Holy cow, I wrote a book!
Raymond comes up with an absurd, arbitrary criterion for filling out
his NCAA bracket.
I studied all the games played in the NCAA men's basketball tournament
since 1985 and computed how many of the games were won by
the favorite and how many were upsets,
broken down by the numerical difference between the seeding of the
I found it interesting that when the teams are seeded N and N+2,
you get an upset more than half the time!
If the probability of the favorite winning is p and I choose
the favorite with probability q, then the prediction would be
correct pq + (1−p)(1−q) =
(2p−1)q + (1−p)
of the time.
If you hold p constant, then this is maximized when
q = 0 if p < ½,
q = 1 if p > ½.
(If p = ½, then it doesn't matter
what you pick for q.)
to maximize the number of correct predictions,
I should always choose the favorite, unless the two teams are seeded
N and N+2, in which case I always choose the underdog.
But that makes for a boring bracket.
Consequently, I went for the suboptimal algorithm of choosing
q = p.
Here is the result: