Friday, June 04, 2004

Money's Worth 

Moneyball attracted notice by writing entertainingly about Billy Beane's ability to find good, cheap players for his financially-underwhelming A's. Because of Michael Lewis' financial reporting background, this discussion came off as if Lewis was writing about a stock fund manager who was finding hidden gems to invest in, continuously generating solid returns.

Amid the debate over what the Diamondbacks should do about the season is the underlying debate over who's worth the money. Is Randy Johnson worth $16.5 million? Steve Finley $7.0 million? Matt Mantei $7.0 million? (OK, there's probably consensus on that last question.)

I've been mulling over this question for some time now and want to present the first of many steps in answering that question for the Diamondbacks.

What I propose to do is compare D-Backs' VORP (Value over Replacement Player) with median salaries for MLB ballplayers. My formula for calculating the Ballplayer Value (BV) for any ballplayer is as follows:

BV = VORP / (Salary/MLB Median Salary)

Now, the median salary for 2004 is about $800,000, so the BV formula for 2004 could be as follows:

BV = VORP / (Salary/800,000)

Using this formula, Steve Finley's BV would be 2.8, or his VORP, 20.6, divided by the ratio of his salary (7,000,000) to the league median (800,000).

Here, then, are the D-Backs position players (leaving out Estalella -- now with the Mets, incidentally; DeVore; and Olson). Salaries are from here -- it didn't include salaries for Tracy and Hairston, so I assumed the major league minimum of $300,000 for them. VORP is from here.

Player Salary VORP BV
S. Hairston 300,000 7.4 19.7
A. Cintron 335,000 4.2 10.0
C. Tracy 300,000 3.6 9.6
M. Kata 315,000 2.3 5.8
R. Hammock 315,000 1.1 2.8
D. Bautista 4,000,000 13.2 2.6
S. Finley 7,000,000 20.6 2.4
S. Hillenbrand 2,600,000 7.9 2.4
L. Gonzalez 8,250,000 14.4 1.4
R. Sexson 8,725,000 7.1 0.7
R. Alomar 924,234 -0.3 -0.3
D. Sadler 400,000 -2.7 -1.4
B. Mayne 800,000 -2.7 -2.7
C. Baerga 1,000,000 -3.4 -4.3
G. Colbrunn 2,750,000 -2.2 -7.6

Here are the faults with the BV formula 1.0 as I see them:
1. It requires manual adjustments when dealing with players with negative VORP -- their formula should be VORP / (Median Salary/Salary) so that expensive, bad players are punished accordingly and cheap, bad players aren't punished so much. Strong bad players will not be dealt with here.
2. It merely tells you who's providing "value" and not who's the most effective. I'd much rather have Steve Finley on my team than Shea Hillenbrand, but it's not my $7 million.
3. It doesn't account for time in the lineup. As far as I can tell, VORP doesn't adjust for playing time. If it did, Sexson would probably be even lower on the list. (And Hairston's value will likely fall over time.) Definitely a correction for BV 1.1.
4. No predictive value, of course, though I never claimed it would have it. But it seems like you could use BP PECOTA cards in place of VORP for predictive value.
5. I'm still not keen on the use of median salary over average salary (about $2.5 million), but average salary just seems to punish highly paid, highly performing players more than they should be. I'm trying to strike a balance between wanting to recognize the value to teams of cheap, interchangeable players and wanting to recognize the top 5% or 10% who might really be worth $10 million per year.
6. No provision for defensive metrics.

I welcome any comments or suggested modifications to the BV methodology. Pitchers rankings will come next week.

VORP does account for playing time. VORP is based on MLV, Marginal Lineup Value, which accounts for playing time. See this discussion of VORP and this discussion of MLV for how it all ties together.
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