Part 1 of my series on DeMarcus Cousins and how NBA players accrue personal fouls.
If you’ve ever talked about the NBA with me for any significant amount of time, you will know that one of my favorite players is DeMarcus Cousins (my favorite player being, of course, Shaun Livingston). I’ve always liked Boogie for the usual reasons related to his abilities on the court, of course, but also because he has been the focus and inspiration of much of my analytics work for the past year. Before I get into all the details and numbers, I’d like to share the story of how it all came to pass.
I am from Berkeley, California. As such, my home team is the Golden State Warriors. Last school year, during my Christmas break I was able to attend the December 28th 2015 matchup between the Warriors and Sacramento Kings at Oracle Arena. Many people remember that game because the end of the first half featured a three-point shoot out between Stephen Curry and Omri Casspi:
It was incredibly exciting and made for a close game.
A few months later, at the 2016 Sloan Sports Analytics Conference, that sequence came up in a conversation with my friend who was also in attendance. I mentioned that I was at that game, but that the end of the first half wasn’t what I remembered most about the game. What I remember is this:
It was my first time seeing Cousins get ejected and even from my seat in the upper bowl, I could feel how frustrated and upset he was about the whole ordeal.
My friend commented that “if only Boogie could be, like, 15% less angry – he would be the most dominant player in the game.” Which of course got me thinking – how *would* you quantify how mad DeMarcus Cousins is at any given time?
A potential answer presented itself several months later at the 2017 Joint Statistical Meetings where I attended a session titled “For the Love of the Game: Applications of Statistics in Sports.” In that session, Douglas VanDerwerken presented “Does the Threat of Suspension Curb Dangerous Behavior in Soccer? A Case Study from the Premier League.” This paper (which can be found here for interested readers) showed that as EPL players approach the yellow card limit, and thus face suspension, they are less likely to foul.
Thinking back to that December 28th game, and many additional Kings games I have watched, it seemed to me that Cousins would get heated and “tilted” and play more aggressively and therefore foul more often. I hypothesized that the more Cousins fouls the more likely he was to foul.
He does. But he’s not the only one.
I’ll get into the math/stats in a later post. But here is a general idea of how we can think about this problem. Given there is a fixed amount of time that a given player is on the court, we might expect fouls to follow a Poisson arrival process with inter-arrival times following an Exponential distribution where each foul is independent of the previous fouls. We can consider a survival model, and look at the “failure time” for each foul – in other words the time it takes a player to commit his 1st found, 2nd foul, etc. If, for example, the time between the 2nd and 3rd foul is significantly longer than than the time between the 4th and 5th foul, we would have evidence of some sort of “tilt.” We can model foul rates using a conditional risk set model for ordered events and do some analysis with a stratified Cox model. From there we can try to identify if there are any actions a coach/team can take in order to mitigate increased fouling rates.
I’ll save the details for later.