Looking at Bracketology

Today is the beginning of the NCAA Basketball Tournament and I wanted to discuss an aspect of bracketology that’s somewhat related to investing. (Yes, it’s one of those posts.)
Most pools following the linear scoring method (i.e. you get 10 points if a #10 seed wins), but the key to understanding the game is that the quality of teams are not spread out linearly.
Generally speaking, the better the teams are, the greater the gap between them and the next seed. The teams are really spread out exponentially. If I had to guess, I’d say that the difference between a #12 seed and a #5 seed is probably about the same as the difference between a #3 seed and a #1 seed.
Here’s something what it looks like:

The black line shows how the teams really are while the blue line shows you how points are awarded. (Note: This isn’t drawn to scale. I’m just trying to show you the principle.)
As a result of this mismatch between exponential reality and linear price, there’s an inefficiency to exploit.
I’ll show you what I mean.
The tournament expanded to 64 teams in 1985 so we now have 25 years of data. Here’s how many Sweet 16 appearances each seed has had over the last 25 years.
Seed…………….Sweet 16……………..Points
#1……………………88…………………… 88
#2……………………64…………………… 128
#3……………………52 ……………………156
#4……………………43 ……………………172
#5……………………36 ……………………180
#6……………………35…………………… 210
#7……………………18 ……………………126
#8……………………9………………………..72
#9……………………3………………………..27
#10………………….18……………………..180
#11………………….11……………………..121
#12………………….17……………………..204
#13………………….4……………………….52
#14………………….2……………………….28
#15………………….0……………………….0
#16………………….0……………………….0
I’ve also included a point total. As you can see, there’s an advantage in picking teams at the optimal spread between quality and points like the #10 and #12 seeds.
The invaluable Abnormal Returns guided us to the Geek’s Guide to NCAA Tournament Pools at Wired. The magazine looked at the bracket picks done by thousands of people at ESPN. They then compared the crowd’s picks with some statistical predictions by two college basketball analysts.
Sure enough, the crowd has responded to incentives. You can see that the crowd has tended to overpick the #10, #11 and #12 seeds (those are the cells in green on Wired’s chart). The process is repeated in the later rounds with the #4 and #5 seeds. (Wired notes that the crowd’s consensus bracket usually finishes in the 80th percentile.)
This is interesting because the crowd is doing two things. One, they can be overruling what the bracket committee did. Also, they seem to be paying close attention to seeding and acting accordingly.
This behavior illustrates an aspect of why CAPM doesn’t work. Historical research has shown that the most volatile stocks aren’t the best performers as they should be according to the model. Instead, they’re among the worst. This makes sense since people are probably willing to overpay for a long shot of a big payoff, and this leaves the “sure-things” underrepresented.
Selecting the #10 and #12 seeds is a good strategy in the early rounds, but just like momentum investing, it quickly turns against you. After the first two rounds, the most logical way to play the brackets is to select the favorite. Yes, it’s boring but it works—just like value investing.
In the basketball tournament, you can see how unloved the #1 seeds are (note the red cells). The key fact of investing is that the most conservative and ignored stocks are often the best investments.

Posted by Eddy Elfenbein on March 18th, 2010 at 10:28 am

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