The sharp decline in RB pay got me to wondering what the dynamics are that drive NFL salaries for veterans. The NFL is a situation where
1) For every position, every team must have (at least) some fixed number of players, and
2) There is a hard cap.
Theoretically this means that player salaries should be governed entirely by
1) The distribution of player skills within a given position group, and
2) The position's contribution to winning.
This is simplifying many other factors such as rookie contracts, switching costs, the fact that a player's skills are not equally valuable for all systems or team circumstances etc. But it gives a baseline. To test this out I made a little script simulating teams operating in a salary cap structure. I assigned players to positions, with skill represented as a single number. Skills were distributed normally with mean 0 and a standard deviation per-position group, representing both the spread of skill as well as the relative impact to winning.
Teams were then allotted a budget. Their goal was to maximize the sum of skills on the team. Many rounds of bidding were simulated, where a team could exchange one of their players for a better player, provided they offered that player a raise and it would fit under the cap. After enough rounds the distribution of salaries becomes more or less stable, and I was able to recreate more or less the distribution of salary allocations we see within position groups in the NFL (ignoring rookie contracts).
This little model's resulting distribution of salaries is really dependent on how you assign variation to the positional groups, and doesn't model things like player loyalty, system fit, team's in GFIN mode or tanking, etc. I am not an economist so I am sure this is something that has been done already, but I found it interesting.
Especially interesting was how slight changes to a distribution of player skills could result in vastly different assignments of budget. For example, infusing the quarterback group with several median-skill players greatly reduced the top echelon of salaries, because a lot of the bottom end of the salary distribution was to avoid having to have a really really bad player. Other positions were less variable based on a few changes simply because there are 3 WR's per team, 2 tackles etc etc. Which also got me wondering about whether these really big, really long QB contracts are taking on a risk that the marginal value of a QB might fall quite a bit with the infusion of just a few more good young quarterbacks.
Let me know if none of this makes any sense.
1) For every position, every team must have (at least) some fixed number of players, and
2) There is a hard cap.
Theoretically this means that player salaries should be governed entirely by
1) The distribution of player skills within a given position group, and
2) The position's contribution to winning.
This is simplifying many other factors such as rookie contracts, switching costs, the fact that a player's skills are not equally valuable for all systems or team circumstances etc. But it gives a baseline. To test this out I made a little script simulating teams operating in a salary cap structure. I assigned players to positions, with skill represented as a single number. Skills were distributed normally with mean 0 and a standard deviation per-position group, representing both the spread of skill as well as the relative impact to winning.
Teams were then allotted a budget. Their goal was to maximize the sum of skills on the team. Many rounds of bidding were simulated, where a team could exchange one of their players for a better player, provided they offered that player a raise and it would fit under the cap. After enough rounds the distribution of salaries becomes more or less stable, and I was able to recreate more or less the distribution of salary allocations we see within position groups in the NFL (ignoring rookie contracts).
This little model's resulting distribution of salaries is really dependent on how you assign variation to the positional groups, and doesn't model things like player loyalty, system fit, team's in GFIN mode or tanking, etc. I am not an economist so I am sure this is something that has been done already, but I found it interesting.
Especially interesting was how slight changes to a distribution of player skills could result in vastly different assignments of budget. For example, infusing the quarterback group with several median-skill players greatly reduced the top echelon of salaries, because a lot of the bottom end of the salary distribution was to avoid having to have a really really bad player. Other positions were less variable based on a few changes simply because there are 3 WR's per team, 2 tackles etc etc. Which also got me wondering about whether these really big, really long QB contracts are taking on a risk that the marginal value of a QB might fall quite a bit with the infusion of just a few more good young quarterbacks.
Let me know if none of this makes any sense.
