from Amazon
Monday, November 12, 2007
Do teams pay exponentially more for top-end talent?
I don’t know. But, I’ll say “no”. Here’s how:
win% Innings G WAR Sal
0.375 090.0 10.0 0.0 $0.4
0.400 108.0 12.0 0.3 $1.7
0.425 126.0 14.0 0.7 $3.5
0.450 144.0 16.0 1.2 $5.7
0.475 162.0 18.0 1.8 $8.3
0.500 180.0 20.0 2.5 $11.4
0.525 189.0 21.0 3.2 $14.3
0.550 198.0 22.0 3.9 $17.3
0.575 207.0 23.0 4.6 $20.6
0.600 216.0 24.0 5.4 $24.2
0.625 220.5 24.5 6.1 $27.4
0.650 225.0 25.0 6.9 $30.7
0.675 229.5 25.5 7.7 $34.1
0.700 234.0 26.0 8.5 $37.6
win%: true talent win%. Consider .700 to be the absolute best you can shoot for.
IP: I made a sliding scale of IP to win%. Nothing based on anything, other than my gut. Looks reasonable enough.
G: It’s simply IP/9, or “full games”.
WAR: G*(win%-.375), with .375 being the replacement level for a pitcher (as a starter). Feel free to use anything between .350 and .400.
Sal: 4.4*WAR+0.40
The salary is a LINEAR relationship to wins. The .500 line looks reasonable, doesn’t it? The .600 line (Oswalts, Zambranos, Zitos, etc), seems a tad high, don’t you think? It certainly is not too low. But, if you believe the supply/demand argument, you need to be paying more for wins from these players.
Perhaps my model is biased somehow. That’s fine. Construct your own. I challenge you guys to come up with a non-linear model of wins to salary, that is believable at the high end, and at .500.