So how can we measure competitive balance? One of the ways is to look at the distribution of championships by franchise. In order to get a good representative sample, let's look at MLB, NFL and NBA champions over the last 40 years. The graph below shows a frequency distribution of championships by franchise from 1971 to current. A sport that was completely balanced would have all franchises winning at least one championship with a few winning two. Clearly, this is not the case. In fact, about half of the current NFL and NBA franchises have not won the big prize. The most useful measure for comparing the "spread" of the numbers is the standard deviation. Put simply, the standard deviation measures the difference of a set of numbers compared with the mean. In order to compare two or more sets of numbers, it is sometimes appropriate to divide the standard deviation by the mean. However, in our case, the difference between the means for each of the sports is negligible. Here are the standard deviations for the three sports; the lower the value, the more the sport is "balanced":
Major League Baseball: 1.5
National Football League: 1.7
National Basketball Association: 2.5
So, comparing the number of championships, we see that MLB and the NFL are similarly balanced and are significantly more balanced than the NBA. It may be surprising that MLB leads the way, especially since they have not established some of the restrictions(hard salary cap, etc.) that the other sports have to improve parity.
Of course, there are other ways to measure competitive balance that might be more revealing. We'll look at others next.