On a recent drive through western North Carolina I heard an interview with James Dodson, author of American Triumvirate (audio). The book is a history of modern golf focusing on three key figures--Sam Snead, Byron Nelson, and Ben Hogan. I am not much of a golfer, but Dodson made a comment that was very interesting. He argued that three dominant players was the perfect number for golf's popularity: it gave a sense of rivalry and competition while maintaining continuity at the top. (The trio had a combined total of 198 PGA tour wins, including 21 majors.)
A similar question has challenged students of international politics: what number of major-power states is optimal for stability? The answers vary: "unipolar" theorists argue that one powerful state is best, "bipolarity" advocates argue that two major powers can balance each other out, and "multipolar" scholars see an oligarchy of states as the most stable international regime. The question is difficult (if not impossible) to answer due to lack of data--we can only observe one historical record.
But sports gives us another opportunity to explore the question, with far more data points. What number of dominant players/teams is optimal for a sport's popularity? If Dodson is right, for golf the answer is three. Baseball, football, soccer, and other sports may be most popular with a different number of teams at the top. If the numbers are different, what is it about each sport that makes this so? Is it the structure of the league, the type of play, media and advertising issues, or something else entirely?
Attempting to answer this question presents a few challenges of its own. First, how does one establish who the dominant players/teams are at any given time? Second, is competition data available for the time period of interest? Third, how should we measure the popularity of a sport over time? If these challenges can be overcome, this might make for an interesting and fun research project.