This article illustrates the difficulty in perceiving ``real" patterns in homerun hitting over the stretch of a season. Even if Mike Schmidt hit homeruns exactly like independent Bernoulli trials with a constant probability of success, the patterns of hot-hitting and spacings between homeruns would resemble his observed hitting data. However, by use of the simulation experiment, we can detect some subtle differences from the coin tossing model. By looking at the group of two-week periods, Schmidt appears to have more cold and hot periods of hitting homeruns that predicted under the consistent hitting model. In addition, the degree of consistency of his hitting appeared to change over time. Schmidt's homerun hitting when he had a long batting stroke appears more inconsistent than the hitting later in his career when he had a more compact swing. The effectiveness of this statistical method partially rests on the choice of the ``right statistic. Some of Schmidt's statistics, such as the number of large spacings between homeruns, did not appear to be that different from the values observed in the coin tossing model.
There has been recent interest in the related issue of streakiness in sports. Tversky and Gilovisch (1989) argued that the ``hot hand" in basketball shooting was a consequence of people' misconception about coin tossing. Albright (1993) looked for streakiness in a large body of baseball hitting data using a number of statistical methods. Albert (1993) developed a different method for the detection of streakiness in hitting. He proposed a ``streaky model" and showed that this model was a better fit than the basic coin tossing model for particular baseball players.
Other baseball papers have focused on modeling. Albert (1992) looked at the seasonal homerun totals for a number of great baseball hitter, including Schmidt. His analysis showed that generally the rate at which a player hits homeruns follows a quadratic form. This allows one to separately measure a hitter's career and peak homerun performance. Barry and Hartigan (1993) used a choice model to predict the outcomes of future baseball games. One notable aspect of their model is the assumption that a team's ability could change over time. Based on the analysis of this paper, it would also seem reasonable to model Schmidt's homerun hitting ability with a parameter that changed over his career.