In our book, The Wages of Wins, we take a look at competitive balance using a measure devised by Roger Noll and Gerald Scully, which we call the Noll-Scully competitive balance measure. Basically, what it measures is the actual standard deviation of winning percent in a sports league relative to a standard deviation of winning percent if wins and losses were randomly distributed, using the binomial distribution. The closer a league gets to one the more balanced the league from a statistical viewpoint.
In The Wages of Wins, we report that for the NFL, from 1922-2006 that Noll-Scully competitive balance metric had an average of 1.56 and for the AFL (1960 - 1969) the Noll-Scully metric had an average of 1.58. We also show that other types of sports have similar measures of competitive balance among different leagues. One sport that we did not report was NCAA football, and here is a first pass at clearing up that oversight.
So, I got the NCAA football schedules from 2002 to 2012 and calculated each season's Noll-Scully measure of competitive balance. The first is with all the games that were played in each season, which includes both bowl (post-season) games and games against non-FBS teams. To be fair, when we calculated the Noll-Scully for the NFL and the AFL we did not include post-season games and there were no games against non-league opponents. In the coming days, I will re-calculate the Noll-Scully deleting out the post-season games and then deleting out games against non-FBS teams and report each in a separate blog post. As for now, here is the full sample over the last eleven years.
| Season | NS | |
| 2002 | 1.539 | |
| 2003 | 1.612 | |
| 2004 | 1.462 | |
| 2005 | 1.435 | |
| 2006 | 1.579 | |
| 2007 | 1.458 | |
| 2008 | 1.458 | |
| 2009 | 1.519 | |
| 2010 | 1.526 | |
| 2011 | 1.515 | |
| 2012 | 1.579 | |
| Average | 1.516 |
You will notice that the Noll-Scully does not change very much from one year to another and that the average over the 2002-2012 seasons is fairly similar to the NFL and AFL over the time periods reported in The Wages of Wins. This fits with our extension of Gould's hypothesis that the underlying population playing a sport has an impact on it's level of competitive balance. (Gould was trying to explain the disappearance of the 0.400 hitter in MLB). Our extension is that the increase in the underlying population of individuals playing a particular type of sport and having particular skills impacts the level of competitive balance in the sport. So we argue that given the tiny population of people seven foot or taller makes basketball less competitive than a sport like soccer which does not rely on drawing highly skilled players from such a small population. Given that soccer is the world's most played sport, it should be the most competitive and overall soccer has a lower Noll-Scully competitive balance measure than say hockey, baseball, or basketball.