Game Theory is the study of games and strategy. It’s focus is all about the choices the players and how that affect the probability of success. A game has players, a set of moves (or strategies) available to those players, each with a specific value or payoffs. As a player you want to undertake moves that optimize your expected value. For the NBA this very much applies. Certain players have a significantly higher impact on the expected outcome of a game. I was inspired by the above xkcd comic to write a post on just those players.
Some quick background. Start at the Basics. For this post I’m judging player importance by their net impact in terms of Wins Produced and Point Margin per Game.I’m also looking for net contribution over the course of the season so far. Since I know each players Wins per 48 minutes from the Automated Wins Produced Site. I can use that number to work out Point margin generated for the team as Follows:
Points Margin Generated for Team per 48 = 31*(WP48-.099)
Points Margin Generated for Team=Points Margin Generated for Team per 48*(PlayerMinutes)*5/Team Minutes
Based on these equations, there are fifty players in the NBA currently that have impacted the bottom line for their by more than 1.5 net point per game. They are :
Paul and Love are in a class by themselves by delivering 7 pts a game for their teams. Garnett, Gasol, Horford and James all deliver 5 points (and Garnett.,Gasol and James all do it on superlative teams which as per diminishing returns is harder).
What’s really interesting is that this list has a dark parallel. A mirror if you would.
There are 52 NBA players that have reduced their teams bottom line by 1.5 points a game or more for the season year to date.
Remember kids, if you’re worse than a .100 WP48 player you’re on a verage costing your team points. The “leader” of this group is Andrea Bargniani who costs his team on average 4 point a game. Landry,Hickson Lopez and Blatche all hover around -3 points a game.
One thing that really pops out from this exercise? If I break this down by team:
The top tier in the league so far comes into very clear relief. There are five teams with at least three players delivering 1.5 points a game or more to their team(let’s call them earners) (Spurs, Heat, Celts, Lakers and Mavs). The Celtics are in a class by themselves with five such player and only one -1.5 point producers (call these wasters) (a rookie center Erden who should not see time in the playoffs). The Lakers have 4 +1.5 earners but their waster will get playing time in the playoffs (three guesses as to who and the first two don’t count). Miami and the Spurs feature unsurprising trios as their three earners and both have additional player who could make it a quartet (Blair for the Spurs and Miller for the Heat). As for the Mavs, we have Kidd,Chandler and Dirk as earners and Barea as a waster but once Rodrigue is back, J.J. role should diminish.
As for the T-Wolves and Kevin Love? Fear not, Amnesty International has been contacted.
And that dear readers is that.