Once again, it's the time of year where many people in the US try to pick the winners of the 63 games in the NCAA college basketball tournament. (The tournament starts with 68 teams with 4 games that occur prior to the Round of 64. Generally, you start with the Round of 64 when picking a bracket.) See Wikipedia for more background on the tournament, brackets, regions, and seeds.

A popular upset pick for many is to choose a 12 seed to beat a 5 seed. (It happens about 37% of the time.) Armed with this knowledge, I generally try to pick 1 or 2 such upsets (a 12 beating a 5) each year. There are a total of 4 such matchups in a single tournament. A few years ago, however, my brother and I noticed that a lot of times this strategy seems to backfire. Even if you pick the correct *number* of 12/5 upsets in a given tournament, if you don't pick the right *particular* upsets, you end up getting more picks incorrect than if you had not picked any upsets.

Last night, I decided to run a simulation of how many 12/5 upsets you should choose to maximize your first round score. (Note here that this strategy might not be conducive to doing well after the first round.) I'm also assuming that I can't rank the likelihood of an upset in the four 12/5 matchups. For my simulation, each matchup has an equal probability (0.367) of being an upset (Round of 64 results). For background, the scoring system in my family's bracket contest is that you get 1 point plus the seed of the winning team if you correctly choose the winner of a game in the Round of 64. The simulation could be adjusted for various other scoring systems.

I compared the expected number of points based on the following picking strategies:

- Choose all 4 of the 5 seeds to win.
- Choose exactly 1 of the 12 seeds (at random) to win.
- Choose exactly 2 of the 12 seeds (at random) to win.
- Choose exactly 3 of the 12 seeds (at random) to win.
- Choose all 4 of the 12 seeds to win.

I was a little bit surprised by the results. According to my simulation, the optimal strategy (for maximizing first round points) would be to pick all of the 12 seeds to upset the 5 seeds. Choosing all the 5 seeds yielded the fewest expected points at 14.96, whereas choosing all the 12 seeds yielded the most expected points at 19.59. The other three picking strategies were in between these two extremes.

I'm not sure how useful this information will be when I'm making my picks this year, and of course, there are many ways to rank the likelihood of each of the 4 games featuring a 12/5 matchup producing an upset.

Enjoy the tournament and best of luck if you're picking a bracket yourself!