Median Salary and Wins

The last post examined total team salary and estimated its effect on regular season win totals. The data showed there was a connection, and that for every standard deviation above average in team salary ($13 million), a team could expect to win an extra 0.33 wins.

In recent years, I've heard some analysts explain the success of some teams, particularly the Patriots, by noting they are a team of few stars but of great depth. Beyond a couple notable exceptions, their best teams were filled with many above average players and very few big stars. They had very few holes in their starting line-up.

It seemed plausible to me. With less salary cap room taken up by big name stars, there is more to spread around at each position and for reserve players. A team composed like that would have very few weak links and would be less vulnerable to injuries.

To see if there is a connection between team composition and winning, I compared team median salary and regular season wins for 2001-2006 (n=191). A team with a lot of highly paid stars would have a low median salary, and a team with few highly paid stars would have a high median salary. However, I need to account for team total salary, because as a team increases its total salary its median salary would naturally increase without any additional "spreading of the wealth." Also, as I did previously, I normalized the salary variables by year because the salary cap grows annually.

I ran a regression model of regular season wins based on median salary and total team salary. The results are:



VARIABLECOEFFICIENTSTDERRORT STATP-VALUE
Z Median Salary0.340.231.470.14
Z Total Salary0.280.181.580.12
r-squared0.03








This result supports the notion that an even team composition is advantageous, but it is not quite conclusive. Median salary is marginally significant, as is total salary. For every standard deviation above average in median salary, a team can expect an additional 0.34 wins, holding total salary constant. The team that is most "fair" in spreading the wealth would be about 2 standard deviations above average, so they could expect to win about an extra 0.68 games per year on average.

When I see results like this, that confirm what we'd expect, but with significance levels around 0.1, I suspect that there is almost certainly a connection but because the effect is small we need a larger data set to see higher significance levels.

Also note that the coefficient of total team salary is revised to 0.28 wins per standard deviation (compared to the previous post). This confirms the effects of total and median salary are not independent of one another.

Ultimately, the effects of total salary and median salary are most likely real and measurable, but small. Even the highest spending team can't even guarantee themselves one full additional win for their spending spree. I believe this underscores the importance of revenue sharing and the salary cap. Without those mechanisms to counter-balance free agency, the NFL would be very predictable, and we'd likely be watching the richest teams in the playoffs every year.

Data was obtained from the USA Today NFL salary database.

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2 Responses to “Median Salary and Wins”

  1. Sky says:

    Just curious, why did you use median wins instead of something like standard deviation to measure salary consistency?

  2. Brian Burke says:

    Standard deviation would have worked as well. SD and median in this context would tell you the same thing. But to be honest, the real reason I used median is that's the data I had.

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