http://math.bu.edu/people/mg/papers/knockout.pdf

Bayesian locally optimal design of knockout tournaments

What a fairer 24 team UEFA Euro could look like

Risk of Collusion: Will Groups of 3 Ruin the FIFA World Cup?

March brings March Madness, the annual conclusion to the U.S. men's college basketball season with two single elimination basketball tournaments showcasing the best college teams in the country. Almost as mad is the plethora of office pools across the country where the object is to pick a priori as many game winners as possible in the tournament. More generally, the object in an office pool is to maximize total pool points, where different points are awarded for different correct winning predictions. We consider the structure of single elimination tournaments, and show how to efficiently calculate the mean and the variance of the number of correctly predicted wins (or more generally the total points earned in an office pool) for a given slate of predicted winners. We apply these results to both random and Markov tournaments. We then show how to determine optimal office pool predictions that maximize the expected number of points earned in the pool. Considering various Markov probability models for predicting game winners based on regular season performance, professional sports rankings, and Las Vegas betting odds, we compare our predictions with what actually happened in past NCAA and NIT tournaments. These models perform similarly, achieving overall prediction accuracies of about 58%, but do not surpass the simple strategy of picking the seeds when the goal is to pick as many game winners as possible. For a more sophisticated point structure, however, our models do outperform the strategy of picking the seeds.

March Madness and the Office Pool

We critically examine a number of flaws in the current knockout bracket of the UEFA Euro 2016 and we suggest two fairer procedures that eliminate group advantage and lack of win incentive and still satisfy the balance and group constraints. The suggested procedures apply to any tournament consisting of a round robin stage made of 6 groups of 4, followed by a knockout stage.

https://papers.ssrn.com/sol3/Delivery.cfm?abstractid=2714199

What a Fairer 24 Team UEFA Euro Could Look Like

In a seeded knockout tournament, where teams have some preassigned strength, do we have any assurances that the best team in fact has won? Is there some insight to be gained by considering which teams beat which other teams solely examining the seeds? We pose an answer to these questions by using the difference in the seeds of the two players as the basis for a test statistic. We offer several models for the underlying probability structure to examine the null distribution and power functions and determine these for small tournaments (less than five teams). One structure each for 8 teams and 16 teams is examined, and we conjecture an asymptotic normal distribution for the test statistic.

Christopher Todd Edwards

Papers

Non-parametric procedure for knockout tournaments