Wednesday, February 25, 2009
MRP and the Baseball EconomistPosted by Colin Wyers
Consider this the "Deleted Scene" from this morning's article on player salaries. It was hard for me to cut it, because it's really what motivated me to write this set of articles in the first place. But it really didn't seem to fit in the article - it was a distraction from the larger issues. Since I hate to kill my own darlings, and since I know there are at least a few others who may care to read this, I'm presenting it here.
It would be remiss of me to not acknowledge that the MRP estimates of J.C. Bradbury (presented in his book, "The Baseball Economist") may well be the most visible in recent years. He follows a model similar to Scully's. But there are some problems that are unique to Bradbury's model, which do not apply to other MRP models. That's what we'll address here.
Bradbury's model starts off with an incremental model, in the spirit of Zimbalist's, comparing a player's production to that of an average player. Credit where credit is due: Bradbury pays more attention to the measure of player value than most economic treatments I've seen, using OBP and SLG as the inputs for hitters and K, BB and HR rates for pitchers. From this, he produces a measure called "$ValAA," or dollar value above average.
Then comes the part where we really run into problems. Quoting Bradbury:
Next, we need to establish a baseline dollar value for the average player, to add to the value above average, which will give us the MRP of a player. ... I estimate that an average team - a team that is predicted to win eighty-one games based on runs scored and runs allowed - will earn approximately $109 million in revenue. Assigning an equal weight to the run contributions of offense and defense, each side is responsible for half of that value; $54.5 million each. Therefore, the average player will produce a percentage of $54.5 million equal to the percentage of his team's plate appearances or innings pitched.
Where to start? Let's start with the figure of $109 million - it's quite simply wrong. Bradbury uses the Forbes estimates, which average out to $142 million in 2004. Where does the $109 million figure come from, then? From the following regression equation, printed in the endnotes:
Total Revenue = (0.125 * Run Difference) + (0.000665 * Run Difference^2) + (3.88 * MSA Population) + 109.022
In order to come up with $109 million using that equation, you need to set population at zero, which doesn't make sense at all. Using the average population (based upon his chart in Chapter 6), a .500 team in an average-sized market should have $130 million in revenue. It's frankly a baffling error.
(A note for those with the hardback edition - Bradbury says he ran his regression on 2005 data, but in the errata says that it was the 2004 data. All Forbes revenue estimates - and a host of other useful data - can be found on Rod Fort's sports data page.)
The other two mistakes are more serious. His first problem is assuming that the sum total of MRP is equal to the sum total of revenue. Nowhere does he even bother to offer a rationale for this decision. If we were to take the assertion at face value, Bradbury essentially suggests that all teams operate at a substantial loss; according to the Forbes data, teams spent an average of $83.8 million on player salaries in 2004 and $54.1 million in other expenses; at very least, Bradbury should subtract those other expenses from revenue before calculating his average player value. (And wouldn't you know it - that yields $88.2 million, almost precisely what MLB teams were paying in player salaries.)
Bradbury then goes on to divide his payroll equally between hitters and pitchers, or "offense and defense," as he terms it.. The problem here is that (as he has already acknowledged by incorporating DIPS into his valuation system) is that pitchers and fielders share responsibility on defense. Unfortunately, at no point does he attempt to assign credit for a fielder's defensive contribution in relation to their MRP, either in his estimates of $ValAA or of average value.
Since there are two factors that underweight a position player's contribution (the error in calculating average value and the incorrect split of revenue between pitchers and position players) and one that overweights (the use of total revenue in determining a player's average value), they seem to counterbalance each other. Bradbury says that the estimates of MRP and the salaries for free agent position players have a median difference of only 8%. Shorting position players part of their value seems to compensate for the use of total revenue in estimating player value. This does, however, lead to a median 36% difference between his MRP estimates and salaries for free agent pitchers.
There is more that could be said about Bradbury's MRP estimates but not, I think, more that needs to be said about them, at least for right now. They seem to have some rather glaring and crucial flaws.
Colin Wyers knows exactly how much of a nerd he is. He is very interested in hearing about any other concerns you may have; you can reach him by e-mail, and he will try his best to respond in a timely fashion. He also blogs at Statistically Speaking.