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The goal of this paper is to develop an adjusted plus-minus statistic for NHL players that is independent of both teammates and opponents. We use data from the shift reports on NHL.com in a weighted least squares regression to estimate an…
We develop the linear programming approach to mean-field games in a general setting. This relaxed control approach allows to prove existence results under weak assumptions, and lends itself well to numerical implementation. We consider…
Several performance metrics for quantifying the in-game performances of individual football players have been proposed in recent years. Although the majority of the on-the-ball actions during games constitutes of passes, many of the…
Real-time inference is a challenge of real-world reinforcement learning due to temporal differences in time-varying environments: the system collects data from the past, updates the decision model in the present, and deploys it in the…
Routing games are used to to understand the impact of individual users' decisions on network efficiency. Most prior work on routing games uses a simplified model of network flow where all flow exists simultaneously, and users care about…
American football is unique in that offensive and defensive units typically consist of separate players who don't share the field simultaneously, which tempts one to evaluate them independently. However, a team's offensive and defensive…
The presence of momentum in sports, where the outcome of a previous event affects a following event, is a belief often held by fans, and has been the subject of statistical study for many sports. This paper investigates the presence and…
We consider multi-player stopping games in continuous time. Unlike Dynkin games, in our games the payoff of each player is revealed after all the players stop. Moreover, each player can adjust her own stopping strategy by observing other…
For some time, point-differential has been thought to be a better predictor for future NBA success than pure win-loss record. Most ranking and team performance predictions rely largely on point-differential, often with some normalizations…
The debate surrounding the hot hand in the NBA has been ongoing for many years. However, many of the previous works on this theme has focused on only the very next sequential shot attempt, often on very select players. This work looks in…
In baseball, every play on the field is quantitatively evaluated and has an effect on individual and team strategies. The weighted on base average (wOBA) is well known as a measure of an batter's hitting contribution. However, this measure…
A same-score streak in sports is a sequence of games where the scores are equivalent in all games. The motivating problem arose from college basketball, however due to the difficulty in collecting data, streaks in Major League Baseball…
Box score statistics are the baseline measures of performance for National Collegiate Athletic Association (NCAA) basketball. Between the 2011-2012 and 2015-2016 seasons, NCAA teams performed better at home compared to on the road in nearly…
Influence functions estimate the effect of removing a training point on a model without the need to retrain. They are based on a first-order Taylor approximation that is guaranteed to be accurate for sufficiently small changes to the model,…
Professional team sports provide an excellent domain for studying the dynamics of social competitions. These games are constructed with simple, well-defined rules and payoffs that admit a high-dimensional set of possible actions and…
Reaction time studies with computers investigate how and how quickly participants respond to changing sensory input. They promise simple and precise measurement of time and inputs and offer interesting insights into human behavior. However,…
In many sports, it is commonly believed that the home team has an advantage over the visiting team, known as the home field advantage. Yet its causal effect on team performance is largely unknown. In this paper, we propose a novel causal…
In this study, a temporal graph model is designed to model the behavior of collective sports teams based on the networks of player interactions. The main motivation for the model is to integrate the temporal dimension into the analysis of…
We construct a statistical ensemble of games, where in each independent subensemble we have two players playing the same game. We derive the mean payoffs per move of the representative players of the game, and we evaluate all the…
The intelligibility of speech relies on the ability of interlocutors to dynamically align their expectations about the rates at which informative changes in signals occur. Exactly how this is achieved remains an open question. We propose…