One interesting bit of NCAA tourney trivia is that this year, apparently for the first time ever, one of the tens of millions of brackets submitted to online bracket challenge games was entirely correct through the first two rounds, or 48 games, of the tourney.
The chance that this bracket will remain perfect through the remaining 15 games is very small, but there will be many eyes on it. One year, there was a $1,000,000,000 prize offered for a perfect bracket (though, apparently for legal reasons, that prize is no longer on offer).
In a related discussion, I ran across a tidbit of expert opinion that may be useful in helping calibrate tourneygeek’s simulator.
At this page, Georgia Tech professor Joel Sokol is quoted as saying that the best predictive models can pick the winner of games in the NCAA men’s basketball tourney about 75% of the time. That suggests that in modeling NCAA basketball, I should set the luck parameter at about 1.4 or 1.5, which yields 75.15% or 74.16% (respectively) wins for the better team.
The reason that basketball, and especially tennis, have such small luck factors has to do, I believe, with the way the games are scored. In tennis and in basketball, there are lots of individual points won. So, though there may be great variability with respect to individual scoring attempts, a single game has enough of them so that the chance factors can even out. Whether a particular three-point shot goes in may be just as uncertain as whether a particular attempt to score from second on an outfield hit succeeds. But there will be more such plays in the basketball game, and thus less chance that any particular one will be critical to the outcome.