Stat Analysis
Advanced analytics on player and team performance

How Much Are NFL QBs Worth?

Kansas City Chiefs QB Patrick Mahomes
Photo: USA Today Sports Images

Guest column by Jeremy Rosen

In July 2020, Kansas City Chiefs quarterback Patrick Mahomes signed a record-breaking 10-year, $450-million contract extension. Not only did this extension make him the highest-paid player in football, but it also made him the highest-paid athlete in professional sports history. In addition, his $45 million average annual value (AAV) surpassed the $35 million AAV of the Seattle Seahawks' Russell Wilson, who since 2019 had been the highest-paid player in football. (Mahomes's AAV is 22.7% of the 2020 salary cap, exceeding the previous record set by the Green Bay Packers' Aaron Rodgers. Rodgers's AAV was 18.9% of the cap in 2018, which is when he signed his extension.) If anyone deserves such a payday, it's the 24-year-old Mahomes, who won an NFL MVP in his second season and a Super Bowl MVP in his third.

But is it really worth it for the Chiefs to pay Mahomes so much money? His off-field value to the franchise aside, one can argue that given the salary cap, paying him so much will impair the Chiefs' ability to afford talented players at other positions. Furthermore, this argument doesn't only apply to him. Wilson, Rodgers, Ben Roethlisberger, Jared Goff, Kirk Cousins, Carson Wentz, Dak Prescott, and Matt Ryan each have AAVs of $30 million or greater, and their contracts -- all of which were signed from 2018 onward -- also cost their teams non-quarterback talent. (Aside: Considering Mahomes' talent and guaranteed money, his contract is in line with the above quarterbacks' contracts. It is unusually long, but a long contract can be team-friendly if the largest cap hits are deferred to future seasons. Nevertheless, all these contracts are unprecedentedly expensive relative to those signed before 2018.)

As such, could the best veteran quarterbacks be overpaid? Because the long-term effects of the above contracts have yet to be observed, there is currently no way to know. However, I found that prior to 2018, rather than being overpaid, the best veteran quarterbacks were significantly underpaid. That is, teams were generally much better off with a good, expensive quarterback than a mediocre, cheap one. But then, in 2018, Jimmy Garoppolo, Cousins, Ryan, and Rodgers each broke Matthew Stafford's salary record in quick succession. By becoming the rare starter to hit free agency, Cousins may have catalyzed this rise in quarterback salaries. In this column, I show how I came to that conclusion, why my findings may explain the post-2018 salary boom, and what that boom may mean for the quarterback market going forward.


QB Spending Model

I start by providing a qualitative overview of my model. (If you're interested in the model's details, they are in my full working paper.) To begin with, I suppose that each NFL team is a single-season win-maximizer, and wins are a function of quarterback talent, non-quarterback talent, and less quantifiable team- and season-dependent factors such as coaching. Also, both quarterback and non-quarterback talent cost money, and teams cannot spend more than the salary cap, leaving aside contract restructurings. (If anything, omitting restructurings may bias the model toward making quarterbacks seem overpaid. That's because a win-now team may push its quarterback cap hits into the future, in which case it will have a deceptively cheap quarterback now. In turn, it may appear that choosing a cheap quarterback contributes more to winning than it actually does.) As such, the maximization problem teams face is to choose the quarterback who, based on his talent and monetary cost, will win the most games.

The price of quarterback talent is therefore the main determinant of what teams do. If this price is sufficiently low, then teams will be incentivized to pursue the best quarterback available and perhaps even trade other talented players to acquire him if he is not a free agent. On the other hand, if the price is sufficiently high, then teams should stay away from the best quarterbacks and instead seek out cheaper ones in order to maximize talent at other positions. Lastly, if the price is neither that low nor that high, then teams may be largely indifferent to their quarterback's talent. Such an equilibrium exists in baseball, where it does not matter whether teams pursue superstars or employ a more balanced method of roster construction (see Jonah Keri and Neil Paine's FiveThirtyEight article for more information).

There is an additional factor I have to consider: the rookie salary scale. High-quality quarterbacks on their rookie contracts, which last four years, must play at a steep discount. For example, Mahomes made fewer than $14 million in his first three seasons combined. To be clear, that does not mean the optimal strategy is to draft a rookie quarterback rather than sign or re-sign a veteran one. Rookie quarterbacks are cheap in terms of money, but they are risky and cost draft capital, which can be used to acquire cheap talent at other positions. In particular, trading up for a top quarterback prospect can cost multiple first-rounders, and a team in position to draft one without trading up faces the opportunity cost of not trading down for multiple first rounders. Having said that, draft capital and its associated opportunity costs are very hard to quantify. For that reason, I omit teams that drafted a first-round quarterback in the previous four years.

Lastly, there is the question of whether teams actually behave like single-season win-maximizers. As far as win-maximization goes, a salary floor prevents profit-conscious owners from indefinitely fielding cheap, inferior teams. Also, while revenue sharing can incentivize small-market teams to lose to large-market ones to expand the total revenue pool, previous research finds that owners generally care about winning, making them unlikely to be that unsporting. As for the single-season specification, while teams interested in sustained success do not necessarily try to maximize wins every year, a multi-season optimization model is infeasible to estimate given the currently available data. Moreover, the single-season model has done well at fitting pre-2018 data and predicting the post-2018 direction of the quarterback market.


Estimation and Results

To estimate my model, I used data of each team from 2013 to 2017 that had not drafted a first-round quarterback in the previous four years. This subset of teams makes up the "partial dataset," as opposed to the full dataset which includes all 32 teams in each year. (Unfortunately, there is no available pre-2013 data on cap spending.) I then measure team quarterback talent with ESPN's Total Quarterback Rating (Total QBR). I use Team Total QBR instead of team passer rating because unlike passer rating, Total QBR attempts to measure quarterbacks independently of their teammates, and my model treats quarterback talent and non-quarterback talent as separate entities. The main regression function I estimate is:

Wins = β1 × Team Total QBR + β2 × Non-QB Cap Spending + β3 × Year + Team Fixed Effects + ε.

Wins are regular-season only, and controlling for Year is necessary because the salary cap increases annually. Therefore, Non-QB Cap Spending must increase as well for teams to maintain the same level of non-quarterback talent. In addition, Team Fixed Effects are necessary because of intangibles, such as coaching, and because some cities, such as Dallas, may be particularly attractive to talented free agents.

Upon running this regression, I find that while Team Total QBR and Non-QB Cap Spending both have positive and statistically significant effects on Wins, Team Total QBR's effect substantially exceeds that of Non-QB Cap Spending. Figure 1 provides a visualization; it shows a representative team's Projected Wins with respect to Team Total QBR under both 2018's salary cap and three different prices per unit of Team Total QBR. The low price is the lowest price observed in the partial dataset (belonging to the 2013 Seahawks with rookie third-rounder Wilson), the middle price is the mean price, and the high price is the highest price (2017 Miami Dolphins with Jay Cutler filling in for an injured Ryan Tannehill).

At all three prices, the highest Team Total QBR in the partial dataset results in significantly more Projected Wins than the lowest Team Total QBR. As the price increases, this net benefit decreases (at the high price, the difference in Projected Wins between the highest and lowest Team Total QBRs is 3.3, versus 6.9 at the low price), but even the high price is too low to make the net benefit a net drawback. In other words, this figure shows that quarterbacks were systemically underpaid through 2017. To clarify, as Team Total QBR increases in this figure, Non-QB Cap Spending decreases. Therefore, at a high enough price, a higher Team Total QBR will result in fewer Projected Wins, and quarterbacks will be overpaid.

Figure 1

Table 1 illustrates the same concept. It ranks the 2017 teams in the partial dataset based solely on their Team Total QBR and Non-QB Cap Spending (for brevity, only the top and bottom five teams based on Projected Wins are shown). Atop the ranking were the Dallas Cowboys, with fourth-rounder Prescott still on his rookie contract. Meanwhile, the Indianapolis Colts, with an injured Andrew Luck no longer on his rookie contract, were at the bottom. The two key takeaways from this table are that Projected Wins are positively correlated with Actual Wins (correlation coefficient for the entire partial dataset = 0.70), and Team Total QBR is much more correlated with Projected Wins (cc = 0.94) than Non-QB Cap Spending is (cc = 0.62). In other words, Team Total QBR matters more than Non-QB Cap Spending, which means that at 2013-2017 prices, teams should prioritize quarterback talent over cap savings. If enough teams do so, then the price of quarterback talent will increase until quarterbacks are no longer underpaid.

Table 1: Top and Bottom Five Teams in 2017 by Projected Wins, Partial Dataset
Top Five Teams
Team Team Total QBR Non-QB Cap Spending Projected Wins Actual Wins
Dallas Cowboys 66.3 $158.1m 11.5 9
New England Patriots 70.2 $149.2m 11.2 13
Seattle Seahawks 58.1 $152.0m 9.7 9
Pittsburgh Steelers 63.2 $143.6m 9.6 13
Detroit Lions 61.8 $145.3m 9.6 9
Bottom Five Teams
Team Team Total QBR Non-QB Cap Spending Projected Wins Actual Wins
Cincinnati Bengals 42.0 $146.1m 6.7 7
Miami Dolphins 41.8 $140.3m 6.1 6
Baltimore Ravens 46.0 $132.3m 6.0 9
Arizona Cardinals 38.2 $140.0m 5.6 8
Indianapolis Colts 35.9 $135.5m 4.8 4

There is a notable counterargument, namely that Super Bowl-winning teams have often had quarterbacks on their rookie contracts (2019 Chiefs, 2017 Eagles, and 2013 Seahawks) or have had Tom Brady (2018, 2016, and 2014 New England Patriots), who intentionally took a discounted salary. (The exception since 2013 was the 2015 Denver Broncos with Peyton Manning.) However, there are three points worth making. First, the sample size of Super Bowl-winners is small, so using team wins instead of Super Bowl championships provides more reliable results. Second, the same quarterback on the same team won three of those Super Bowls, which effectively makes the sample even smaller. And third, the Patriots may have still won one or more of those Super Bowls even if they had paid Brady more.


Conclusion

I started this research in 2017, and at the time, I was surprised that the best quarterbacks could be significantly underpaid. (It is worth emphasizing that it is still a bad idea to give a big contract to a mediocre quarterback.) As a result, I wondered if not accounting for a potentially important factor, such as non-win-maximizing teams, had somehow skewed my results. But the substantial post-2018 increase in quarterback salaries relative to the salary cap has made me more confident in my conclusions because it appears that teams, quarterbacks, and agents may have also come to those conclusions.

In that light, what will happen to the quarterback market going forward? I think the answer ultimately depends on whether the best quarterbacks are still underpaid or whether that is no longer the case. The Chiefs in particular should be a good litmus test; Mahomes is one of the best, if not the best, quarterbacks in the NFL, but the Chiefs will now pay him the highest salary in league history. It may take up to a few years to provide the necessary data, especially since his largest cap hits are deferred to future seasons. However, as long as the NFL does not change the rules and exempt quarterback contracts from the cap, my model should be able to help determine the optimal level of quarterback spending.

Jeremy Rosen is one of the creators of the functional mobility model for quarterback prospects, which is also featured on Football Outsiders. He is currently between PhD programs in economics, and he runs a tennis analytics website called Topspin Shot Research that uses advanced statistical techniques to better contextualize traditional tennis statistics.

Comments

9 comments, Last at 16 Sep 2020, 4:25pm

1 no such thing

It should be pointed out nobody gives a big contract to a mediocre quarterback. If Tannehill bombs this year, yeah, plenty of folks will say 'look how much the Titans gave to a mediocre quarterback!' Except they didn't. They gave a big contract to a guy they hope will be as good as he was last year, rather than the prior 5 years. Same would apply if you reverse that, if they give a big contract to a 'proven' quarterback coming off of one mediocre season.

Doesn't look to me like your study particularly addresses this. Which if so is perfectly fine.

2 It should be pointed out…

In reply to by BigRichie

It should be pointed out nobody gives a big contract to a mediocre quarterback.

Plenty of teams do that.

 

That said, so long as the NFL insists on bending the rules towards QB and passing, there's really no spending ceiling on QBs. You've basically completely devalued 14 positions, so you might as well go crazy on the remaining 8.

4 I worry about using total…

I worry about using total qbr as a point in time covariate. In a sense teams aren't just spending for a single seasons worth of QBR, but some baseline expectation of good performance.

Disclaimer Nerd talk

It's been a while since my graduate school days, but determining whether QBs or overvalued or undervalued I probably would treat this like an asset pricing problem and see if the discount factor matches the expected win probability.

There's also some endogenity baked into the total qbr and the win probability metric. I might consider using Vegas is expected odds as a proxy for wins. 

Finally there are some issues with measurement due to bargaining power. Quarterbacks who sign in free agency are able to leverage themselves against multiple teams for the best offer. Those Ricky quarterbacks are essentially taking somewhat of a discount to fast track their contract earlier. As you mentioned, it might be worth looking at post initial contracts after the rookie contract. Basically Russell Wilson's second raise.

5 Russell Wilson wasn't a rookie in 2013

Wilson was drafted in the third round in 2012 and won the starting job over Flynn, who had just been acquired that same offseason. 

2013 was Wilson's second season. 

7 How much

How much does non-QB spending interact with having a consistently good QB?

I know players offered discounts to join the NE Pats for the chance to win a SuperBowl. Probably will happen in KC as well. 

Other teams with bad QBs have to offer more money for star non-QBs. 

I think giving Mahomes a 10 year contract will definitely attracted better players for lower prices. That makes this deal even better.

8 It's an interesting point…

In reply to by SevenMountains

It's an interesting point. It's definitely better to be a desirable destination than an undesirable one (although, Kansas City the place probably negates some of the Kansas City team desirability). But in football, where careers are so short, salaries not fully guaranteed, and rookie contracts are so low for anyone outside of the top of the first round, I wonder how many players are ever in a position to take a discount.

9 I have been saying this for…

I have been saying this for years now. The Quarterback market is totally insane. You had guys like Tom Brady making 25 million per year, then guys like Joe Flacco making 27 million per year. Even ignoring Brady, if Rogers is making 30 million per year, then Matt Stafford, even though he is quite good, should not be making 28 million per year. Either the top tier guys are massively underpaid, or the mid tier guys are massively overpaid, or possibly some combination of the two.

Before even getting into statistical analysis, taking a step back and asking ourselves "would we prefer 30 mil in cap space, or Aaron Rogers," should answer this question for us. Nobody could possibly want the cap space, unless you think Rogers has taken a permanent step back. Even with Mahomes's contract, would anyone rather have 45 mil in cap space over Mahomes? Would your offense be better with Michael Thomas at 20mil + top tier LT at 15mil + good center at 5mil + Case Keenum at 5 mil? I think not, making Mahomes probably still underpaid even at his asking price.

On the other hand, the mid tier guys can definitely be overpaid. Case Keenum + Michael Thomas could very well be vastly superior to Joe Flacco, Andy Dalton, Cam Newton, Jamies Winston, Ryan Tannehill, or god forbid Jacoby Brissett at 28 mil. The asking price for prime Drew Brees/Tom Brady/Russel Wilson/Aaron Rogers would need to be something like 60 million before I would prefer to not have them. As of right now, they don't cost enough to make it anything other than a no-brainer to have one.