Back in 2004, the late Doug Pappas came up with a simple way to evaluate how well each team was spending their money: marginal payroll per marginal win. Here’s Doug’s original formula:
(club payroll – (28 x major league minimum)) / ((winning percentage – .300) x 162)
Simple enough, and it managed to give us yet another way to show how great Billy Beane and the A’s were. But while it was a decent first step, it failed even the simplest laugh tests: were the Yankees really one of the bottom ten teams, even when they were running away with their division every year? Are the Marlins consistently one of the best-run teams, just by virtue of not spending much beyond the minimum on payroll? Probably not.
Looking at it now, the biggest problems are fairly obvious. First off, not all wins are created equal-as Nate Silver touched on in Baseball Between the Numbers, a team’s ninetieth win creates significantly more marginal revenue than its seventieth (see chart below). Also, each team has its own marginal revenue curve-the Yankees’ ninetieth win is much more valuable than the Marlins’ ninetieth win, at least in terms of pure revenue potential.
So while Doug’s original formula punished large-market teams for spending significant sums on payroll, the reality is that the Yankees would have to have a brain lapse to cut their payroll below $100 million. The question really should be: How well are they spending their $200 million, and is that the right number, given their competitive position and market size?
First, we need to know how much marginal revenue each team is likely to bring in, based on its win total and market size. To do this, we’ll use Nate’s MR/MW curve, updated for 2009 revenues. We’ll then assign each team a market-size factor based on its 2007-2008 gate receipts. (We already know that this is the only short-term revenue source that significantly impacts a team’s payroll spending). The Red Sox won 95 games last year, which should generally lead to $108 million in marginal revenue. Multiply that figure by Boston’s market-size factor (2.48), and we get expected revenue of $267 million.
Next, we’ll use a regression equation (MW = 0.1106*MP + 22.538) to determine how many games a team should win-and, therefore, how much revenue it should bring in-based solely on its payroll. For example, Boston’s $133 million payroll in 2008 should have led to 86 wins. According the win curve, multiplied by the team’s market-size factor, that would create $165 million in marginal revenue.
Then we just divide these numbers: 267 / 165 = 1.61. In other words, given their payroll and revenue potential, the Red Sox performed about 61 percent better than average in 2008.
Let’s compare the top and bottom teams from 2008, first using Doug’s approach, and then using our new one:
|Team||Marginal Payroll||Marginal Wins||
MP / MW
Of the top five teams, only one-the Rays-actually made the playoffs, and of the other four, only the Twins should have even been close. The Marlins, D’backs, and A’s performed reasonably well given their small payrolls, but still only averaged 80 wins.
Let’s see how those results compare to our new method:
|Team||Marginal Revenue||Expected MR||MR / ExpMR|
This seems a lot closer to reality. The Rays run away from the pack, with the 100-win Angels and 97-win Cubs coming in a distant second and third, respectively. Instead of punishing large-market teams, the system accounts for their inherent advantage, and judges them on how well they actually use it. The Yankees remain in the bottom five-which is actually identical to the previous list, just with a different order-but it’s no longer their fait accompli, as they would have finished in the top half had they played up to expectations. The Red Sox, for example, finish nineteenth on the old list despite winning 95 games, as compared to fifth on the new list.
If we want to make it even more meritocratic, we can use third-order wins instead of actual wins, in order to strip out some of the luck involved:
The Rays remain in front, while the Red Sox, Blue Jays, and Dodgers all move up a few spots.
Here’s the same chart for 2009, assuming each team’s current third-order winning percentage holds:
You can see the full data here.
If there’s still a piece missing, it’s the value that comes with finishing last. The first pick in the draft is worth a lot more than the fifth or the tenth or the fifteenth, so a team that wins 59 games, as the Nationals did last year, should have that factored into its marginal revenue figures. But we’ll leave that for another day.
For now, some other notes on the data we do have:
Andrew Friedman and the Rays are clearly the class of Major League Baseball right now. Ignore their actual 2009 record; first-, second-, and third-order wins have them as the second-best team in the American League, and they’re only trailing a team that will spend three and a half times as much on payroll. Combine that with a runaway victory in 2008, in both actual and third-order MR/ExpMR, and it’s hard to argue they’re not the best around right now.
The Yankees are currently twelfth in MR3/ExpMR (we seriously need a name for this, if anyone has any ideas), but only 27th in the classic MP/MW-despite being on pace to win 101 games. I think the new method is a pretty fair approximation; the marginal returns clearly diminish very quickly after about $120-$130 million (which is where the Red Sox usually are), and the Yankees could obviously win a lot of games with a $150 million payroll, if managed correctly. That they’re about average seems right-when you spend fifty percent more than anybody else, you probably should win 101 games.
The Mets are a disaster.
The Pirates, Royals, Orioles, and Nationals would definitely benefit if we included the value of their ensuing draft picks. Of those teams, I’d guess that the Pirates are the only one that actually understood this coming into the season.
It doesn’t surprise me that the Nationals aren’t in the bottom five-they’ve tracked well ahead of their actual record all year, and they actually aren’t that far behind the Mets in the adjusted standings.
Now, about that name…
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