Instead of filling out a NCAA basketball tournament bracket the traditional way with the predicted winner of every game, submit a function that predicts a winner between the meeting of any pair of the teams in the tournament. One simple functional form would be to rank the teams 1 through 68. Or one could also design a multi-parameter function. Ultimately, simply submit a table predicting the outcome of all 68*67/2=2278 possible matchups.
Score the bracket by number of correct predictions. Unlike the traditional method, this allows people to stay involved even if their favorite teams are eliminated.
A further sophistication is for the function not to predict an outcome but to give probability of winning. Sum the probabilities of the winner of each game. This is backward compatible with the traditional filling out of a bracket: matchups not in the bracket are scored as 0.5.
An even more complicated contest allows submission of functions which may use the results of previous rounds to predict an outcome.
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