Over at the Wages of Wins, Stacey Brook discusses the issue of payroll and wins in baseball. I’m surprised at how many problems people are having with an argument that they make in their book: payroll is not the largest determinant of wins. Using data from 1988-2006, Brook reports that payroll differences explain approximately 18% of the variance of wins across teams. This result come from regressing wins on a measure of relative payroll. Now the point is that if 18% is responsible, then 82% of other stuff is playing a bigger role. It seems pretty straight forward, but some people are getting caught up in the argument. Let me clarify a few things.
An R2 of .18 does not mean that there is no correlation between payroll and wins. Quite the opposite. There is strong and statistically significant correlation. In fact, the authors make this quite clear in the book. The coefficient on salary is statisitically significant. However, the point is that sum of other factors appear to be more important. The results indicate it’s quite a stretch to say that success on the field is a product of financial determinism.
Using data on salaries and wins from 1985-2006 I estimated the impact of payroll on wins using linear regression, while correcting for a few problems in the data. I used the percent difference of a team’s salary from the league mean to account for different values of players over time. Also, I used year dummies to capture influence of individual seasons. The result: every 10% above the mean in payroll is worth about 1 win, and salary explains about 17% of wins. These estimates conform to what the WoW authors find: a majority of the explanation is determined by factors other than salary. However, let’s take it a bit further. Having a payroll of one standard deviation (34%) above/below average is associated with 3.4 more/less wins. Is that a lot? Well, let’s see how well it predicts.
Below is a table of the percentage salary differences from the mean by franchise from 1985-2006 (excluding 1994). The table includes the average wins, the regression predicted wins above average (based on the 10% ==> 1 win prediction) and the actual wins above average. To me, the data indicates a trend, but not a strong one. For example, the Royals have spent a little less than average, but they’ve lost a lot more than average. The Braves have spent more than average, but won more above the average than predicted.
Club Wins % Diff Pred. Actual ANA 82.05 9.93 0.98 1.05 ARI 80.89 13.30 1.31 -0.11 ATL 87.19 28.36 2.79 6.19 BAL 75.81 10.11 0.99 -5.19 BOS 86.67 33.68 3.31 5.67 CHC 77.38 11.15 1.10 -3.62 CHW 82.86 -7.53 -0.74 1.86 CIN 80.52 -8.62 -0.85 -0.48 CLE 80.33 -8.11 -0.80 -0.67 COL 74.77 -6.66 -0.65 -6.23 DET 73.62 -8.95 -0.88 -7.38 FLA 76.15 -33.16 -3.26 -4.85 HOU 84.24 -4.18 -0.41 3.24 KCR 73.81 -12.41 -1.22 -7.19 LAD 83.43 33.05 3.25 2.43 MIL 75.43 -24.52 -2.41 -5.57 MIN 79.90 -26.08 -2.56 -1.10 NYM 84.05 27.73 2.72 3.05 NYY 90.24 70.35 6.91 9.24 OAK 86.81 -13.39 -1.32 5.81 PHI 77.48 -5.26 -0.52 -3.52 PIT 74.52 -30.87 -3.03 -6.48 SDP 78.43 -11.21 -1.10 -2.57 SEA 79.90 -7.15 -0.70 -1.10 SFG 84.24 3.87 0.38 3.24 STL 85.71 9.78 0.96 4.71 TBD 64.33 -38.87 -3.82 -16.67 TEX 79.38 -0.27 -0.03 -1.62 TOR 84.00 2.63 0.26 3.00 WSN 77.95 -36.49 -3.58 -3.05
This figure makes a similar point.
There is clearly a positive trend between average payroll and average wins, but it also shows a wide variance in performance outside the prediction. The points are not clustered closely around the line, and that is because other factors are affecting how teams perform. There is plenty of room for other factors to matter. That’s how the Marlins can compete for the Wild Card with $15 million and the Mets can come in last with a $90 million payroll. Just compare the Cubs and the A’s in the graph. Does money have an effect on winning? Yes, but that impact isn’t as certain as it’s widely believed to be. That’s the point. Winning isn’t as simple as spending.
Now, in an effort to offer full disclosure, let me say the following. I have met or corresponded with all of the authors of the book—we are economists working in the same field. The book was largely written before I met the authors, though I did check a fact for them right before the book went to press. I also gave the book a postive review in the International Journal of Sport Finance, as I really do like the book. If I thought they were wrong, I’d tell them. Heck, I’d write up my critique and submit it to the Journal of Sports Economics. I’d love the line on my vita. I’d also like to ask for politeness among those arguing. The tone of the response has been too harsh to be productive. If we are all after the truth, it’s best to keep things civil.