# Play-by-play theater: Revisiting consecutive fouls

Play-by-play theater is a feature (that I just started) where I use the comprehensive play-by-play archive from the past three seasons to hunt for extreme, and possibly silly, events that have occurred in a college basketball game. And who doesn’t like extreme, and possibly silly, events? I do! I mean, I don’t! I don’t not like extreme, and possibly silly, events!

On Saturday, “BigH1313” of twitter fame, wondered which game listed in Friday’s consecutive foul table featured ten consecutive fouls by the same team to start the game. The answer: Whoops! There actually wasn’t such a game.

Thanks to BigH1313, though, I was forced to recheck my work which determined that the logic used to produce Friday’s table was a bit off. It turns out the forces working against consecutive fouls being called on the same team are even stronger than shown last week. Here’s the corrected table which includes the 200+ additional play-by-plays from games over the weekend.

Probability of (x+1)th foul being called on Team A when first x fouls of game have been called on Team A

```x      n    n(a)   Chc(a)
1   13326   6158    46.2
2    6158   2683    43.6
3    2683   1057    39.4
4    1057    386    36.5
5     386    129    33.4
6     129     37    28.7
7      37      8    21.6
8       8      1    12.5
9       1      0     0.0
```

x: number of consecutive fouls called against Team A since beginning of game
n: total number of cases
n(a): number of cases where Team A was called for the next foul
Chc(a): percentage of cases where Team A was called for the next foul

Instead of there being a single game with the first ten fouls called against one team, there’s actually only one nine-foul game since the beginning of the 2009-10 season. That one-in-13,326 event took place on December 3, 2010 when UMBC committed the first nine fouls of a game at UConn before Donnell Beverley was whistled with 5:55 remaining in the half. The final foul count in the game was UMBC 17, UConn 12.

For reference, if you assumed a sequence of fouls was completely random, with either team having a 50% chance of getting the next call, you would have expected 52 cases of a nine-foul game in a sample of this size. You even would have expected one game with 15 consecutive fouls against the same team to start the game. Imagine the riot that would ensue in that case!

As I alluded to Friday, there are other forces at work here besides officials trying to avoid a full-blown riot. It figures that teams that have committed a string of fouls might try harder to avoid them on the following possessions and teams that aren’t committing fouls might get a little more frisky. It seems like that’s not enough to completely explain this effect, but I’m not sure how one would isolate the influence of pure officiating on the data. Anyone?