March Madness and Inevitability

Last year I proposed a very simple model that could be used to generate plausible brackets for March Madness under the assumption (not to be taken too seriously) that a team's seeding accurately reflects the team's overall ability.  I will post my predictions for 2015 shortly after Selection Sunday, but in the meantime I have had some fun by simulating 100,000 tournaments to see how often each seeding tends to win.  The results are displayed on the graph above.  About 37.5% of the time, a 1-seed wins the tournament.  In the real world, they win about 62% of the time, so the model needs to be tweaked.  It is interesting that the likelihood of winning drops off approximately exponentially with the seed value, but it is not immediately obvious why that should be.

I have succeeded in tweaking the model to produce more realistic brackets, but sadly at the expense of simplicity.  The difficulty comes in having 1-seeds dominate the championships while still having a reasonable number of early-round upsets.  The tweaked model has a 1-seed winning about 61% of the time, but again it has the odds of bringing home a championships fall exponentially with seed.

Just as importantly, there is a 47% probability that at least one 5-seed will lose to a 12-seed in what I will continue to call the First Round (the NCAA now calls the play-in games the First Round).

As for "inevitability", I find that it is easy to come up with story lines for the brackets I am generating.  For example, Cinderellas emerge and go deep in the tournament only to suffer heartbreaking losses late.  A team "gets hot at the right time" or "was snubbed by the committee" -- except I know that in my model that the committee was right about which teams were better and which worse, and it is only by luck that anyone but a 1-seed wins a championship.  This no doubt happens all the time in real sports, which is why sometimes the NCAA Tournament winner did not win their conference tournament.  

It happens in history and in life, too.  I'm not one to dismiss the guiding hand of God in earthly affairs, but we have a strong tendency to misunderstand that and pretend that issues were never really in doubt, or even that the future is not really in doubt, because we know how "the story" is supposed to go.