Pappas - Marginal $ / Marginal Wins (March 9, 2004)
I did this a few years ago at Fanhome, and it might be interesting to some. I use 3 million/win here (because of regression), though 2 might be better.
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While I do not have the salaries as I would like them (see prior posts), I will use the salaries I have. Here are the
column 2 - total payroll of each team for the 1995-1999 time period,
column 3 - with each year's dollars normalized to 1999 baseball dollars, and relative to league average
column 4 - team wins over .500, normalized to /162GP for each year
column 5 - expected team wins, giving salaries paid (basically 3 million$/win)
So, the Yankees have paid out 349 million $ for that 6 year period, which, when adjusted for 1999 dollars, and compared to league average, was 226 million$ more than the average team, and that resulted in 84 more wins than an average team. Given the amount of money paid, they would have been expected to win 76 games more than average.
Team Payroll Payroll (+/-) W/L Expected W/L
NYY $349,019,520 $226,112,284 84 76
BAL $319,547,520 $180,491,494 18 61
ATL $296,325,540 $150,539,632 102 51
CLE $273,216,180 $115,101,225 80 39
TEX $274,251,990 $108,648,874 28 37
LA $252,788,160 $77,583,032 21 26
COL $238,304,490 $61,637,229 -3 21
BOS $230,989,230 $45,760,059 41 15
CHW $212,671,860 $34,133,945 -8 11
SAF $220,715,700 $33,223,859 3 11
SEA $216,292,800 $32,670,626 14 11
STL $215,009,790 $27,771,100 -15 9
CHC $215,064,630 $22,010,096 -22 7
TOR $208,061,610 $18,508,968 -20 6
CIN $199,296,810 $11,914,451 20 4
ARI $100,655,940 $11,386,663 3 4
SAD $206,859,300 $10,476,815 13 4
NYM $205,447,470 ($2,076,582) 16 -1
HOU $196,039,350 ($5,613,666) 46 -2
ANA $183,195,630 ($24,252,246) -8 -8
TB $59,483,580 ($41,229,417) -30 -14
PHI $136,699,710 ($90,682,052) -40 -31
KC $131,463,240 ($95,839,635) -47 -32
FLA $128,859,420 ($100,224,626) -39 -34
DET $127,978,860 ($104,367,966) -71 -35
MIN $124,349,190 ($109,935,648) -62 -37
MIL $129,431,670 ($111,141,779) -25 -37
OAK $112,492,680 ($124,448,888) -26 -42
PIT $82,616,220 ($171,844,703) -40 -58
MON $73,527,690 ($186,313,141) -32 -63
Posted 7:26 p.m.,
March 9, 2004
(#2) -
Neil
(homepage)
A little bit ago, I messed around with marginal$/marginal projected win for the 2004 season... (see homepage)
I am very surprised that there is not more investigation done in the area of converting payroll into wins: when winning percentage increases, it's harder to use the $2mill/win figure to calculate worth, as salaries seem to be exponetial? I could be way way way way wrong, but I sense some kind of statistical distribution that could categorize the distribution of salaries in relation to talent.
Posted 7:57 a.m.,
March 10, 2004
(#3) -
Bob
The results seem to be giving a relative advantage to the high payroll teams and disadvantage to the low payroll teams. I'm wondering if subtracting the minimum possible salary (maybe $300K x 25 players) from each payroll before the other calculations are made would work better. This is the baseline that every team has to start from.
Bob
Posted 9:24 a.m.,
March 10, 2004
(#4) -
tangotiger
Bob, the results of what? Pappas? Me? Neil?
In any case, we ALL use marginal wins per marginal dollars. The equation is the following:
wins = a (salary) + b
Even if you want it to be:
wins = a (salary - c) + b
or
wins - d = a (salary - c) + b
it's ALL the same thing.
LEt's do that last one:
wins - d = a (salary - c) + b
adding "d" to both sides and this becomes
wins = a (salary - c) + b + d
expand the "a" part and we get:
wins = a (salary) - a(c) + b + d
make z = a(c) + b + d
and we get"
wins = a (salary) + z
Posted 10:01 a.m.,
March 10, 2004
(#5) -
tangotiger
(homepage)
I took the above chart, and plotted it. r = .81.
In terms of how much money teams pay and how much production they get out of it, I think a linear fit works pretty well.
Posted 10:13 a.m.,
March 10, 2004
(#6) -
tangotiger
More tidbits:
If your team payroll is 60 million$ below league average (say 10 million compared to a league of 70), your expectation is 30 wins below league average (or 51 wins or .315) with a 2 million$ / win converter and 20 wins below league average (or 61 wins or .377) with a 3 million$ / win converter. I have other reasons that I've discussed at length for using 2 million$ / win, so that's the one I prefer.
For a team that is 60 million$ above league average (say 130 million$ in a league of 70), at 2 million$ per win, that give you 111 wins. I think that's about as good as you can expect. Any team that spends more than this amount is hoping to get a benefit beyond just wins.
The Yanks have NOT amassed a team that will win commensurate with their payroll. Being over 100 million$ above league average would translate to 131 wins. Their actual talent is more indicative of a team with 101 wins (or an equivalent payroll of 110 million$ or 40 million$ above league average).
What the Yanks are doing are spending 60 million$ more than they should for equivalent talent. The teams should be REJOICING that the Yanks are spending tons of money like this (unless they think these extravagant contracts are setting the market; but Kevin Brown and ARod were inherited, Vazquez is similar to Halladay, Sheffield is in-line with the market).
The Yankees are wasting 60 million$ on the hope that this money generates at least that much money based on the "brand" of players that they have.
Posted 11:45 a.m.,
March 10, 2004
(#7) -
f_k_a Scoriano
The Braves run is yet again shown to be awfully impressive.
I am not so sure that the talent pool is so deep that the Yankees, already having a having a veteran core each year, can be reasonably sure to remain at playoff win totals each year without spending a lot, especially with other relatively high spending teams in their division.
Posted 12:03 p.m.,
March 10, 2004
(#8) -
Matt
You could try doing everything with the log of salary, instead of just straight salary. That's common when working with income data, of course, and would take care of any exponential problem.
As a Dodgers fan, I am very surprised by those numbers. (1) I am surprised that their adjusted payroll number is not higher, (2) surprised that they have won more games than would be expected from their payroll. All I hear about is all the fat contracts the Dodgers have sunk into bad/injured players (Darren Dreifort being the poster boy), and how they don't live up to expectations every year. Of course, this is from reading the LA papers, where they will never live up to expectations unless they win the WS, and where expectations aren't based on actual talent level.
Posted 12:36 p.m.,
March 10, 2004
(#9) -
tangotiger
What does the log of the salary have to do with it? The r using that is .76. I get a best-fit with salary^1.5. The r of that is .818. Otherwise, with no exponent, it's .812. Linear works fine.
All data is from 1995-1999.
Posted 1:31 p.m.,
March 10, 2004
(#10) -
MGL
I am amazed how the actual/expected wins for many teams do not match up with the popular perception of whether the team spends money wisely or not. Of course, I'm not sure what the perception was in that time period (95-99).
I am also surprised at how fairly efficient many teams are. I would have thought that there would be a lot more inefficiency.
An interesting study would be to see whether and by how much teams are becoming more efficient in spending money for talent (wins). Would the "r" represent that efficiency? Tango, is that what your r's are (each team's marginal dollars spent, regressed on their marginal wins)?
Posted 1:46 p.m.,
March 10, 2004
(#11) -
tangotiger
MGL, you might want to follow Pappas' series. It would be more useful if Doug were to normalize his data to 2003 dollars at some point.
The "r" represents the relationship between payroll and team wins. There is NO CAUSAL effect here. The causations are:
talent + luck = performance = wins
talent + years to free agency + mismanagement = salary
So, when I run a regression of wins to salary, we would hope that:
1: talent is the prevailing variable
2: teams have the same distribution of players with respect to years to free agency
Since we know that "2" is nowhere near the same, and since we know that teams have alot of mismanagement, it's quite interesting that the r is as high as it is. Of course, if every team mismanages in the same way, that cancels out.
In terms of efficiency, like I said, each team should only be spending 2 million$ / win. That the best-fit shows 3 million$ doesn't mean I'm wrong. I could be. It just so happens on this small sample that it's 3.
Posted 2:23 p.m.,
March 10, 2004
(#12) -
MGL
I'm reading Pappas' articles now (I just got my BP 2004 yesterday).
It seems to me that if you want to evaluate a team's efficiency or "smarts" in spending, using long-term salary/wins data is not bad but that in the short-term, it is terrible. In the short-term, you have the gap between pythag wins and actual wins, you have the gap between a player's projection and his actual perforemnce and you have the injury factor. All of these things are beyond the team's control and create a lot of noise in the short term. Even if a marginal dollars/marginal wins model is good for "evaluating" teams in the long-term, you have different GM's and even different owners, so the results are not that meaningful.
Judging a team's overall "managment talent" or efficiency is REALLY complicated. Much more complicated than just comparing marginal dollars to marginal wins. You have drafting and player development (if a team is good at that, they get good players really cheaply for a few years), you have the years before arb and FA, etc.
It seems to me that the most simple and effective way of "evaluating" a team's efficiency ("smarts") in spending is to compare each individual player's post-arb and FA salary with his projection at the time of the signing.
Tango, it also seems to me that the progression of "r" (from marginal wins regressed on marginal dollars for each team) over the years should give you a very nice idea as to whether and by how much teams are getting more efficient (better in evaluating player talent). I'd love to see a list of the year by year "r's" using Pappas' data...
Posted 2:32 p.m.,
March 10, 2004
(#13) -
tangotiger
The answer to figuring a team's efficiency has already been given by my two equations here:
talent + luck = performance = wins
talent + years to free agency + mismanagement = salary
That second line shows you how smart/lucky a team was in matching salary to talent.
Posted 12:03 p.m.,
March 11, 2004
(#14) -
Matt
Sorry, with my log comment I was just thinking off the top of my head. I was thinking about it at the player level -- usually at the individual level, salaries are distributed more exponentially, so using a log of salary works better for regression. But you're completely right, when you look at the graph at the team level, it just looks linear.
