From the fan's point of view, one of the disadvantages of having a large number of teams at the top level of a professional sport is that a large number of playoff games must be played after the regular season. Chance plays a larger role in determining the outcomes of such playoffs than in determining who wins the most games in the regular season, and fans often feel that championships are won fortuitously by inferior teams.
How often does this really happen? What is the role of chance in determining the outcome of a series of playoffs? Using Chez Scheme's random-number generator, we can simulate a team's post-season play to collect evidence that might help one answer these questions.
A Scheme program that carries out such a simulation can be found at /u2/stone/courses/scheme/html/world-series.ss, in partially complete form. Copy this program into an appropriately named file in your account, load it into XEmacs, and study it. Read the comments on the various procedures to get an idea of how they are supposed to work.
The body of the better-team-wins-game? procedure is missing.
Add it and experiment with the first few procedures in the program.
Complete the program by writing the body of the
championships-for-better-team-kernel procedure. Run the
program and decide whether the results are plausible.
In contemporary professional baseball, the postulate that the better team can defeat its playoff adversaries sixty percent of the time is only rarely true. If the rate at which the better team wins games is reduced to fifty-five percent, how often does the better team win the championship?
In the early years of professional baseball in the United States, the World Series was often played as a best-of-nine series (five victories needed to win). If we decided to return to that arrangement, would it be more likely or less likely that the better team would win? By what margin?
To win the WNBA championship, a team must win a single ``semifinal'' game against an opponent from the other conference, then a single championship game against the winner of the other semifinal. Adapt the program so that it simulates such playoffs. How often does the better team win the championship in this case?
To win the Stanley Cup, a professional hockey team must win four successive best-of-seven series. Adapt the program so that it simulates such playoffs. How often does the better team win the championship in this case?
This document is available on the World Wide Web as
http://www.math.grin.edu/~stone/courses/scheme/world-series-project.html
created September 18, 1997
last revised September 18, 1997