On opening day of this year, payroll of the New York Yankees was around 206 million dollars. The payroll of the Pittsburgh Pirates was around 35 million dollars. Surprising nobody, the Yankees won a lot more games (95) than the Pirates did (57).

Such imbalances result inevitably from a system that includes free agency for veteran players and no salary cap. In baseball, teams with greater resources, either in revenue or in owners’ wealth, can spend more money than teams with fewer resources while remaining profitable. The sport does have a revenue-sharing system that requires high-revenue teams essentially to pay a certain amount to low-revenue teams, but revenue sharing counters only a fraction of the imbalances. (It also creates perverse incentives. Leaked documents recently revealed that the Pirates, whose payrolls are consistently among baseball’s lowest, have been one of the most profitable teams.)
The Pirates and many other teams cannot sustain team payrolls like the Yankees’, and the era of free agency has played out to the background music of fans, commentators and small-market owners pleading for increased competitive balance.

This year, however, the playoff teams were not necessarily those with highly paid stars, as we can see in a simple ranking of the teams by payroll.

Only two of the top eight teams here ended up among the eight playoff teams. The teams’ actual win totals, of course, reflect much more than payroll: good or bad management, good or bad luck, and more.

That basic insight can take us to a more complex question. Which teams got the best value for their money?

Happily, we have a tool for answering questions such as that one, questions that require determining the effect of one variable on a given outcome. A linear regression allows us to determine how much one thing affects another. In this case, our question is, “How much does payroll affect team wins?” A regression analysis plots the two variables and finds the line that most closely represents their general relationship. In our case, the number of wins per team rises as payrolls go up, as you’d expect.

This technique allows us, for example, to quantify the common-sense notion that the Yankees ought to win more games than the Pirates. The regression analysis leads us to expect something like 92.5 wins for a team with the Yankees’ payroll, 75.4 for a team with the Pirates’.

When we compare each team’s actual wins to the number predicted by payroll alone, we get a neat measure of how much each team over-performed or underperformed its payroll. That difference (the residual, in statistical terms) lets us create a new set of standings based on wins relative to payroll. This time we’ll sort by the difference between expected and actual wins.

Let’s call these the residual standings. The Rays had an extraordinary season, finishing almost 17 wins above the level implied by their below-average payroll, thanks in part to their stockpile of salary-controlled young players. The Mariners had the worst season by this measure, and the Pirates were dreadful even relative to their league-low payroll.

If you want to see the playoffs populated by teams who manage their assets well rather than simply loading up on pricey players, this was a good year. Seven of the top eight teams in the residual standings were among the year’s eight playoff teams. The exception is the Padres, who had an extraordinary season relative to their tiny payroll but barely missed the playoffs. Contrarily, the Yankees were the only playoff team outside the top eight in the residual standings. They were, in other words, the team you could most easily say bought their way into the playoffs. The Red Sox, widely perceived as a grand disappointment, came closer than any other team to their expected wins.

This is one simple method of dealing with the data. I like it as a way of producing a quick approximation of team and management performance excluding payroll effects, but you could do much more with this kind of analysis. In baseball, you could measure the influence of payroll effects over time (for example, I have found that payrolls were more strongly correlated with team wins in 2009 than in 2010). You could tweak the model to measure performance relative to revenue (or media market share, or owner’s wealth) rather than payroll, to correct for the distortions of revenue sharing. Extending the applications to other sports, you could, for instance, measure distance runners’ performance relative to age with much more subtlety than the usual age groupings provide.

In baseball in 2010, the results are in. The Giants won the World Series, but the Rays secured my championship. The residual champagne is on me.

My buddy Dan Moriarty contributed his mathematico-editorial skills to this piece.