Analyzing NHL Draft Strategy with Game Theory
https://repository.upenn.edu/joseph_wharton_scholars/26/
In many sports, amateur drafts are the most common way for new players to enter a league. In the case of the National Hockey League, around 90% of current players entered through the draft. A draft presents a scenario where teams make decisions in sequence to select players that they believe will give value to the team as they develop. There are a multitude of ways to attempt to define the value of a player, but an easy one is the generally non-negative Career Point Shares, which estimates a players contribution to the points the team won (2 for a win, 1 for a tie or overtime/shootout loss) over their entire career. Obviously a metric like this works only in hindsight, and the analysis presented admits to only being useful for what-if style ‘re-drafts’. In grading a team’s drafting, the CPS for each player in that draft can be used to provide perfect information for just the team in question. Their goal is to draft as much value as possible, but the game presents itself in the difficulty that players you pass over are very likely to be drafted by one of the many other teams picking between yours. This leads to situations, especially in later rounds, where teams may intentionally pass on a player if they believe other teams don’t have the same information they do about their potential. This allows the team in question to ‘spend’ less draft value (use a later pick) to gain a higher player value.
The analysis present covers the 2000-2009 NHL drafts, which all featured 7 rounds and 30 teams each. To compare to the total CPS a team drafted, two re-drafts were done. In one, the absolute best player available at each pick (by future CPS) was taken. The other strategy is to take the list of available players and go scan up the list backwards to find the best option at a certain pick value. This method, a form of backward induction, produced a higher (or the same) total draft value that the simple best player available in all cases. The qualitative explanation is that teams perform best when selecting talent just before another team would decide to. While this simple, perfect information game-theoretic approach can grade a team’s performance in a vacuum, it doesn’t model well the butterfly effect of early picks in a draft.