## Payroll and Wins

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 R^{2} 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.

JC,

What would we see (or what would you predict we would see) if the study was based on something slightly different like number of players paid above the league average, or something of that sort. This is where I think the Braves’ winning can be explained: great expensive talent and then good cheap pieces added on. Any thoughts?

I don’t know, but I suspect it would predict much worse, since it doesn’t weight for the quality of the player.

I haven’t read the book, but the problem I have with this sort of argument is that it ignores the basic structure of baseball. When you have almost 40% of your total value coming from players who are, by “law”, paid the minimum or close to, of course your correlation between salary and wins will be significantly less than one.

Depending on how the authors interpreted their finding, it can be misleading.

Having a high payroll gives you a better chance to land the best free agents and to keep your own young stars. But of course it’s also possible to spend $200 million on players like Carl Pavano and Jaret Wright and then not make it to the World Series.

I agree that the reserve rules are one of the reasons the correlation is so low. The reserve clause is one of the big equalizers for small-market teams. Instead of going after big-name free agents, the Marlins (who really don’t play in a small market, but pretend to) concentrate on finding young talent that is cheap. It also means that teams who spend a lot don’t necessarily win. The rule contributes to dampening financial determinism.

I think what you can take from this, and I have always felt spending doesnt neccessarily equal wins, that to have winning club you need a good mix of very good young/cheap talent, mixed with more expensive pieces to fill those holes. In other words, being efficent, for example this years mets team. This is why the Yankees have to spend so much money, they have no good cheap players on their squad, and have to overspend dearly to get any kind of value. All in all, you should aim to have a payroll around the average, this chart also shows how the Cubs are screwed for the next few years. They have no farm system, so the cubs would need to spend about 140-150 million just to have an ample chance to post 82-84 wins, and that isnt guaranteed.

I did a study here of 1999-2005, that basically corresponds to what JC is saying, that every 10% of payroll is 1 win:

http://www.insidethebook.com/ee/index.php/site/comments/competing_on_payroll/#9

Posts #6 and #7 give you the equation of how to convert payroll into wins.

The key point that you’ll find there is that the structure of baseball makes it so that it’s not an efficient market, and therefore, looking at payroll in isolation will tell you only a little about what is happening.

Cyril Morong writes:

“Is there some kind of divisional effect? The Yankees and Red Sox both pay very high salaries, yet they play each other alot (19 times each year? when beofe it was 11-12). Before 2000 or 2001, teams played a balanced schedule. You played every other team in the league about the same number of times. Now you play almost half your games against your own division. What if the top 4-5 teams in salaries were all in one division? If they play each other alot, they can’t all win. This would hold down their pct. And teams with low payrolls in other divisions will see increases in their pct. So I wonder if somehow this analysis could be done divsion by division. Maybe have some kind of variable in there for what division you play in. I don’t know what that would be, though.”

I look at it a little differently. It seems to me if you have one element that accounts for 18% of the variance, that means something. High payroll, by itself, doesn’t guarantee wins if you piss it away, but it makes it a lot easier and gives you more leeway for mistakes. In the case of the Braves, it means the difference between keeping Andruw Jones and losing him. Clearly, the teams with more resources to spend, all other things being equal, have an advantage over those that don’t. Of course, I guess the question is, are there gradations; ie, obviously, a $200 mm payroll will give you an advantage over an $80 mm payroll, but is there the same difference between $80 mm and, say, $95 mm?

I wonder if efficacy of payroll spending would be found to be higher if instead of using “wins” as the desired outcome one used “successfully qualifying for the post-season” as the desired outcome. It is not clear to me that large payroll increases to get a team from say a .450 winning percentage to a .490 winning percentage are likely to be an efficient way for teams to spend money, and much of the payroll/wins relationship for teams unlikely to compete seriously for post-season spots may be noise. As a hypothesis I would suggest that perhaps a significant portion of additional payroll spending is spent to acheive additional percentages of probability of making the post-season rather than simply wins. Or to put it another way, not all wins are of equal value to a team and part of the reason behind a finding of a relatively low payroll efficacy in achieving wins might be that it is not really wins that are being sought but high-value wins (i.e., wins that achieve the highest increase in probability of making the post-season).