Game Theory and the NFL Draft

Each year the NFL holds it Annual Player Selection Meeting (or NFL Draft) where the 32 NFL teams select players from college. In total there are 256 players drafted in the 7 rounds of the draft. I am a huge football fan and the NFL Draft is one of the things that fascinate me about the league. You can look at the NFL Draft as a game and apply the concepts we have learned in game theory to the draft.

The NFL Draft is in essence a very large extensive form game. It is obvious that the game is sequential since teams pick one player at a time and in a particular predetermined order. Solving this game using the tools of game theory is nearly impossible on the other hand.

Before the draft each team has spent a large amount of money on scouting the college players that are being selected. The teams assign a certain value to each player with the best players having the greatest value of course. The teams then rank the players according to their value and in the end they have their value board. The value of each player is not an indicator of how good he was in college but how good the scouts predict he will be in the NFL. Now when it comes to selecting players there are two main strategies that teams use:
1. Picking the best player available (BPA) according to your value board
or
2. Picking a player that plays a position of need.

I think it clear that playing the BPA strategy is better because if you don't follow it then you are letting your competitors have a player that you think is better than the player you got. This might end up being really bad since the player(s) you passed on could end up becoming great and your team has to play against them for the next decade. Therefore it should be best to pick the player that gives you the greatest expected value each time.

Now if you would have the value board for each team, assume that each team plays the BPA strategy and would eliminate trades of draft picks, then you could predict how the draft would play out. But would this result in solving the game?

At first you might think the answer is no because you are not using backward induction. Backward induction would result in maximizing the expected value of the whole draft class of the team selecting first given what the other teams would select. What the BPA strategy does on the other hand is maximize the expected value of each draft choice. So there is the possibility of deviating from the BPA strategy at some time might lead to a greater expected value of the whole draft class.

To test if this was correct I set up a small example where I had three teams choosing two players each. The results of that experiment resulted in the same result whether the BPA strategy or backward induction was used. This worked in my small example and I would think the same would hold for the NFL Draft. However testing the theory on the NFL Draft would be nearly impossible. As I said before there are 256 players drafted. Also I found that after the 2009 NFL Draft the teams signed a total of 378 undrafted rookie free agents. Then there are some players that did neither get drafted nor signed and lets just say there were 66 such players giving us a total of 700 players that could possibly be drafted. So we have 700!/(700-256)! possible outcomes of the draft. This number is so large that trying to use backward induction would take days to solve the game. Of course there are thousands of possibilities that can be thrown out since they are not logical. They are not logical since there are only a few players worthy of the number one overall pick but the number of possible outcomes is still very high after throwing out these illogical possibilities.

Based on my small experiment I would conclude that it is in each teams best interest to pick the best player on their value board and if each team follows this strategy the game should solve the same way as if backward induction was used. Also there is no incentive for teams from deviating from the BPA strategy since that lowers the expected value of your draft class while it increases the expected value of your competitors draft class. In the end it would all come down to how good your scouts performed in predicting the talent of college players and how the players performed in the NFL.