March madness is over. You might be feeling bad about your bracket so I thought I would give you a little ego boost. Your bracket probably isn’t as bad as you think.
The past two years I have done very well in my bracket pool. Also, I like to brag. I was bragging about how well I have been doing picking brackets the past two years on facebook (my exact words were, “Data driven/statistical decision making pays off again!”) and my college genetics professor asked if my picks were actually better than a “Wild Assed Guess”. He has a point. I might have just been lucky. So, I wanted to investigate this in more detail (so I could brag some more of course).
Last year the bracket pool was set up with an “upset bonus” which I exploited statistically and ruined everyones fun (if someone wants to partner with me, we could make a lot of money in Vegas betting in bracket pools with upset bonuses). This year the bracket pool was set up with the “standard” format. The first round of games were worth 1 point each, the second 2 points, and so on. Picking the champion was worth 32 points. Standard set-up. There were 20 people in our bracket pool and I finished in 2nd with 111 points. To pick my bracket I just used the most popular bracket picks supplied by Yahoo Sports. My rationale was that the collective reasoning of the masses was probably better than whatever I would choose. I could have also chosen to go with the rankings established by the NCAA committee that sets up the tournament. That would have earned 112 points, which would have still placed 2nd. Anyway, you might think it is a stretch to call my approach “data driven” and “statistical” but it really was. My choice was based on millions of other peoples choices, and I was unbiased in the decision making. Yahoo just did the analysis for me.
Was this method better than a “Wild Assed Guess”? When picking winners of games, I am assuming that a “Wild Assed Guess” is equivalent to a coin flip, 50/50. I used this estimate to simulate 1 million brackets based on “Wild Assed Guesses” and determined how many points each bracket would have earned in this years tournament. The distribution of points earned by the brackets looks like this:
The hump on the right is caused by brackets which randomly picked the correct champion. In the graph below brackets which didn’t pick the champion are on the left panel, and those which did are on the right panel. The scales are the same.
My bracket scored better than all but 283 of the 1 million brackets based on “wild assed guesses”. I did this same experiment a second time and my bracket scored better than all but 303 of the 1 million brackets. This implies that there is a 0.03% chance that a bracket would perform as well as mine based on a “Wild Assed Guess”. In science we summarize this concept as a p-value, where a 100% chance is 1, and a 0% chance is 0. It is a commonly accepted practice to use a p-value cutoff of 0.05. If a p-value is less than 0.05 (p<0.05) we conclude that the odds of an observation this extreme are rare enough that we can reject the null hypothesis of no difference. Many scientist are sticklers to the whole p<0.05 thing. I actually think being a stickler for “p<0.05″ is pretty dumb because the p-value itself contains the information about the certainty/uncertainty we are looking for. For example, P=0.051 isn’t that much different than p=0.049. Here is an example of how we would use a p-value: I conclude that the method I used to pick my bracket is better than a “Wild Assed Guess” (P=0.0003).
Now for the cheerful, ‘non-braggy’ part. Your bracket was probably better than a “Wild Assed Guess”. If you abide by the whole P<0.05 thing, your bracket only needs to have scored 50 points for you to conclude that your method was better than a “Wild Assed Guess”. In my bracket pool only 2 people had scores less than 50. Even then, their brackets were better than 94 and 92 percent of brackets based on “Wild Assed Guesses”.
One last thought: the NCAA committee which chooses the tournament seedings deserves a lot of credit. It is obvious that their seedings are better than a “Wild Assed Guess” (p = 0.000236). They deserve real credit here. Without the seeding information I doubt that the collective conscious of Yahoo bracketologists would have performed so well.
Things I find interesting:
1. Picking the champ has a HUGE effect on whether you win your bracket pool.
2. The NCAA tournament committee does a really good job picking the seedings.
3. Most people do better than a “Wild Assed Guess” when they pick their brackets.
4. The guy who won my bracket pool is a badass. However, I am not sure that we are statistically different.
5. Next year I should try to beat the NCAA seedings.
Acknowledgements: I would like to thank my undergraduate genetics professor for inspiring this blog post. He will remain unnamed unless he requests otherwise.