The NFL Market for Damaged Goods

While lots of discussion has gone into the diagnosis, treatment, prevention, and abatement of concussions in the National Football League, little attention has been given to the financial losses experienced by the injured player. 

Is it possible to measure the cost of a concussion? I tackled this topic once before but I admittedly fumbled my way through it. Now it's time to push this idea over the goal line.

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Nearest-neighbour matching is a rather simple process in which each observed item can be pared with its closest nieghbour. For example, home-lenders will use nearest-neighbour matching to collect prices on recently sold houses, known as 'comparables,' to assess the appraisal value for the home they are underwriting a loan for. They consider all sorts of observable information, such as number of bedrooms, bathrooms, square footage, attached/detached garages, etc.

Similarly, we can use nearest-neighbour matching to assess similar National Football League (NFL) quarterbacks. We can consider everything from the athletes' age, experience, passer rating (or quarterback rating), etc. Once we have a set of pared quarterbacks, we can calculate the impact small differences can have on the future salary of a free-agent quarterbacks.

For example, it's logical to say that two quarterbacks who each played in 9 games and threw for roughly 2,000 passing yards and 11 touchdowns would be very similar individuals. In fact, one would imagine that two such individuals, such as 2013 Matt Cassel and Jason Campbell, should be in line for a very similar compensation in free agency: See the table below to see how similar these two quarterbacks faired in the 2013 season.

Matt Cassel		Jason Campbell
2013	Year	2013
31	Age	32
9	Games Played	9
1,807	Yards	2,015
11	TDs	11
81.6	Rating	76.9
10.5M/ 2 Years	Next Contract	1.5M/ 1 Year

But what if I told you that one of the two aforementioned free-agent quarterbacks received seven times as much money as the other? Is there some other variable we have not considered that can explain why Matt Cassel would be valued at $9 million more than Jason Campbell?

That's right - in 2013, Jason Campbell had a concussion!

Browns need another QB after Campbell leaves with concussion http://t.co/2pRRire71w

— ProFootballTalk (@ProFootballTalk) November 25, 2013

Despite Jason Campbell's concussion keeping him out of NFL action for only one game, it appears that NFL executives may have viewed him as 'damaged goods.' In fact, repeating this exercise for all the free agent quarterbacks with concussions from 2012 to 2015, leads to similar findings: Jimmy Clausen played a lot like Ryan Mallet in 2014 but missed one game due to concussion and subsequently received less than one-third what Ryan Mallet made in 2015; similarly, Brian Hoyer and Ryan Fitzpatrick were very similar in 2015 but a 3 game absence from a concussion led to Brian Hoyer making only 17 percent of what Ryan Fitzpatrick did in 2016 (despite Brian Hoyer being younger and arguably better when he was healthy).

Unfortunately (but for their sake, fortunately) there are not many quarterbacks entering free agency after a concussion: consider that only nine quarterbacks suffered a concussion prior to free agency while one of them, Johnny Manziel, never played again in the NFL (but perhaps a concussion was the least of his issues). The lack of concussion events makes it difficult to assess how general this finding is. 

Assuming these findings are true, however, presents a new type of arbitrage: since some studies have found that performance after a concussion is comparable to pre-concussion levels, bargain-hunting teams may be able to sign post-concussion free agents below market value. Consider that after his concussion in 2015, Brian Hoyer went on to throw an average of one touchdown per game with a passer rating of 98, all while making just $2 million for the 2016 Chicago Bears; at the same time, Ryan Fitzpatrick re-upped with the New York Jets for $12 million and threw for 0.86 touchdowns per game with a passer rating of 70. 

Again, while anecdotal, this could be evidence that some teams are taking advantage of the damaged goods, just dented cans at the grocery store.