The major league baseball attractor

Abstract

In the following work we regard any given Major League Baseball game as constituting a dynamic system, characterized by a sequence of inherently unpredictable events (the results stemming from pitches to batters, mainly). Hence, and also due to the game’s extreme sensitivity to initial conditions (imagine, for example, attempting to play the game with a ball whose coefficient of restitution approaches one, i.e., a superball; pitchers, infielders and fans close to the field would become especially at risk for serious injury or death from the missiles leaving the home plate area at well over 200 mph; games played in indoor stadia would look more like some wild form of pinball than baseball, games in general would be interminable, and all structures as part of all ballparks would be in jeopardy), Chaos theory applies to the game of baseball in classic fashion, the ordered end of its spectrum represented by the sublime beauty of the 1–0 pitching duel and the chaotic end by the “Keystone Cops-like” performances resulting in the 20 or 30 or even 40-plus run games. Concomitant with extant chaos is the system’s “attractor”, which is representative of an underlying order associated with the system. We will focus upon the “essential product” of the Major League Baseball game, i.e., the scoring of the run. Specifically, we seek to identify a statistical model for the runs-per-game frequency distribution, which is to say a ”Universal Function” to which said frequency distribution tends for any Major League Baseball team, any year. Nine recent Chicago Cubs teams (the 1995–2003 Cubs) along with all their opponents over a total of 1456 games provide the data from which such “Universal Function” as mentioned above is derived with approximately 98% confidence. In order to be consistent with the root philosophical idea as to the applicability of Chaos Theory, we will call the above-mentioned Universal Function the “Major League Baseball Attractor” in the sense (as will be statistically shown with high confidence) that over a large number of games the runs-per-game frequency distribution is expected to be “attracted (inexorably) towards” the derived Universal Function. Said attractor, however, is an “attractor” of a frequency distribution only, not of the game of baseball itself.