A Markov Chain Approach to Baseball
A Markov Chain Approach to Baseball
复制标题
棒球的马尔可夫链方法
作者：
B. Bukiet;E. Harold;J. Palacios
大多数早期的棒球数学研究都需要基于一小部分进攻可能性的特定模型来推进跑者。其他努力只考虑具有相同能力的球员的球队。我们引入了一种马尔可夫链方法，该方法考虑了由不同能力的球员组成的团队，并且不局限于给定的跑步者进步模型。我们的方法仅受现有数据的限制，当没有足够详细的数据时，可以使用任何合理的确定性模型来进行流道的推进。此外，我们的方法可以调整为包括投球和防守能力的影响，以一种直接的方式。我们应用我们的方法来找到最佳的击球顺序，每半局和每场比赛的得分分布，以及一支球队应该赢的预期场次。我们还描述了我们的方法的应用，以测试一个特定的交易是否会使一个团队受益。
Most earlier mathematical studies of baseball required particular models for advancing runners based on a small set of offensive possibilities. Other efforts considered only teams with players of identical ability. We introduce a Markov chain method that considers teams made up of players with different abilities and which is not restricted to a given model for runner advancement. Our method is limited only by the available data and can use any reasonable deterministic model for runner advancement when sufficiently detailed data are not available. Furthermore, our approach may be adapted to include the effects of pitching and defensive ability in a straightforward way. We apply our method to find optimal batting orders, run distributions per half inning and per game, and the expected number of games a team should win. We also describe the application of our method to test whether a particular trade would benefit a team.