The smell of freshly mown grass, the endless summer sun, barefoot little kids, and baseball: these are some of the essences of summer. The game of baseball has been part of summer for more than one hundred and twenty years. It is a sport with a rich history and tradition. Nothing typifies the game better than the crack of a slugger's bat as a line drive is driven deep into center field.
Hitting is central to the excitement of baseball. A recent example is last summer's home run race between Mark McGwire and Sammy Sosa. Their race drew international attention and renewed interest in a sport that had suffered since the strike-shortened season of 1994. It had been believed that beating Roger Maris' single season record of 61 home runs, set in 1961, was impossible. Both McGwire and Sosa exceeded Maris' record with McGwire winning the race with 70 home runs. The duel captivated news headlines, and provided a welcome relief from the presidential impeachment turmoil.
Part of the fun of this race was the debate among fans. Friendly arguments raged over whether they would do it and whether McGwire was better than Sosa. These kinds of debates have been part of the fun since the game's inception in 1876. One of the most argued questions is "who is baseball's all-time best hitter?" This question is usually answered by calculating a hitter's batting average, which is just the number of hits the player has, divided by the number of times the player batted. The "traditional" all-time best hitter is Ty Cobb, who had a lifetime batting average of .366. Filling out the remaining top five all-time hitters, we have Roger Hornsby, ("Shoeless") Joe Jackson, Ed Delahanty, and Ted Williams, with batting averages of .358, .356, .346, and .344, respectively.
If batting averages can be used to decide whom the best hitters are, then why are there debates among fans? The answer to this question lies in the history of the game and is central to the role of the book under review. The sport has undergone many (radical) changes. Some of the more notable changes are increases in the distance from the pitching mound to home plate, various scoring changes (e.g., batters not charged with an at bat on a sacrifice bunt that advanced a runner), league expansion, and the (much-debated) designated hitter rule, where a hitter bats for a pitcher.
These changes suggest that it is perhaps unreasonable to simply compare batting averages. Indeed, the top fifteen traditional all-time best hitters all played before 1960, with the majority of them playing in the early part of the century.
The author develops an alternate method in the first five chapters of the text. It is richly motivated, using baseball's history, facts and anecdotes. Technical details of the method are given, but are placed in boxes labeled "Technical Notes." The intent of the author was to allow readers with no statistical knowledge to understand the basic ideas of the method while enjoying the book. To a large extent, he succeeds in doing this, but on a few occasions, such as the sections on ballpark differences and linear regression, the details may hinder some readers.
After presenting the method and the adjusted all-time top 100 hitters, the method is used to determine facts such as top hitters by position played and best single-season batting averages. In so doing, the author has provided a wealth of baseball trivia and statistics. The style of writing is engaging and often lively, and in fact, encourages continued debate over the data and conclusions presented. The text will undoubtedly become a part of the baseball statistics fan's library.
The text could also be profitably used as an innovative supplement for an introductory course in statistics or as a supplementary reading in a course in mathematics for the liberal arts student.
So, based upon this method, who is baseball's all-time best hitter? He is not Ty Cobb or Roger Hornsby or Joe Jackson but a player currently playing for the San Diego Padres.
Randall J. Swift (firstname.lastname@example.org associate professor of mathematics at Western Kentucky University. His research interests include nonstationary stochastic processes, probability theory and mathematical modeling. He is a coauthor of the MAA text A Course in Mathematical Modeling.
His non-mathematical interests are primarily devoted to his wife and two young daughters, but, when he has the time, he enjoys science fiction, history, listening to public radio, cooking and baseball.