from Amazon
Friday, March 07, 2008
Free agent salaries and pitcher roles
I introduced my salary scale last year. It works fantastically well. There’s nothing “black box” about it. You can create your own. It’s just very basic. Vince Gennaro introduces something similar, but instead of WAR, he simply uses the pitcher’s role. Does his conform to mine? Let’s see:
The win% of the 7 starters (top 5 plus all your emergency starters) would roughly be:
1. .600
2. .540
3. .490
4. .450
5. .420
6. .400
7. .390
You can see the pattern, right?
Let’s give the following “full games” (innings divided by 9): 21, 19, 17, 15, 13, 11. That gives you 105 complete games, which is 65% of the season’s innings, which is roughly what really happens. It’s an easy to remember rough guideline.
The weighted average is .489, which corresponds to what really happens.
Ok, so we’ve got a reasonable model. (Feel free to tweak it to something more realistic if you like.) We can easily convert to WAR, as win% minus .380, times games. And to convert to dollars, you multiply WAR by $4.4MM per win and add $0.400MM. You get:
This is what you get:
Role G win% WAR $
1 21 0.600 4.6 $20.7
2 19 0.540 3.0 $13.8
3 17 0.490 1.9 $8.6
4 15 0.450 1.1 $5.0
5 13 0.420 0.5 $2.7
6 11 0.400 0.2 $1.4
7 9 0.390 0.1 $0.8
Now, let’s compare to Gennaro’s. He calls the #1 guy 19MM, which is fairly close. Don’t forget that I’m looking at it from a one-year standpoint, while actual free agents are paid based on them aging and losing effectiveness (but also gaining on baseball inflation). His #2 is 14MM, so that’s a bingo. His #3 is 9MM, so that’s a bingo. His #4 is 6MM, which is a bit higher than mine. His #5 is 3MM, so that’s a bingo.
For closers, if we presume 8 full games, a win% of .630, and the GuyM method of accounting for leverage, and we get:
WAR = 8 * ( (.630-.570) * 2 + (.570-.470) ) = 1.76
That gives us $8.1MM. Gennaro says 12MM, which really doesn’t make sense. There are 30 closers, and he must be basing his numbers on the elite of those closers (Rivera especially). Basically, closers are paid like #3 starters. If he assumes only 15 closers, then maybe the win% is .650, and we get $9.6MM.
As for setup guys, let’s assume a win% of .530 or so, with 9 games. That gives us a WAR of $2.8MM, which again is much lower than Gennaro. Again, Gennaro must be focusing on elite setup guys. If we give them a .570 win%, I get $4.4MM.
Chamberlain however would be a top closer in the role of setup guy. So, he’d probably be worth this much:
WAR = 9 * ( (.630-.570) * 1.3 + (.570-.470) ) = 1.6
That makes his value as $7.4MM. If as a starter, he’d put up numbers just below that of a #3 guy, it’s a wash.
More importantly, as I’ve mentioned last year in the Liriano thread, I follow the Weaver rule of using a guy in a long relief role before you bring him into the starting rotation. I’d use Chamberlain as my one- or two-inning setup guy this year (with emphasis on the two-inning). It’s crazy otherwise.
I just noticed that the pattern above follows a Fibonacci sequence. That is, the last two numbers, when added, gives you the next number. For example, start at
21
You get that by having the previous two numbers as 13, 8
You get 13 by having the previous two numbers as
8, 5
You get 8 by having
5, 3
You get 5 by having
3, 2
You get 2 by having
1, 1
The sum of these 7 numbers (1,2,3,5,8,13,21) is 53.
The sum of my 7 WAR numbers above is 53.0.
Cool, right?
***
FY: The Fibonacci sequence at its infinite point can be calculated as sqrt(5)/2 + 0.5. That number is 1.618034. It’s recipricol is 0.618034. You’ll also note that x minus 1/x equals 1. Politcs of Glory fans will be happy.