Friday, March 13, 2009

Syracuse vs. UConn 6OT: Probabilities

As you've probably heard, Syracuse defeated UConn last night in the Big East tournament in a 6 Overtime thriller. Did you miss it? Well, you may have missed a one in a million game - or maybe only one in a hundred thousand. The subject of this post is to determine the probability that a game between two evenly matched teams would go at least 6 overtimes. Six Overtimes! After 70 minutes of action Syracuse finally put UConn to rest with what was actually an anti-climatic final period. To put that in perspective, the longest Big East tournament game ever only went 3 overtimes.

If you were watching, you might have wondered to yourself, "Boy, what were the chances of seeing that?!" Here at Behind the Scoreboard, we try to have an answer for you.

One approach is a theoretical model. In basketball things are measured in time, so I caluculated the probability of scoring a set amount of points in 1 minute of game action. Using the actual Syracuse vs. UConn game to set the probabilities, I found the following distribution of points scored for a team in 1 minute of game action:

0 points: 34%
1 point: 4%
2 points: 34%
3 points: 15%
4 points: 7%
5 points: 5%
6 points: 1%

As you might imagine, in a single minute it was most common to score either 0 or 2 points. 3 points was the next most common, followed by 4, 5, 1 and 6 points. Neither team ever scored 7 or more points in a 1 minute interval.

Now that we have this distribution, we can draw from it to simulate thousands of minutes and thousands of 40-minute games to determine the probability that the game will remain tied.

Playing one million games, after 40 minutes the game was tied 2.9% of the time. So the probability of an overtime game between two evenly matched teams is approximately 2.9%. Then I played another one million 5 minute overtime periods - after 5 minutes of action the game was still tied 8.2% of the time.

Of course UConn and Syracuse didn't just play one overtime period, they played six - tying once after regulation and 5 times after an overtime period. What's the chance of that? .029*.082*.082*.082*.082*.082 comes out to a 0.00001% chance or roughly 1 in 9,382,974.

BUT, and this is a big but, the theoretical model, while it may be good for 39 out of 40 minutes, may not hold for that last minute. The theoretical model is built on data that come from regular gameplay. But in that final minute, teams don't play like usual - they foul, they pass up open threes, they take threes when they otherwise wouldn't, they hold the ball, and all sorts of other things that change the point scoring probabilities - and it's likely they change the probabilities in a way that makes a tie more likely.

Looking at empirical data, this appears to be so. According to the Wall Street Journal blog, looking at over 136,000 games, games go to overtime 5% of the time, and overtime periods end in a tie 18% of the time, not 3% and 8% as the model above shows. Using these numbers gives a 1 in 105,000 chance that the game would go that long - something that's consistent with the fact that there have been 3 such games so far.

The game has changed a lot since 1981 when the data began, a shorter shot clock, more reliance on the three pointer, better shooting, and other things that may have made overtimes more likely in the past than they are today. But while 1 in 105,000 may be a little low, it's probably a lot lower than 1 in 9 million - an important lesson about making theoretical assumptions.

Whatever, the case, it was a great game and I hope you didn't miss it - there won't be another one in a long, long time.