for your OF).

I’m not at home right now, but I thought Lahman tracked that data in the separate “FieldingOF” table, at least for some players.

Yes, but I was only looking at the Fielding table.  It’s not important anyway for what I was presenting here.

It’s almost certain that the CF are biased toward non-free agent players, as would the SS.

I don’t know if the 2B+SS+3B would be biased toward the non-free agents when compared to LF+CF+RF.  They could be.

Also, as you move down on the defensive spectrum, you probably get more and more free agents (would be my wager). How many of the full-time DH in the AL are under team control?

For 2008, the following players have over 40 games at DH:

• Aubrey Huff (BAL - 7 years)
• Jim Thome (CHA - 15 years)
• Jason J Kubel (MIN - 3 years)
• Milton Bradley (TEX - 6 years)
• Matt Stairs (TOR - 12 years)
• Jose Vidro (SEA - 10 years)
• Hideki Matsui (NYA - 5 years)
• Billy R Butler (KC - 0 years)
• Jonny Gomes (TB - 2 years)
• Gary Sheffield (DET - 19 years)
• David Ortiz (BOS - 9 years)
• Craig Monroe (MIN - 5 years)
• Travis Hafner (CLE - 5 years)
• Cliff Floyd (TB - 13 years)
• Mike Sweeney (OAK - 11 years)
• Frank Thomas (OAK - 17 years)

Only 3—Kubel, Gomes and Butler were under 5 years. I’d wager that you’d see a similar pattern for corner outfielders and first basemen too, as offensive contributions decline more slowly than defensive ones do. The 2B Chase Utley of 29 may become the DH Chase Utley of 37, but it’s far less likely that the SS Ramirez of today will be the SS Ramirez in 10 years.

I could be totally wrong (and often am) though.

Sal, agreed, and I said as much here:
“Unless of course the 1B is biased with free agents (which may certainly be the case). “

I can see the bias at the 1B+DH level.  I don’t think the bias is anywhere as strong when comparing the 3 IF to the 3 OF positions.  There is some bias, but I don’t think it has much effect.

I’d rather be wrong and unique than right but repetitive. My apologies.

Do you have a DB of average age/average service time by position? It would be an interesting factor to check correlation on.

Service time data is very, very unavailable. I do, however, have a list of free agents generated from the Retrosheet transactions database that I’m looking at.

I can’t make this look good, but:

FA NonFA FA%
1B 443 356 0.55
2B 528 370 0.59
3B 450 403 0.53
C 709 461 0.61
CF 338 456 0.43
DH 241 122 0.66
LF 520 495 0.51
P 4031 3090 0.57
RF 477 429 0.53
SS 466 297 0.61

Not exactly what I was expecting, I’ll admit.

Free agent salaries by position, 1996-2007:

Pos;$;%
1B;$1,046,545,970.00;7.65%
2B;$687,865,186.00;5.03%
3B;$763,641,033.00;5.58%
C;$702,883,719.00;5.14%
CF;$717,819,588.00;5.25%
DH;$535,531,734.00;3.91%
LF;$1,003,296,556.00;7.33%
P;$6,285,351,933.00;45.94%
RF;$1,192,104,835.00;8.71%
SS;$746,260,188.00;5.45%

Total;$13,681,300,742.00

IF;$2,197,766,407.00;16.06%
OF;$2,913,220,979.00;21.29%
1B/DH;$2,284,961,423.00;16.70%

It seems obvious that 1B/DH is more highly compensated than anywhere else on the field - especially consider that only half of all teams need to fill the DH spot at all.

Essentially spending on a position and a half outstrips spending on the three key defensive positions on the diamond. Positions where there should be pleny of scarcity, because only RH can play them.

Now, for non-free-agents:

Pos;$;%
1B;$812,294,476.00;10.97%
2B;$369,830,887.00;5.00%
3B;$643,850,899.00;8.70%
C;$535,902,388.00;7.24%
CF;$649,238,839.00;8.77%
DH;$219,782,409.00;2.97%
LF;$660,474,385.00;8.92%
P;$2,401,897,505.00;32.45%
RF;$652,295,246.00;8.81%
SS;$457,365,192.00;6.18%

Total;$7,402,932,226.00

IF;$1,471,046,978.00;19.87%
OF;$1,962,008,470.00;26.50%
1B/DH;$1,032,076,885.00;13.94%

Increased spending in the infield and outfield, compared to 1B/DH types. Defensive premium positions (CF, C, SS, 3B) outside of 2B take up a larger share of the pie. Pitching is the biggest loser here, though.

Colin: fantastic!  Beautiful really.

It does go into what I was observing regarding the non-FA salaries, that the middle infielders were giving a far bigger discount as arb-eligible than the power positions.

If every position is “around” equal, we’d expect the salaries of the non-FA and FA players to be roughly the same.  It’s nothing close to that.

It doesn’t look like you adjusted by year.  I typically divide the player salary by the average team payroll, and add those up.  If you can do that, I’d like to see the difference.

We can see here that pitchers as free agents are overvalued.  MLB should allow pitchers to become free agents after 4 years to increase supply.  Barring that, make everyone a free agent by age 28, if they don’t qualify by service years.

I’ll look into that. In the meantime, I figured out that I should be subtracting the league minimum salary from everything. (I have that by year, so that’s something, at least.)

Free agents:

Pos;$;%
1B;$965,612,970.00;7.85%
2B;$600,039,186.00;4.88%
3B;$682,257,033.00;5.55%
C;$583,511,719.00;4.74%
CF;$659,410,588.00;5.36%
DH;$496,188,734.00;4.03%
LF;$919,885,556.00;7.48%
P;$5,619,906,933.00;45.69%
RF;$1,109,887,835.00;9.02%
SS;$662,098,188.00;5.38%
Total;$12,298,798,742.00

IF;$1,944,394,407.00;15.81%
OF;$2,689,183,979.00;21.87%
1B/DH;$1,461,801,704.00;11.89%

Controlled:

Pos;$;%
1B;$747,350,476.00;11.68%
2B;$308,335,887.00;4.82%
3B;$576,962,899.00;9.02%
C;$464,389,388.00;7.26%
CF;$572,453,839.00;8.95%
DH;$202,122,409.00;3.16%
LF;$583,582,385.00;9.12%
P;$1,949,633,505.00;30.47%
RF;$584,473,246.00;9.14%
SS;$408,633,192.00;6.39%
Total;$6,397,937,226.00

IF;$1,293,931,978.00;20.22%
OF;$1,740,509,470.00;27.20%
1B/DH;$949,472,885.00;14.84%

I don’t think anything’s drastically changed there.

This has been sitting in the back of my head for a while, and I finally got back around to it. Here are average baseball salaries, 1985 - 2007:

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

“FA” is free agent, “CTL” is controlled - I don’t have service time data, so I can’t differentiate between Super 2s, arbitration-elibable, and players who have had free agency years bought out in arbitration. “MIN” is league minimum.

Then, everything is indexed to inflation using the Consumer Price Index in the second set of columns.  Line graphs of both are provided.

The interesting features of the graph, to me, are:

1) Free agents make less than their peers all the way through ‘89, and free agent salaries don’t really take off until ‘92.

2) Again in 2000 free agent salaries make another big jump over what controlled players are making.

3) The league minimum, in constant dollars, actually drops steadily from 1990 to 1996. It also doesn’t track free agent compensation nearly as well as controlled player salaries on the whole.

And, salary by position, in 2007 baseball dollars, seperated by free agents and controlled players, from least to most compensated:

POS FA salary players
2B F 1738118 640
P F 1769591 3896
C F 1966151 514
LF F 2049871 1200
C T 2382242 591
2B T 2633676 826
1B F 3036402 1050
3B F 3361814 369
P T 3502108 4345
SS F 3558008 234
1B T 3748711 1257
SS T 3883506 269
DH F 4112132 417
LF T 4289254 1068
3B T 4422071 213
DH T 5654168 525

Looking at that makes me feel very, very sorry for catchers.

Method: players were divied up into two classes - controlled and free agents. Salaries were divided by the average salary for their class in that year, and multiplied by the average 2007 salary for their class. Then they were sorted by position and averaged.

Did you know there are three outfield positions? Let’s try this again:

POS FA salary players
P F 1772468 3923
LF F 1891216 298
C F 1903564 716
2B F 1968136 514
RF F 2274353 289
C T 2446277 813
CF F 2532817 290
SS F 2608206 463
3B F 2651994 634
2B T 2983719 671
SS T 2994400 604
3B T 3127033 566
1B F 3471711 666
P T 3505045 4360
DH F 3735779 527
CF T 4361513 174
1B T 4566380 627
LF T 4772562 298
RF T 4782499 257
DH T 5418882 724

Kids, never perform sabermetrics after midnight! The fielding and fieldingof tables in the BDB were giving me some headaches that I didn’t realize I was having. Without further adieu, correct numbers:

POS FA salary players
2B F 1738118 640
P F 1769559 3895
LF F 1771917 536
C F 1966151 514
C T 2382242 591
CF F 2429511 877
RF F 2506405 427
2B T 2633676 826
1B F 3036402 1050
3B F 3361814 369
P T 3501708 4341
SS F 3566561 229
1B T 3748711 1257
SS T 3855324 263
CF T 3863925 651
LF T 4160572 569
3B T 4422071 213
RF T 4738349 416
DH F 5438879 199
DH T 6447661 348

And now, numbers for starters only:

POS FA salary players
2B F 2464515 340
C F 2631265 343
LF F 2766137 230
CF F 3490339 424
3B F 3504265 349
SS F 3580935 228
C T 3626764 304
RF F 3853779 213
SS T 3855324 263
2B T 4384358 328
3B T 4788818 193
1B F 4962055 403
LF T 6308026 220
DH F 6817210 103
CF T 6938114 245
RF T 7409503 183
1B T 8602027 286
DH T 8894423 150

For these purposes, a starter is defined as a player in the top 30 for PAs that season among players at that position. (Top 14 for DHs.)

I don’t mean to update this thread from the dead, but I noticed an interesting observation on Baseball Prospectus’ new compensation pages: the average payroll % for pitchers is 50-56% over the last 5+ years.  This is interesting because Tango had mentioned it being 43% only three years ago.

Any thoughts?

I forgot to mention that I did similar calculations myself in July of this year (before the new compensation pages came out) and the numbers by team were much closer to Tango’s 43%.  Also, if you go to BP’s individual team compensation pages the numbers are closer as well...maybe it’s just something with their homepage?

Here are the links:

http://www.baseballprospectus.com/compensation/?cyear=2011&team=&pos=

MLB Avg. for 2011 is: 56% pitching

http://www.baseballprospectus.com/compensation/index.php?team=ARI&cyear=2011

DBacks 2011 Avg: 38% pitching

Good question, Brent.  I will look into it.

Brent, the team pages appear to be correct, but the league totals appear to be incorrect, at least for the pitchers.  We are investigating why the league totals are off.

Great thanks, Mike.  Appreciate the response and the compensation pages do look great overall.  Keep up the good work.