March Madness

Each March/April, the National Collegiate Athletic Association basketball tournaments are held. These tournaments, especially the men's division I tournament, are known as March Madness, and it's common for workplaces to hold competitions based on who can predict the winning teams in the tournament.

I'm not a particular basketball fan (this season I watched approximately 0.6 games of basketball before the tournament, which is probably more than every other year put together), but I saw posters up advertising the James Franck Institute's competition, so I entered.

This being a department full of nerds highly intelligent people with a natural interest in numbers, the scoring system was not simply based on games increasing value with rounds, but on the average probability of a particular seed winning a particular game. For example, a team seeded 1 winning its first game was only worth 10 points, because that outcome has occurred every single time since the tournament took on its current structure, while a team seeded 16 (the tournament is based on a 64-team bracket, split into four regions, each seeded 1-16) winning the championship would earn 200 million points.

Now being nerdy even among nerds having a particular interest in analysing possibilities and making logically defensible decisions, and not knowing anything about college basketball, I found a website that estimated probabilities of each team winning each game, and multiplied the probabilities by the rewards according to the scoring system, to find the best value picks. Essentially, I was looking for teams that were seeded lower than they deserved (or, in the case of Kentucky, so good that even the first overall seed didn't represent how good).

I did have two concerns about this strategy. First, I was attempting to maximise my expected number of points, but that's not necessarily the same as maximising my probability of winning. I ignored teams with less than 1% chance of winning a particular game, because in that case the expected value would come as an unnecessarily large windfall very rarely, but I did wonder if I should have biased my picks towards more moderate upsets. Second, I worried that working where I do, others might have adopted the same strategy and come up with an almost identical bracket!

Fortunately, neither of those seemed to be a problem, and I was happy with how I did: I managed second place in a field of 33. And to support the suggestion that my position was the result of my strategy, not any particular skill at picking winners: first place picked 11 more winners than I did (49-38, not a small margin). And if the scoring had been a more conventional system, I would have come 24th.

My best wins (by points gained):
7-Michigan State defeated 4-Louisville in the elite 8 (392)
7-Michigan State defeated 3-Oklahoma in the sweet 16 (132)
11-UCLA defeated 14-UAB in the round of 32 (105)
14-Georgia State defeated 3-Baylor in the round of 64 (82)
7-Wichita State defeated 2-Kansas in the round of 32 (54)
7-Michigan State defeated 2-Virginia in the round of 32 (54)
Thank you Sparty!

My worst picks (by round mismatch)
11-Texas (predicted to make the elite 8, lost in the round of 64)
10-Ohio State (predicted to make the final 4, lost in the round of 32)
5-Utah (predicted to make the championship game, lost in the sweet 16)
12-Buffalo (predicted to make the sweet 16, lost in the round of 64)
1-Villanova (predicted to make the elite 8, lost in the round of 32)

There was no single tournament-swinging pick that first place caught that I missed: he won because he picked 7 of the teams that reached the elite 8 while I had 2. On the other hand, had UCLA beaten Gonzaga in the sweet 16 (or Georgia State beaten Xavier in the round of 32), I would have won easily (but then, the reasons these would have been worth so many points is that they were both unlikely).