Saturday, March 2, 2013

2013-03-02: NFL 2013 Salary Cap

The NFL salary cap for 2013 has been calculated to be about $123 million. All NFL teams must be in compliance with the salary cap by March 12th when the new league year starts. March 12th also marks the start of the free agent market in the NFL. Teams that are over the salary cap must let some players go and teams that are under the salary cap are looking to add new players to their rosters.

The process sounds simple on the surface but in reality it becomes confusing rather quickly. Many teams routinely exceed the salary cap by manipulating contracts. The Pittsburgh Steelers were about $14 million over the cap until they modified Ben Roethlisberger's contract and changed most of his pay into a signing bonus. Signing bonuses can be amortized over the life of a contract. Instead of receiving an $18 million dollar salary, the player gets a $2 million dollar salary and a $16 million dollar bonus. The bonus will be divided by the number of years in the contract and thus reduce the impact on the salary cap.

This type of contract modification is taking place with many of the top players this year.
Tom Brady just signed a new contract that gives him a $7 million dollar salary and $30 million in bonuses over the five years.

At its core, the salary cap is about revenue sharing between the players and the team owners. One of the purported benefits of the salary cap is to help level the playing field between teams and improve competitive balance. The NFL instituted the salary cap in 1994 in part to prevent some teams from buying up the best players and dominating the game.

It is now close to twenty years after the salary cap was implemented and many people argue about the efficacy of the salary cap to promote equality on the field or if it brings mediocrity to the game. One way we can take a look at this is to compare the number of wins per year between teams. Each game has a winner and a loser and there are 16 regular season games for each of the 32 teams every year. Therefore the mean value of the number of wins per team will be 8 (controlling for fewer team in pre-expansion years). We are going to take a look at the distribution of the number of wins. If team parity is low you will see a larger standard deviation as the number of wins is spread out. Conversely if the standard deviation is small, most of the teams will be clustered around the mean 8 wins per year. Using data from 1990 (before the cap) to 2012, we plotted the standard deviations from each year with a trend line.


Our data shows that the standard deviation averages about 3.0 and clearly displays an increasing trend. The spread in number of wins per year has been increasing slightly since the salary cap has been in place. In the book Wages of Wins the authors introduced a metric the call the Noll-Scully measure which compares the idealized standard deviation to the actual standard deviation. For the NFL the idealized standard deviation is 2, to calculate Noll-Scully divide the actual standard deviation by the idealized. Using the trend line this results in a 1.45 in 1990, increasing to a 1.6 in 2012. This is similar to the overall score the authors found in Wages of Wins. By itself the Noll-Scully does not mean much but when the authors compared it to American Baseball, Basketball and other sports, the NFL displayed more parity. Finding this not quite convincing we decided to try another metric, the Gini Index.



The Gini Index is a measure of statistical dispersion and is commonly used by economists to measure inequality of wealth. The index ranges from 0 to 1 ( or 0 to 100 ). A score of 0 means perfect equality, a score of 100 means perfect inequality. In our case when measuring 32 teams that either win or lose, the worst case would be 16 teams with 16 wins and 16 teams with 0 wins. This would result in a Gini Index of 50 so our score will range from 0 (every teams has 8 wins) to 50. The Gini Index was calculated using the same data from 1990 to 2012 and plotted with a trend line. All of the values are below 25 which is considered very good by economists for wealth distribution. For our purposes it is still quite good however the data displayed almost the same upward trend as the standard deviation.

To find out if the upward trend was statistically significant we used Mann-Kendall trend analysis. Mann-Kendall is a non-parametric test used for identifying trends in time series data. The data values are evaluated as an ordered time series. Each data value is compared to all subsequent data values. The result of the analysis indicates that the upward trend is not statistically significant at 95%.

Overall the parity in the NFL appears to rather good, especially compared to some of the other American sports. The salary cap is not the only tool used to improve the team parity. Draft picks and strength of schedule are both determined based on last years performance. Teams that did poorly are given better draft picks and easier strength of schedules. The levers that the NFL have put in place appear to be working as far as promoting a competitive balance without negatively impacting gameplay. The performance of the Indianapolis Colts and the New England Patriots in the 2000s proves that dynasties are still alive and that a well managed team can still excel.

--Greg Szalkowski



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