Abstract
INTRODUCTION The of baseball have an intriguing quirk that other major-league sports do not have, namely, the sequential order of play which always affords the last at-bat to the home team. We became interested in exploring the strategic effects of this quirk. If there is a significant strategic advantage (or disadvantage) to having the last at-bat, it may show up as a difference in win percentage of the home team in close games, where strategy is more important, compared to the win percentage of home teams in games which are blowouts. Our paper is motivated by attempting to exploit the natural experiment of comparing close games to blowouts. In previous literature, the possibility that strategic effects might come into play because of the sequential nature of the play is only partially recognized. For example, Carmichael and Thomas state as their third reason for home field advantage, rules factors that may extend special privileges explicitly favoring the home team, such as the home team in baseball and softball always having the last 'bat.' (1) These authors only recognize the possibility that the last at-bat might give the home team the advantage when there is reason to believe that it is the visitors who actually have the advantage. Indeed, among baseball, basketball, hockey, football, and soccer, the strategic effect due to sequential play is only operative in baseball, yet baseball has the lowest home-field advantage of these five major sports. The difference between the home winning percentage and the away winning percentage is statistically significantly positive for all major sports, but differs from sport to sport. In baseball, from 1901-2002, the average difference per team per year was 0.082, which for a .500 team in a 162 game season would lead approximately to records of 44-37 at home and 37-44 on the road. (2) By contrast, in the National Basketball Association, the rule of thumb is that the home team wins about 61% of the time, which implies a difference in winning percentages of about 0.220. (3) The corresponding statistics for the National Football League, the National Hockey League, and European soccer are 0.160, 0.113, and 0.380 respectively. (4) Why should baseball's home field advantage be smaller than that of the other sports? One possibility concerning the rigors of travel is that baseball's travel schedule is much different from that of football and soccer, which are different again from that of basketball and hockey. While these differences are obvious, it is far from obvious how to statistically capture this effect, and we choose to not explore this possibility. However, it is possible to examine what happens because of baseball's distinct, sequential nature of the play, what we call the last-ups effect. In baseball, the home team always bats last. Therefore, in the last inning of a tied game, or in extra innings, the optimal offensive strategy of the home team (and defensive strategy of the visiting team) depends upon what happened in the top half of the inning and, consequently, may differ from the optimal strategies employed in the top half of the inning. For example, the visiting team needing only one run to pull ahead may have considered a sacrifice bunt, which may increase the probability of scoring one run even though it decreases the probability of scoring two or more runs. Meanwhile, if the visiting team did, in fact, score two runs in the top half of the inning, the home team will never sacrifice to move one runner into scoring position because they know they need at least two runs. Batting last gives the home team a relative advantage in employing offensive strategies in the bottom of the ninth or in extra innings. Batting last gives the home team some advantages with respect to offensive strategies, but the visiting team has its own set of defensive strategies that may give it an advantage in extra innings. For example, the visiting team can save its closer until it knows that it has scored in the top half of the inning, whereas the home team cannot wait until it is ahead in extra innings to employ its closer. …
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