Non-Linear Cost-Per-Win Part III

In the comments of Part I, a reader suggested using a measure of team talent other than actual wins in the calculation of payroll efficiency.  Not a bad idea.  I'm going to use Baseball Prospectus' third-order wins metric, which adjusts for run differential (via EqA) and strength of schedule.  The average third-order win totals for NL and AL teams were 78.5 and 84.8, respectively.

The merits of third-order wins and other Pythagorean-like win estimators have been debated before, so I won't mention much about them here.  There are pluses and minuses, but it's all a gray area.  From reading a lot of things written on the topic and crunching a lot of numbers throughout the years, I tend to think that, on average, 40% of the difference between actual record and Pythag record is due to skill (extreme bullpen leverage, non-SB baserunning, and doing the little things) while 60% is luck (clutch hitting, the way batting events combine into runs, run distribution, alignment of RS and RA, etc.)  Certainly it can be (mostly) all luck or all skill for a given team in a given year.

Anyway, the table below uses the same methodology as Part II.  Using the logistic model, I've calculated the expected payroll to produce a team with that much talent and compared it to each team's actual payroll in order to find their savings or wastings.  All dollars are in millions:

 

Lg Team 3O Wins Exp Pay Act Pay Savings
A Tampa Bay Rays  97.0 $222 $44 $178
A Boston Red Sox  102.1 $280 $133 $146
N Chicago Cubs  94.5 $203 $118 $84
A Toronto Blue Jays  92.0 $174 $98 $76
N Florida Marlins  81.1 $94 $22 $72
N Milwaukee Brewers  86.4 $128 $81 $47
A Minnesota Twins  82.9 $99 $57 $42
N Arizona Diamondbacks  83.6 $107 $66 $41
N Philadelphia Phillies  86.8 $131 $98 $33
A Cleveland Indians  84.1 $111 $79 $32
N Los Angeles Dodgers  88.7 $146 $119 $27
A Oakland Athletics  76.7 $65 $48 $17
A Chicago White Sox  88.1 $137 $121 $16
N St. Louis Cardinals  84.6 $115 $100 $15
A Texas Rangers  78.7 $75 $68 $7
N New York Mets  88.0 $140 $138 $3
A Kansas City Royals  76.2 $59 $58 $1
N Colorado Rockies  77.0 $64 $69 -$4
A Los Angeles Angels  84.0 $254 $110 -$9
A Baltimore Orioles  73.7 $48 $67 -$19
N Atlanta Braves  79.1 $77 $102 -$25
N Houston Astros  75.8 $60 $89 -$29
A New York Yankees  91.3 $168 $209 -$41
N San Francisco Giants  70.1 $26 $77 -$51
A Detroit Tigers  79.4 $79 $138 -$59
N San Diego Padres  67.9 $15 $74 -$59
N Washington Nationals  63.4 -$5 $55 -$60
N Cincinnati Reds  67.8 $14 $74 -$60
N Pittsburgh Pirates  61.8 -$14 $49 -$62
A Seattle Mariners  65.2 $2 $118 -$116

Notes:

  • No suprise the Rays look good again, although their actual win total was a bit above their true talent level.
  • The Red Sox vault up to second in efficiency.  Going into 2009, there's no doubt the Sox should be the favorite in the AL East, if you look beyond 2008's actual record.
  • In general, teams are more clustered in the middle.  That makes sense, because third-order wins attempt to remove luck, and luck causes the distribution to spread wider.  It adds to the overall variance.

We can also compare the savings computed using third-order wins to the savings computed using actual wins.  This is the same thing as comparing the two win totals directly, but puts it on the payroll scale.  A positive difference means the third-order method gives the team more savings (or less wastings):

 

Lg Team 30 Sav Act Sav Diff
A Boston Red Sox  $146 $88 $58
N Atlanta Braves  -$25 -$77 $52
N Los Angeles Dodgers  $27 -$22 $50
A Toronto Blue Jays  $76 $43 $34
N San Diego Padres  -$59 -$91 $32
N Colorado Rockies  -$4 -$33 $28
N Washington Nationals  -$60 -$87 $27
N Arizona Diamondbacks  $41 $17 $24
A Detroit Tigers  -$59 -$79 $21
A Baltimore Orioles  -$19 -$40 $20
A Seattle Mariners  -$116 -$126 $10
N New York Mets  $3 -$5 $8
A Cleveland Indians  $32 $24 $8
N St. Louis Cardinals  $15 $11 $4
A New York Yankees  -$41 -$44 $3
N San Francisco Giants  -$51 -$51 $1
A Oakland Athletics  $17 $19 -$2
A Kansas City Royals  $1 $6 -$5
N Chicago Cubs  $84 $89 -$5
N Florida Marlins  $72 $78 -$6
N Milwaukee Brewers  $47 $59 -$12
N Pittsburgh Pirates  -$62 -$48 -$14
A Texas Rangers  $7 $22 -$15
A Tampa Bay Rays  $178 $199 -$21
N Cincinnati Reds  -$60 -$38 -$22
A Chicago White Sox  $16 $39 -$23
N Philadelphia Phillies  $33 $58 -$26
A Minnesota Twins  $42 $95 -$53
N Houston Astros  -$29 $25 -$54
A Los Angeles Angels  -$9 $158 -$167

Notes:

  • The top of this list reads like a list of teams you shouldn't forget about going into next season.  And the bottom is a list of teams that will likely disappoint.
  • The Angels and Twins do have a habit of out-performing their Pythag, mostly due to team baserunning skills.  I still expect a fair amount of regression, just not all the way.  And don't expect their clutch hitting skills to continue.
  • The fall of Ed Wade will not be pretty.
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