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:
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?
Thank you for reading
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