Saturday, March 21, 2009

Stathead Bracketology

I participate in two NCAA bracket competitions every year. One (through this site) uses fairly straightforward scoring based on the round and nothing else. The other uses upset bonus points: when the lower seed wins, you get the normal points for the win (one for the first round, two for the second, etc.) plus bonus points worth the difference in the two seeds. For example, for picking a 12-seed over a 5-seed in the first round, you get one point for the win plus 12-5=7 bonus points, for eight points total.

Now, being statistically inclined, I wanted to use mathematical methods in each. Here's what I did.

Straightforward Scoring: The Pomeroy Ratings

For my straightforward bracket, I decided to employ the Pomeroy Ratings. I used the Fremeau Efficiency Index Ratings with great success in our BCS Bowl Pick 'Em a few months ago, so I wanted to go with a similarly statistically-inclined system for the basketball pool.

I did it the simplest way possible, too. For each matchup, first round through final, I picked the team with the higher Pomeroy Rating. (Note that the ratings are being continuously updated through the tournament, so the ratings as they are right now do not match what they were when I made my picks the day before the tournament started.) Some notes:
  • Memphis is number one in the ratings, and therefore my champion.

  • The ratings "predicted" Wisconsin's win over Florida State.

  • All of the 6 seeds were apparently undervalued by the selection committee. Going by the Pomeroy Ratings, all of the sixes except Marquette were expected to beat the 3 seeds in their respective brackets and advance to the Sweet 16.

  • West Virginia was in Pomeroy's top 10, which should have gotten them into Elite 8. But I guess Dayton had something to say about that.

  • I did "cheat" and pick Cleveland State in the first round, since my dad was a two-time basketball letterman there. I'd be kicking myself this morning if I hadn't picked them.

My "straightforward bracket" can be found as a Google Doc here.

Upset Bracket: The Expected Value Method

Last year, I outlined a method for using expected values to make picks in a pool with upset points. Well, I'm happy to say that my method worked. Thanks to a bevy of first round upsets last year, I built a big lead and was able to withstand a single competitor to win the pool. I did have to sweat out the last rounds as my bracket started to fall apart, but I was so far ahead that it didn't matter.

As with last year, I used a different method for each regional. Two were methods (b) and (c) from Part 2 of last year's post. The other two were "controls." On one regional, I would pick only the top seeds for every game. On the other, I would pick by feel. Actually, I even took the human element of "feel" out this year, instead picking by the Pomeroy method chosen above.

Thanks to the Pomeroy bracket I filled out first, I was able to pick and choose which method I would use on each regional. And I will admit that I did allow for the human element to creep in when making my decisions. I used the two different expected value upset methods on the Midwest and South regionals. This mainly allowed me to advance West Virginia to the Elite 8 again (whoops), and pick Cleveland State in the first round.

I made the East my Pomeroy regional, mainly so I could take Wisconsin in the first round and put 6 seed UCLA in the Sweet 16. That left the West as my higher seeds only regional. Unfortunately, that means I won't have Memphis as my winner in this bracket, but maybe hedging my bets isn't a bad thing.

Once I got to the Final Four, where the seeds don't matter anymore, I went back to the Pomeroy Ratings to determine the finals participants and eventual winners.

First Round Results

My straightforward bracket isn't doing so hot, garnering only 23 of a possible 32 points, with one Elite 8 team (West Virginia) and one Sweet 16 team (Utah) down.

My bonus points bracket is doing fantastic, though, as it nailed all three 12 seed wins plus the Cleveland State upset. I am down an Elite 8 team in West Virginia, but the 57 points I did pick up should again give me a lead that's difficult to catch.