Game Theory and Equilibrium in Fantasy Football Drafting
As the NFL season begins, many people are obsessing over their new fantasy football lineups. Using Game Theory to dictate one’s drafting strategy could have given these people a serious lead over their competition. Many people claim that practicing the draft many times with random people will help them gain the most responsive strategy. However, the article claims that player’s trend towards a Nash Equilibria whereby “each player’s strategy is the best response to the strategies of the other players.” When each person believes that they are responding optimally to each other’s strategy they become less inclined to change to another one.
The article attempts to identify where these equilibrium positions might occur in order to avoid them. A common strategy in smaller leagues involves drafting a Quarterback in a late round – at least in the second half of the drive. However, even when all players are waiting until this time to draft a quarterback, the top quarterbacks in the league will always be drafted quite early and thus a Nash Equilibria drafting strategy cannot draft a quarterback that late.
Another strategy that is quite popular is drafting only running backs in the first two or three rounds. When all but one of the players draft using this method, the last team should avoid running backs and try the equally popular “zero running back” strategy. This is also true when the positions are switched and most players choose wide receivers. However, this does not form a Nash Equilibria.
The most popular strategy that is used involves value-based drafting (VBD). Each player available to be drafted is ranked by an algorithm that “the worth of each player is not how many points they will give us over the season but rather how many more points they will give us than the alternatives available late in the draft.” In order to test if there exists a Nash Equilibria, the outcome of drafters using various strategies was simulated. When all players use VBD to draft, they become unable to deviate from the ranks because each player will always choose the NFL player with the highest rank. This means that there is no incentive to change because each choice is the best response given the choices of everyone else. When compared to the draft results used on the website 4for4, drafters trended to the expected equillribrium position and thus point to the authenticity of the equilibrium position.
http://www.4for4.com/fantasy-football/2014/preseason/game-theory-draft-strategy-equilibrium-and-4for4-advantage