Parametric Whole-Bracket Optimization
Tom Adams · 2019
The majority of brackets are submitted to standard scoring pools without upset incentives. B. Clair and D. Letscher introduced a full-bracket probability model for pools. They developed the only full-bracket parametric method publicly available for estimating the return on investment of a bracket submission to a pool. One of the Clair and Letscher method’s basic assumptions is that the score of a bracket is normally distributed. A normal distribution is defined by two parameters: a mean and a variance. Each candidate bracket score covaries to some extent with the typical opponent bracket score. The covariance of a candidate bracket score can be positive or negative. The score of the bracket will tend to move in the opposite direction from the scores of opponent brackets. Different candidate brackets have different score means and variances. Each candidate bracket also has a distinct covariance versus the typical opponent bracket.