By Nick Lopez, Elliot Chin, Pranay Varada, Moritz Miller, Jack Meyer

Also contributing: Kieran Farrell, Sterling Rosado, Aryan Naveen

Five weeks ago, the Denver Broncos signed former-Seahawk Russel Wilson to a five-year, $245 million contract extension. Wilson’s $49 million per-year deal takes up, on average, a whopping 23% of the Broncos’ cap space each year. It’s a high-risk, high-reward play. Was it worth it?

On a case-by-case basis, the answer to questions like that depend on a number of factors, most notably Wilson’s present and future performance. It is difficult for a team to forecast a player’s future success, so large deals that don’t pan out are not just frequent but inevitable. Both players and teams, however, still often opt for long contract terms to ensure stability and team control. Indeed, these large deals often end well—such as the 49ers’ now-lauded $138 million agreement with Trent Williams.

Beyond assessing large signings and extensions on a player-by-player basis, it may be useful to quantify whether large deals in general are beneficial for NFL teams. To do so, we created a metric dubbed **NFL-HHI** to measure how salary is spent within a team based on their concentration of spending among players.

NFL-HHI is built off of the Herfindahl–Hirschman index (HHI), an economic metric that quantifies the level of oligopoly and competition in a given industry. The NFL-HHI sums the square of the market share of each player in a market; a higher total sum indicates a more concentrated market. For economic usage, the NFL-HHI’s formula is as follows:

where = the market share of firm expressed as a decimal.

To adapt NFL-HHI into NFL-HHI for usage in salary allocation evaluation, we sum the squared proportion of salary cap allocated to each player on an average yearly basis. For example, if an NFL team is allocating half of its salary cap to the quarterback and a quarter of its salary cap to two wide receivers each, the NFL-HHI would be .375.

Most NFL-HHI scores tend to be between .01-.04, given the large number of players (~ 50) on a roster. The variation is primarily due to large amounts of spending on star players such as the quarterback. In this article, we propose the usage of NFL-HHI scores to rate teams based on salary cap concentration—and thus investment in high-cost star talent. Additionally, we offer preliminary analysis of how NFL-HHI scores correlate with team success.

**NFL-HHI as a Team Metric**

To evaluate the effectiveness of NFL-HHI as a team metric, we first evaluated its distribution across NFL teams over the past ten years. We found that NFL-HHI values are lognormally distributed, as pictured below. After taking the logarithm, base 10, of each NFL-HHI value, the Kolmogorov-Smirnov test, commonly known as the K-S test, was applied. The test statistic value D = 0.04026, with a p-value of 0.70025, implies the NFL-HHI values do not differ significantly from a standard normal distribution, and there is a low probability it occurred by chance.

Lognormal distributions themselves have many close connections to human behavior. They represent the length of chess games, Rubik’s cube solves, and human reactions to acoustic stimulation. In the context of NFL-HHI, it reveals that the majority of teams have historically had NFL-HHI’s much lower than the mean, thanks to a strong right-skewed distribution of the data towards higher values. This intuitively makes sense — most teams maintain similar salary cap distributions as their peers. In some cases, however, NFL-HHIs will rapidly increase at the signing of a superstar player, earning significant investments in the hopes it will pay dividends for the team.

**Case Studies on NFL-HHI**

Next, to evaluate the usefulness of NFL-HHI, we looked into how a team’s historic performances varied with their NFL-HHI rating. As an unbiased metric for team success, we took SRS rating, a rating system based on point differentials that acts as a simple, widely-accepted baseline to compare on-field performance.

Ten years ago, Tom Brady and Peyton Manning were among the sport’s highest-earning athletes. With Manning receiving an annual salary of $19.2 million and Brady $18 million in 2012, they led two of the best teams of the 2010’s. This can be supported by their high SRS scores (2012 Broncos: 10.1, 2012 Patriots: 12.8). Additionally, both teams exhibit relatively high NFL-HHI scores of 0.02304 (Broncos) and 0.01690 (Patriots). These examples show that high NFL-HHI can correlate with success, particularly when that high NFL-HHI stems from a superstar player. This trend, however, is not universally present.

In contrast, the 2013 Seattle Seahawks won the Super Bowl with a very balanced spending structure, perhaps due to their Legion of Boom defense. At an NFL-HHI of 0.00677, Percy Harvin was the highest-earning player receiving $10.707 million and Russel Wilson, their rising-star quarterback, was still on his rookie contract. Despite that value, the 2013 Seahawks had an exceptional SRS score of 13. In a similar manner, the 2017 Philadelphia Eagles won it all with an NFL-HHI of just 0.00721. In that year, the Eagles’ SRS score was 9.4. Thirdly, the highest-ranked team (SRS score of 15.4) of the last ten years was the 2019 Baltimore Ravens. Going into the playoffs as the top-seeded AFC team, the Ravens would later be upset by the #6 Titans in the divisional playoff round. Notably, the NFL-HHI of that year’s Ravens team was only 0.00652. Interestingly, all three of these high-performing, balanced teams had a quarterback on a rookie contract.

A team that is well-balanced in terms of payroll, however, doesn’t always translate to success. According to the SRS model, the 2012 Kansas City Chiefs (-14) and the 2012 Jacksonville Jaguars (-13) are the two worst teams during the 20-year time period we examined. Interestingly, both franchises exhibited very low NFL-HHI scores of 0.00567 (Chiefs) and 0.00305 (Jaguars). In fact, the Jaguars’ score of 0.00305 is the lowest NFL-HHI score recorded throughout the past ten years. Another team that naturally comes to mind when thinking of poor NFL performances are the 2016 Cleveland Browns. Of course, the SRS model ranked the Browns relatively low with a score of -10.1 in 2016 and -11 in 2017. However, with NFL-HHI scores of 0.00962 and 0.01340, respectively, the Browns’ paying structure didn’t particularly stick out.

Additionally, we examined how teams perform the year after they offer a major contract to a star. The most prominent recent example of this phenomenon is the Kansas City Chiefs’ signing of quarterback Patrick Mahomes to a 10-year, $450 million deal. After signing Mahomes in 2020, the Chiefs’ NFL-HHI in 2021 was the second-highest recorded score (0.03906), second only to the 2021 Houston Texans (0.03963) after paying Deshaun Watson $39 million annually. With an SRS score of 7.4, the 2021 Chiefs also performed well above average. Still, the Chiefs were not necessarily the best: the 2021 Dallas Cowboys recorded an even higher SRS score (9.9). After renewing Dak Prescott’s contract that year, the Cowboys’ capital concentration rose dramatically, with their NFL-HHI score going up to 0.03190.

NFL-HHI, in a particularly relevant case study, can provide insight into the teams competing in the 2022 Super Bowl. As one might expect, both the Los Angeles Rams and the Cincinnati Bengals (both No. 4 seeds) had above average but not spectacular SRS scores of 5.3 and 3.1, respectively. However, neither team had an unusual payment structure. At 0.01418, the Rams’ NFL-HHI score was just about normal. On the other hand, the Bengals exhibited an NFL-HHI of 0.00543. Considering that they were led by Joe Burrow, who was on a rookie contract, it makes sense that they came so far without paying a quarterback as much as the Cowboys or the Chiefs.

**NFL-HHI and SRS Over Time**

Perhaps taking a closer look at individual teams’ NFL-HHI and SRS over time can offer some insight into front office strategy. The graphs above were created by scaling all 32 NFL team’s HHI and SRS for each year so the new values corresponded to the number of standard deviations a team was above or below the league average.

One team that immediately jumps out is the New England Patriots, who have been higher in scaled SRS than scaled NFL-HHI for the past decade. The Patriots’ emphasis on role players—plus the willingness of their quarterback during most of this period, Tom Brady, to take a pay cut in order to improve cap flexibility, was the recipe behind this success. Unsurprisingly, New England’s front office has been lauded by agents as one of the smartest in the league.

Other teams that regularly maintained a lower scaled NFL-HHI than scaled SRS are the Chiefs, who only recently became a league leader in NFL-HHI thanks to Patrick Mahomes’ massive extension, as well as the Bengals, Eagles, 49ers, and Buccaneers. On the flip side of this are the Detroit Lions: the only team to have a higher scaled NFL-HHI than scaled SRS in every year since 2012. Matthew Stafford was the constant star throughout these years, while Calvin Johnson, Ndamukong Suh, and Darius Slay were among the other $10M+-per-year earners. The Lions simply weren’t able to build success with just a few star players and a myriad of smaller contracts.

As shown earlier, there doesn’t seem to be much of a correlation between NFL-HHI and SRS in general. One interesting case, however, was the Atlanta Falcons, who went to Super Bowl LI in one of their lowest NFL-HHI seasons and generally had opposing trends with regards to the two metrics. The Denver Broncos, meanwhile, interestingly had a visible decline in both NFL-HHI and SRS over the past decade. For them, spending more evenly after Peyton Manning’s retirement was met with less success on the field.

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**Relationship between SRS and NFL-HHI**

One way to test if there is a correlation between two variables is a linear regression, or a “trendline” which attempts to mimic the data as closely as possible. In this case, it was our belief a team’s success (SRS) might depend on the distribution of capital (HHI), and thus we placed NFL-HHI on the horizontal axis and SRS on the vertical axis, and made a scatter plot with every data point (each representing one of the 32 teams during a given year) throughout the past decade. Then, we fit a linear regression to the graph.

Evidenced by the trendline, the NFL-HHI score does not have much of a relationship with SRS. This is also indicated by the very low R^2 value of 0.009. The confidence intervals of the trendline include 0, indicating that our results are not statistically significant.

Although NFL-HHI is not necessarily predictive of team success, it does have a slight correlation with team performance variance. Absolute value of SRS versus logarithm of NFL-HHI is statistically significant with linear and quadratic correlations. That is, logarithmic NFL-HHI has a negative correlation with the absolute value of SRS rating. This implies that more concentrated cap spending, while not making a team better, may decrease the variance of a team’s rating. Teams with high NFL-HHI may be slightly less likely to perform extremely well or extremely badly. These teams likely have average or above average QBs (e.g. Kirk Cousins, Derek Carr) on relatively large contracts that raise the floor of a team but aren’t likely to lead them to a Super Bowl. Qualitatively, this makes sense: teams with low NFL-HHI may be subpar across the board, or could be bolstered by strong low-salary rookies. Last year’s Super Bowl matchup showed the dichotomy of the two types of successful team building. The Bengals had a budding star quarterback in the second year of his rookie deal in Joe Burrow and the Rams had veteran Matthew Stafford in his 13th NFL season.

*Linear correlation: 95% confidence interval on intercept: **[-2.182425 , 4.65247251] and slope: [-1.63462334, -0.0855768 ]*

*Quadratic correlation: 95% confidence interval on intercept: [16.30077537, 67.00307764], slope: [ 6.10055448, 29.11058308], and quadratic: [ 0.78808964, 3.37810829]*

## Conclusion

Overall, we propose NFL-HHI as a metric to measure salary cap concentration among NFL teams. It is useful as a way of condensing multidimensional—that is, 55+-dimensional—data into a single scalar value. NFL-HHI varies as conventional analysis predicts and provides quantitative backing to qualitative analysis on team performance on a case-by-case basis. For example, NFL-HHI can provide useful, easily digestible context to the performance of a given team in a given year. This context is particularly important when looking at teams that recently signed players to large contracts, performed particularly well, or performed particularly poorly.

When considering NFL-HHI as a predictive measure, though, conflating factors dampen its usefulness. NFL-HHI does not have strong correlation with SRS ratings, a proxy measure for team strength. The metric, however, does have a slight relationship with rating variance, so while we cannot conclude unilaterally whether large signings are helpful for teams, spending distribution likely has a correlative effect with how extreme teams’ performance is. Overall, spending more on big deals, over the past ten years, reverts teams to the mean.

Ultimately, NFL-HHI is primarily useful as a descriptive measure for evaluating team strength and roster construction. In the future, analysis of how NFL-HHI compares with other statistics may prove fruitful. Additionally, HHI applied to other sports, such as the NBA—where the market for players is restrained by salary caps and thus much less efficient—could yield insights on how front offices should adapt signing strategies.