Nash Equilibrium of NBA starting lineups
Over the numerous years professional basketball has been in existence, the composition of the lineups have come to an equilibrium to where everyone plays a mix of big players and small players. Yet why has it become that the best option for a lineup is this balanced mix of big and small? Why not play teams of all big players or all small players?
In this article the author Ari Caroline uses game theory to find the reason why basketball lineups have equilibrated to the typical PG, SG, SF, PF, C lineup. On average it has been found that Centers have the highest productivity percentage while Point Guards have the lowest. By this data the best option seems to be a team of all Centers, but that is not the case. Ari Caroline then introduces a term called floor stretch, which accounts for a player’s quickness and ability to stretch the floor. This term favors a smaller quicker point guard contrary to a bigger slower Center. Using this term he applies game theory to find the reason why a basketball lineup has a Nash Equilibrium with the typical PG, SG, SF, PF, C lineup.
This article applies game theory in order to understand and identify why a system is operating the way it does. Ari Caroline uses a payoff table that lists the options that each team has for a lineup ranging from a team of all Centers to all Point Guards and the corresponding payoff for the team. In doing this he found where the Nash equilibrium lies regard to a situation when just the player productivity is accounted for and when regarding both productivity and floor stretch.
Sources:
http://wagesofwins.com/2012/11/06/an-introduction-to-nash-equilibrium-lineups/
http://wagesofwins.com/2012/11/20/a-beautiful-lineup-nash-equilibrium-lineups-part-ii/