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Sabermetric value analysis of Cleveland Browns defensive players

By Elliot Kennel

INDIANAPOLIS, INDIANA - AUGUST 17: Sheldon Richardson #98 of the Cleveland Browns watches action during a preseason game against the Indianapolis Colts at Lucas Oil Stadium on August 17, 2019 in Indianapolis, Indiana. (Photo by Stacy Revere/Getty Images)
INDIANAPOLIS, INDIANA - AUGUST 17: Sheldon Richardson #98 of the Cleveland Browns watches action during a preseason game against the Indianapolis Colts at Lucas Oil Stadium on August 17, 2019 in Indianapolis, Indiana. (Photo by Stacy Revere/Getty Images) /
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CLEVELAND, OHIO – AUGUST 29: Cleveland Browns owner Jimmy Haslam listens to general manager John Dorsey prior to a preseason game against the Detroit Lions during a preseason game at FirstEnergy Stadium on August 29, 2019 in Cleveland, Ohio. (Photo by Jason Miller/Getty Images)
CLEVELAND, OHIO – AUGUST 29: Cleveland Browns owner Jimmy Haslam listens to general manager John Dorsey prior to a preseason game against the Detroit Lions during a preseason game at FirstEnergy Stadium on August 29, 2019 in Cleveland, Ohio. (Photo by Jason Miller/Getty Images) /

Mathematical Notes

You don’t need to understand the mathematical details to understand this article, but in case you are interested, the plots of salaries versus ranking tend to resemble negative exponential functions of the form

S = Aexp (-BR) +C

where S is the salary or monetary value of the player’s services as reflected by the salary cap number according to overthecap.com. A is usually the maximum interior lineman salary in the league minus the league minimum salary. C is the league minimum of $495,000 for a first year player and B is chosen to make the curve fit the data. The Pro Football Focus rank according to grade is equal to R +1. That way the y-axis intercept is equal to the maximum salary in the league.

In some cases a two-exponential function was used in order to better account for the sky-high salaries of those very top ranked players.

S = A1exp (-B1R) +C1  + A2exp (-B2R) +C2

Limitations of the model: We can predict in advance that some players will come from out of nowhere and move up the rankings. Hence the overall trend is for veteran players to slide several places. That is not accounted for in this model.

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Likewise, value is not based purely on performance but also reflects age, injury history. If Mr. Haslam wants to give me a job, I will be happy to incorporate those features in a future 2.0 edition of the sabermetric value analysis. For now it is enough to know that the underachievers are outweighing the overachievers on the Browns.

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