ABSTRACT
In contrast to many other sports, baseball is a game of intermittent action, separated by (sometimes extended) periods of time between pitches, where (usually) nothing happens. While for some this leads to boredom, for baseball fans these times of inaction increase anticipation, particularly at times when one team is building a scoring rally through several at bats. The natural impression a fan often gets as a team puts together several hits or walks
and scores some runs is one of momentum — a sense of the inevitability of yet another hit leading to still more runs — but is that really the case? Does the outcome of a particular at bat depend on what has come before, or is it just a function of the current out and runners on base situation (the current state), current pitcher, batter, and so on? This question can be explored using play-by-play data, starting with simple models for the transition from one state to another that depend only on the initial state, then extending those models to include other characteristics of the current situ-
ation (situational effects), and finally including effects depending on previous at bats (momentum effects). This is different from questions of whether individual players or teams are streaky (that is, they have periods of time when they are more or less successful than would be expected by chance), which have been examined, for example, by Albright (1993) and in Chapter 9 of Albert and Bennett (2003), but is related to the same issue of whether fans’ perceptions of non-randomness are real or not. In the next section we describe how batting transitions from one batter to the
next can be modeled statistically. We outline the simplest model for transitions from one state to another, the Markov chain, and then discuss how this model can be generalized to allow for situational and momentum effects. The models are then fit to actual play-by-play data, in order to see if there is evidence for situational and momentum effects. We also examine models for scoring that allow for momentum effects, and explore whether certain plays can be viewed as rally starters or rally killers (and hence momentum-causing events).
