Setting the Luck Parameter

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 makes basketball one of the less luck-dependant games for which I’ve attempted to calibrate my simulator. Backgammon came in at about 3.0. Tennis at about 1.15. Baseball at 6.0.

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.



One thought on “Setting the Luck Parameter”

  1. Basketball is 5-on-5 while Tennis is, at most, 2-on-2. One of the most hyped 1-on-1 interactions in the second round was Duke’s uber-talented Zion Williamson versus UCF’s uber-sized Tacko Fall, yet Fall, being in foul trouble early, was only on the court for 25 minutes. 3 of Duke’s Starters, including Williamson, were on the court for all 40 minutes, while only Aubrey Dawkins could say the same for the Knights. And yet, UCF was a missed layup and/or a missed rebound by Dawkins from upsetting the Blue Devils. You could factor in Fall’s size into UCF’s team “skill”, (since 7′ 6″ is practically always 7′ 6″,) but a team of reliable 3-point shooters would neutralize that advantage on Defense.

    As for last year’s major upset, #16 UMBC over #1 Virginia, most of the pundits that I read gave me the impression that Virginia was “unlucky” only insofar as they drew a team whose normal “playing style” matched up to the Cavaliers’ weaknesses; looking at a raw skill-to-skill comparison, Virginia would have won hands down.

    Unfortunately, that’s what the more basic models do. Even the advanced ones are restricted to team-on-team stat specifics, since you can’t tell how long an individual will be on the court and who that individual will face. So it is partly luck, but also partly how the styles play, an issue of “sample simplification”

    Looking at the numbers, might I suggest that Basketball’s “luck factor” be set at the square root of 2?


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