|
|
|
|
Stochastic ModelsStochastic modeling is a broad field concerned with quantifying observed randomness. What makes modeling sports difficult isn't the inherent randomness (a coin-flip is inherently random but very easy to model). Rather, the difficulty is due to the compound nature of random phenomena. For example, it easy to think about the possible outcomes of a play in a football game or an at-bat in baseball. But imagining two or three events downstream is quite difficult, because future outcomes depend on random events which haven't happened yet. Consider the first inning of a baseball game. It's possible that the cleanup hitter could hit a grand-slam. However, his chances of doing so depend not only on his own plate appearance, but on those who preceded him. (It's hard to hit a grand slam when there's no one on base.) Stochastic models area a valuable tool in many decision problems. Strategy can be assessed and improved by determining which decisions maximize chances of winning1 the game. By simulating each circumstance repeatedly, we can "observe" how often certain strategies lead to wins. Simulation algorithms also provide deeper insight into the games, since they require in-depth analysis of every potential outcome. Over the course of developing the model, patterns (and tactics to exploit them) reveal themselves. 1. Although the goal of any coach or manager should be to maximize his team's chance of winning, many coaches are unnecessarily risk-averse. Their decisions are often made to reduce the chance of being second-guessed or to delay (not avert) the eventual loss. [For an example, click here.]
ExamplesTo illustrate the progression of a sporting event, we've developed two simulation algorithms that capture their stochastic nature. The NFL Game Simulator randomly finishes a game from any starting point (e.g. opening kickoff, down by 3 with 5:00 left, etc.). It uses the current game situation (possession, down, distance, timeouts, etc.) to determine the play call and its result. Once the game state is updated, the routine is repeated until the game ends. The Lineup Optimizer lets you compare offensive production of various lineups consisting of a given set of nine players. |
Send mail to
webmaster@sportsquant.com with
questions or comments about this web site.
|