Knowledge Problem

Michael Giberson

The NCAA post-season basketball tournament is seeded such that better teams are paired against weaker teams in the first round.  In fact, the highest seeded team is paired against the weakest team, the second highest seeded team against the next weakest team, and so on.  If the better seeded teams win each game, the pattern of highest seed against lowest remaining seed carries over into the second, third, and forth round.

However, as Robert Baumann, Victor Matheson, and Cara Howe of the College of the Holy Cross point out in a paper, “Anomalies in Tournament Design: The Madness of March Madness,” if a lower seeded team wins a game, then the pattern of matching the strongest team to the weakest will not hold in the NCAA b-ball tournament. For example, if in the first round #1 beats #16, #7 beats #10, and #8 beats #9, but #2 loses to #15, then the second round will feature #1 playing #8, but #7 playing #15. The first round upset by #15 in effect rewards #7 with a (purportedly) easier match than the #1 seeded team faces.

The result is an anomalous blip in the pattern of teams advancing from the second round to the third round:

While a number 10, 11, 12 seed has a lower chance of advancing to the second round than an 8 or 9 seed, their chances of advancing to the third round are much higher than those of 8 or 9 seeds. In fact, number 10 seeds have advanced to the third round, known as the sweet sixteen, 6 times as often as number 9 seeds and over twice as often as number 8 seeds.

Interesting, and those third round games are high profile “Sweet Sixteen” games.

This surprising result is easily explained by the lack of reseeding. First, while number 10 seeds are less likely to advance to the 2nd round than a number 8 or 9 seed, once they get there they will face a number 2 seed or perhaps even a number 15 seed in the event of a first-round upset. An 8 or 9 seed will almost certainly face a tougher 2nd round opponent since number 1 seeds are stronger than number 2 seeds and number 1 seeds are less likely to be upset in the first round. Similarly, number 11 and 12 seeds likely face weaker number 3 or number 4 seeds, respectively, in the second round and are far more likely to benefit from first round upsets than number 8 and 9 seeds. These advantages in the second round outweigh the disadvantages seeds 10 through 12 face in the first round of the competition.

They calculate that each tournament game win yields over $1 million in direct revenue from the NCAA to the schools athletic conference over six years, and observe there are other less tangible benefits, so the extra tournament games played by #10 seeds is significant.

The authors note that, in theory, reseeding the tournament at each round would eliminate the problem.  However, reseeding could require substantial shifts by teams between venues in between each round, which would significantly complicate the scheduling for teams and fans.  In addition, popular forms of gambling on the tournament are based on the fixed seeded approach.  The authors suggest the NCAA would be loathe to admit it, but also loathe to upset the role that March Madness plays in popular American culture.  As a result, they expect the anomalous success of #10 seeds to live on.

(HT to Daniel Houser at George Mason University.

Recall that GMU was a #11 seed the year they reached the Final Four.  They upset #6 Michigan State in the first round, so in the second round a #3 seed played a #11 seed, while the higher-seeded #2 faced a higher seeded #7.  As it turned out, both the #3 – North Carolina – and #2 Tennessee lost, and in the third round #11 GMU faced off against #7 Wichita State, while #1 Connecticut had to face #5 seeded Washington.)