Evolution of Team Sports: A Case Study for National Basketball Association

Article excerpt

The enterprise of sports has risen in popularity all over the world and along with it the study of sporting events from various angles. With participation increasing from all quarters of life, cutting across race, gender and other distinguishing human characteristics, the importance of the economics of various sports has also increased dramatically. The revenues associated with various popular sports such as baseball, soccer, football and basketball, to name a few, run into billions of dollars. The scientific study of sports ranges from sports medicine, to various human characteristics of physiology, morphology, and biochemistry of the body suitable for various sports. Special issues and sections of journals have been dedicated to the study of sporting events.

Recently, Stephen Jay Gould (1986) in many of his popular essays has examined the progress of the game of baseball, particularly with regard to hitting, from an evolutionary biologists perspective. A theory in evolutionary biology states that stable systems display decreasing variability. Thus improvement of a system (for the species as a whole) is not typically displayed in a linear growth in average of some desirable attributes but rather in the declining deviation (from the average) of those attributes. This idea that more is not necessarily better is somewhat counter intuitive when encountered for the first time. However, if we view not the individual (and its excellence) but rather the group (and its ability to specialize for a firm grip on a niche for existence), then the declining variation is the proper measure of improvement. Gould's intriguing work on team sports such as baseball display the broader theories of evolutionary biology . Does data from professional basketball yield similar conclusions? We explore this question. The present work involves an examination of data for the National Basketball Association (NBA) over its entire history. Gould's work is reviewed while a brief history of the NBA is also given. The statistical analysis looks at the distribution of several scoring statistics, trends in such statistics and finally how the great players have fared over time and against each other. The analysis here is kept simple because the focus is primarily on understanding the evolutionary history of the game and not in statistical methods per se. The final section gives our summary and conclusions.

A Brief Summary of Gould's Work on Baseball

In baseball, hitting for an average of .400 (number of hits / number at bats) is considered a great feat which has not been duplicated since 1941. Some summary measures of historical data for professional baseball for the twentieth century are given in Table 1. (This table has been extended by us to include the decade of 1990). The table shows that only two players have reached the 0.400 mark and only two others, George Brett (0.390 in 1985) and Tony Gwynn (0.394 in 1994, though based on only half the season because of a strike of major league players), came close to that mark. We know the standards of baseball, and for that matter all modern sports, have undergone dramatic improvement in this century. How, therefore are we to account for the apparent decline in hitting, or to state it in a slightly different form, the disappearance of a 0.400 hitter?

Gould's findings can be summarized as follows: The batting average for all players in a given season is computed and this average for all years remains relatively constant. The batting averages of all players for all years (about 90 years) is about 0.267 with some minor variation. The standard deviations of batting averages, on the other hand, have decreased steadily and surely in an almost law-like fashion over baseball's history starting from 0.0371 and declining to 0.0317 (see Table 1). In this light, we calculate the standardized scores of the four players that are given below:

zCobb = 0.420-0.266/0.0371 = 4.2, zWilliams = 0.406-0. …