“Salary Adjusted” Baseball Standings

Leveling the playing field. So to speak.

(Note: Originally written in 2013)

In baseball, as with most things in life, having money is a considerable advantage. Teams with more money tend to win more, as well they should. This post provides an overview on a methodology for a theoretical application of a “salary handicap” to adjust baseball standings based on how much money a team pays out in salary.

There is a wide distribution in the payroll of various teams. The 2012 MLB season salary distribution is shown below. That year, the lowest paying team (The Oakland A’s) paid a total of $49,137,500, which was almost 4x less than the $195,998,004 team salary from the highest paying team (The New York Yankees).

Data source: USA Today Salaries

Considering data on both Salary and Winning Percentage over time, we can see that there is indeed a correlation between how much money a team pays out and how many games a team wins. The following chart shows the results from three teams over the 15 year span between 1997 and 2012.

The big spending New York Yankees have won a lot of games as we would expect. The low spending Pittsburgh Pirates have not won much. And the Oakland A’s, of Moneyball fame, despite not spending much, have still managed to win a fair number of games.

Note that to normalize for different years, the independent variable on the x-axis is salary as a percentage of the league mean for that season, rather than an absolute number. The y-axis is simply the winning percentage of a team in a given year.

Using a simple best-fit natural log regression (a good choice since it will asymptote, and even an infinite salary level will not produce more wins than games played…just don’t tell the Yankees…) we can determine a formula to predict how many games a team will win.

Expected Winning Percentage = .082 * ln(Team Salary as a Percentage of the League Mean) + .5065

Then, using a team’s expected winning percentage, we can “handicap” that team’s current record, using the following ratio:

(Actual Winning pct./Expected Winning pct.) = (Adjusted Winning pct./.500)

In other words, instead of assuming that the team would be performing at an average level if it had a .500 record, we assume that it would be performing at an average level if it has exactly its expected winning percentage given its salary. Teams that are exceeding their expected winning percentages will have adjusted winning percentages greater than .500, and likewise, teams that have an actual winning percentage less than their expected winning percentage, which have an adjusted winning pct. that is less than .500.

For example, the 2003 Yankees. True to form, their team salary of $151 million dollars far exceeded that of any other team. And by plugging this salary into the above formula, their expected winning percentage was .645. Their final records was 101–61, or .623. Though an impressive record in absolute terms, relative to their expected winning percentage, the Yankees actually performed worse that expected, and their Adjusting Winning Percentage was just .482 (.500 * .623/.645 — see above ratio) good enough for a third place finish in the AL East behind Boston and Baltimore.

Applying this methodology to the final standings of the 2013 Season, we see that the “Salary Adjusted” Playoffs would have looked a lot different than the actual playoffs — the Indians (not the Tigers) win the AL Central, with the Royals getting the Wild Card.

Salary Adjusted AL Central Standings for the 2013 Season

If you are interested in exploring further, this Google sheet that I put together has all the data, an interactive bubble chart of all of the data points, and live adjusted standings.

Disclaimer: I grew up in Oakland, and am a lifelong A’s fan :)