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February 8, 2007

When Is A Win Not A Win?

Improving on MP/MW

by Neil deMause

It's a fact of life that if you invent a popular statistic, that's what you're going to be remembered for. Charles Richter is known for his Scale, Virginia Apgar is known for her Score, and just try to tell me that if I say "Chicago Sun-Times sportswriter Jerome Holtzman," the first thing that pops into your mind isn't "the save rule."

So it is, to some degree, for Doug Pappas. Of all the many and varied things that Doug did in his too-short life, probably his best-known creation is Marginal Payroll/Marginal Wins, a measure designed, as he explained when he introduced it in the 2004 edition of the Baseball Prospectus annual, to "evaluate the efficiency of a club's front office by comparing its payroll and record to the performance it could expect to attain by fielding a roster of replacement-level players."

The idea was both simple and brilliant: Take the amount of money a team spent on payroll, subtract the minimum that it would take to field a 25-man team, then divide this by the team's wins, less the number of wins an all-minimum-wage team would be expected to rack up (calculated by Pappas as a .300 winning percentage.) It was a metric that would go on to inspire Michael Lewis' best-seller Moneyball (Lewis was impressed with how the Oakland A's under Billy Beane continually ranked at the top of the MP/MW charts), and become an annual feature of this Web site; since Doug's death, the annual MP/MW tabulations have been carried on by BP's Ben Murphy and Maury Brown.

It was not, however, perfect. Doug readily acknowledged that merely counting the number of wins a team had racked up above a perceived minimum (about 49 wins per year, a mark that the 2003 Tigers managed to undershoot, effectively breaking the model and resulting in a meaningless team MP/MW of negative $7.3 million per win) ignored the fact that not all wins are created equal: Spending $80 million to finish a distant third place isn't necessarily a more efficient use of money than spending $50 million to finish last.

Unfortunately, there didn't exist a metric at the time to measure just how much more valuable a team's 90th win, say, is than its 70th. We have one now, though. For his "Is Alex Rodriguez Overpaid?" chapter in Baseball Between the Numbers, Nate Silver developed a scale that shows the "marginal economic value" of each additional win--in other words, how much additional cash a team can be expected to earn based on each added win. The resulting chart takes the form of a curve with a large lump from 80 to 98 wins--the "sweet spot" where each additional win dramatically increases your chance of making the postseason and garnering the cash windfall that comes with playing in October:

image 1

With Nate's figures in hand (adjusted upwards by eight percent to account for inflation from 2005 to 2006), I've taken a shot at updating MP/MW to something that better answers Doug's original question: Which teams are getting the most for their investment in players? The formula is the same as Doug's original, with one twist: The denominator is now what I'll call Weighted Wins, where each win counts for a multiplier of how many times its revenue potential exceeds the $806,597 that a "replacement-level" win counts for. (The 90th win, for example, which can be expected to generate $4,744,481 under Nate's formula, is worth 5.88 weighted wins.)

Here's how Marginal Payroll/Marginal Weighted Wins looks for the 2006 season, alongside Maury Brown's calculations of the original MP/MW formula:

     W  L   Pct.  Payroll       Marg. Payroll  MW    MP/MW      MP/MWW
--------------------------------------------------------------------------
NYY  97 65  .599  $194,663,079  $185,507,079   48.4  $3,832,791 $2,147,686
TOR  87 75  .537  $71,915,000   $62,759,000    38.4  $1,634,349 $1,294,697
BOS  86 76  .531  $120,099,824  $110,943,824   37.4  $2,966,412 $2,510,271
BAL  70 92  .432  $72,585,582   $63,429,582    21.4  $2,963,999 $2,963,999
TB   61 101 .377  $35,417,967   $26,261,967    12.4  $2,117,901 $2,117,901

MIN  96 66  .593  $63,396,006   $54,240,006    47.4  $1,144,304 $638,682
DET  95 67  .586  $82,612,866   $73,456,866    46.4  $1,583,122 $882,885
CHW  90 72  .556  $102,750,667  $93,594,667    41.4  $2,260,741 $1,438,058
CLE  78 84  .481  $56,031,500   $46,875,500    29.4  $1,594,405 $1,586,678
KC   62 100 .383  $47,294,000   $38,138,000    13.4  $2,846,119 $2,846,119

OAK  93 69  .574  $62,243,079   $53,087,079    44.4  $1,195,655 $677,808
LAA  89 73  .549  $103,472,000  $94,316,000    40.4  $2,334,554 $1,589,840
TEX  80 82  .494  $68,228,662   $59,072,662    31.4  $1,881,295 $1,858,074
SEA  78 84  .481  $87,959,833   $78,803,833    29.4  $2,680,402 $2,667,413

NYM  97 65  .599  $101,084,963  $91,928,963    48.4  $1,899,359 $1,064,297
PHI  85 77  .525  $88,273,333   $79,117,333    36.4  $2,173,553 $1,938,483
ATL  79 83  .488  $90,156,876   $81,000,876    30.4  $2,664,503 $2,643,871
FLA  78 84  .481  $14,998,500   $5,842,500     29.4  $198,724   $197,761
WAS  71 91  .438  $63,143,000   $53,987,000    22.4  $2,410,134 $2,410,134

STL  83 78  .516  $88,891,371   $79,735,371    34.7  $2,297,849 $2,206,759
HOU  82 80  .506  $92,551,503   $83,395,503    33.4  $2,496,871 $2,419,866
CIN  80 82  .494  $60,909,519   $51,753,519    31.4  $1,648,201 $1,627,857
MIL  75 87  .463  $57,568,333   $48,412,333    26.4  $1,833,800 $1,831,627
PIT  67 95  .414  $46,717,750   $37,561,750    18.4  $2,041,399 $2,041,399
CHC  66 96  .407  $94,424,499   $85,268,499    17.4  $4,900,488 $4,900,488

SD   88 74  .543  $69,896,141   $60,740,141    39.4  $1,541,628 $1,132,893
LAD  88 74  .543  $98,447,187   $89,291,187    39.4  $2,266,274 $1,665,411
SF   76 85  .472  $90,056,419   $80,900,419    27.7  $2,920,593 $2,946,976
AZ   76 86  .469  $59,684,226   $50,528,226    27.4  $1,844,096 $1,840,602
COL  76 86  .469  $41,233,000   $32,077,000    27.4  $1,170,693 $1,168,475
As you can see, there are some interesting shifts. No longer are the Colorado Rockies judged to be a more efficient franchise than the Oakland A's, because the A's spent an extra $21 million to win a division title while the Rockies finished in a tie for last. The broad strokes are still the same--the Marlins spent well, the Cubs craptastically--but MP/MWW gives more credit where credit is supposed to be due: for getting to the postseason, and reaping the financial rewards that come with it.

Moreover, Nate's chart enables us to come up with another performance indicator to estimate how much actual monetary return teams are getting for their investment--let's call it Return On Payroll Expenditure (ROPE). Figure the average marginal revenue expected from the number of wins a team had, divide by the amount of payroll a franchise dedicated to the cause, and we have:

     Marg. Payroll    Marg. Rev.  ROPE
--------------------------------------
NYY   $185,507,079   $70,584,464  0.38
TOR    $62,759,000   $38,880,284  0.62
BOS   $110,943,824   $35,731,641  0.32
BALT   $63,429,584   $18,281,313  0.29
TB     $26,261,967   $11,021,938  0.42

MN     $54,240,006   $69,348,606  1.28
DET    $73,456,866   $67,854,953  0.92
CHW    $93,594,667   $52,040,186  0.56
CLE    $46,875,500   $24,825,503  0.53
KC     $38,138,000   $11,828,535  0.31

OAK    $53,087,079   $63,545,585  1.20
LAA    $94,316,000   $47,295,705  0.50
TEX    $59,072,662   $26,598,287  0.45
SEA    $78,803,833   $24,825,503  0.32

NYM    $91,928,963   $70,584,464  0.77
PHI    $79,117,333   $33,284,330  0.42
ATL    $81,000,876   $25,692,259  0.32
FLO     $5,842,500   $24,825,503  4.25
WAS    $53,987,000   $19,087,910  0.35

STL    $79,735,371   $29,885,689  0.37
HOU    $83,395,503   $28,643,560  0.34
CIN    $51,753,519   $26,598,287  0.51
MIL    $48,412,333   $22,334,281  0.46
PIT    $37,561,750   $15,861,521  0.42
CHC    $85,268,499   $15,054,924  0.18

SD     $60,740,141   $42,783,763  0.70
LA     $89,291,187   $42,783,763  0.48
SF     $80,900,419   $23,154,078  0.29
AZ     $50,528,226   $23,154,078  0.46
COL    $32,077,000   $23,154,078  0.72
Now, there's a big drawback to ROPE: It assumes that every team earns the same amount of revenue from each added win, and that's clearly not true--a postseason appearance for the Yankees means a lot more coin than one for the Royals. (Speaking hypothetically in the latter case, of course.) But on the whole, those differences should average out.

And what the overall numbers show is incredible: Only three teams--the Twins, the A's, and the amazing Marlins--managed to do well enough that they should expect to earn more in marginal revenues than they spent in marginal payroll. Every other team in baseball would have been better off, from a revenue perspective, by fielding a minimum-wage team and taking their lumps on the field.

On one level, this is good news: It implies that baseball owners probably really do have more than just the bottom line in mind when they set a team payroll--they want to win pennants, too, regardless of whether it makes economic sense to do so. Either that, or aside from Billy Beane, Terry Ryan, Larry Beinfest, and the GMs of perhaps a couple of other teams that came close (the Tigers, the Mets), everyone else is simply spending money really badly. But it couldn't be that ... right?

Neil deMause is an author of Baseball Prospectus. 
Click here to see Neil's other articles. You can contact Neil by clicking here

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