An intuitive Markov chain lesson in baseball

One of the biggest challenges when teaching about Markov chains is getting students to think about a Markov chain in an intuitive way, rather than treating it as a purely mathematical construct. We have found that it is helpful to have students analyze a Markov chain application (i) that is easily explained, (ii) that they have a familiar understanding of, (iii) for which a large amount of real data is readily available, and (iv) that teaches them new insights about the application they thought was so familiar. Finding such examples can be difficult; introductory textbooks provide numerous examples that are easily explained, but the examples are generally written in “toy problem” form so that there is no need to work with real data; this makes it difficult to obtain believable new insights from the models. We feel that taking students through at least one in-depth example is useful, becuase it gives them a chance to experience a model with real-world complexity that is detailed enough to provide realistic insights. In this paper, we suggest an example from the world of sports – analyzing baseball with Markov chains.