Program

09:00am - 09:30am: The Madness of March Madness

Speaker: Jeff Decary, University of Connecticut, USA

Abstract: This paper investigates multi-entry betting strategies for single-elimination tournaments with top-heavy payoff structures. In these betting pools, participants select a winner for each game in the competition, and the number of correct guesses determines their score. Since higher-scoring entries in top-heavy payoff pools offer greater returns than several above-average ones, bettors aim to choose sets of entries that maximize the expected result of their best-performing entry. There is no known closed-form expression that computes this expectation for two or more entries, so we present a Monte Carlo simulation algorithm to estimate it. To identify high-quality sets of entries, we embed this method within optimization procedures tailored to the problem, including algorithms based on sample average approximation. We evaluate the performance of our algorithms on every March Madness tournament played since 2017, and our results show that simultaneously selecting entries outperforms a sequential approach. Furthermore, we show that our best entries would have won $1 million against some of the best sports bettors in the world in a contest organized by DraftKings.

09:30am - 10:00am: Picking Winners in Daily Fantasy Sports Using Integer Programming

Speaker: Tauhid Zaman, Yale University, USA

Abstract: We consider the problem of selecting a portfolio of entries of fixed cardinality for contests with top-heavy payoff structures, i.e. most of the winnings go to the top-ranked entries. We model the portfolio selection task as a combinatorial optimization problem with a submodular objective function, which is given by the probability of at least one entry winning.  We then consider a scenario where the entries are given by sums of constrained resources and present an integer programming formulation to construct the entries. Our formulation maximize the expected score of an entry subject to a lower bound on its variance and an upper bound on its correlation with previously constructed entries. To demonstrate the effectiveness of our integer programming approach, we apply it to daily fantasy sports contests that have top-heavy payoff structures. We find that our approach performs well in practice. Using our integer programming approach, we are able to rank in the top-ten multiple times in hockey and baseball contests with thousands of competing entries. 

10:15am - 10:45am: Beyond the Traveling Tournament Problem

Speaker: Michael Trick, Carnegie Mellon University, USA

Abstract: The Traveling Tournament Problem was introduced at the 2001 Constraint Programming conference.  That short paper is currently the most cited paper from that conference and has generated wide interest in sports scheduling.  But there are a number of related problems that have both theoretical and practical interest that have not been as well studied.  I will review a selection of these problems, both old and new, and show how approaches in integer and constraint programming can address these problems.

10:45am - 11:15am: Designing Fair Handicap Systems for the Game of Darts using a Markov Decision Process Framework 

Speaker: Rachael Walker, University of Toronto, Canada

Abstract: Handicap systems are commonly used in sports to create competitive balance between players with different skill levels. The game of darts has two existing methods for handicapping. However, their effectiveness has never been rigorously evaluated and they have no guarantee of truly balancing competition. We develop a novel Markov Decision Process (MDP) framework that is capable of modeling darts with different handicapping methods and players of varying skill levels. Powering our model with real data from professional dart players, we find that the existing handicap systems – which heuristically calculate a head-start for the weaker player – do not in fact create true competitive balance. We use our model to develop optimization-based versions of these head-start systems that resolve this imbalance. However, we find that even the optimized head-starts can be impractical or even infeasible to implement if the difference in skill level is high enough. This is because the main source of imbalance between players occurs at the end of the game and cannot be addressed by a head-start advantage. In response, we propose a novel handicap system that uses dynamic credits, which can be used at any point in the game and allow a player to deterministically select an outcome for a single dart throw. Moreover, we prove that this more flexible handicap not only creates competitive balance but is guaranteed to be practical and feasible to implement regardless of the difference in skill level. 

11:25am - 11:55am:  From Machine Learning to Optimization in Sports Analytics

Speaker: Oliver Schulte, Simon Fraser University, Canada

Abstract: This talk provides an overview of machine learning methods, including reinforcement learning, for evaluating player actions and assessing player performance. I describe several optimization problems that make the results of machine learning actionable for sports decisions. These include moneyball-type problems, where the task is to find the strongest team, given a player performance metric and sports-specific constraints on team composition (e.g., must include a goalie, defensive/offensive players). 

11:55am - 12:25pm: Uncertainty-Aware Reinforcement Learning with Application to Risk-Sensitive Player Evaluation in Sports Games

Speaker: Pascal Poupart, University of Waterloo, Canada

Abstract: Most reinforcement learning techniques optimize expected utility.  However, in various application domains such as finance, sport analytics and medicine, it is often desirable to take into account the risk induced by variability in utility beyond just the mean.  In that respect, distributional reinforcement learning provides a nice framework to estimate the entire distribution of utility instead of the mean only.  However, modeling distributions instead of point estimates is much more challenging.  In this talk, I will first describe a new technique to represent distribution quantiles with rational monotonic splines.  Then, I will show how to derive a risk-sensitive game impact metric to evaluate players in professional hockey and soccer.