In our book, The Wages of Wins, we show that historically MLB is more competitively balanced now than it was in its early history and that competitive balance in MLB has been improving over the last few decades. Yet, MLB is still not as competitively balanced as European football (soccer) or American football. In The Wages of Wins and in published peer-reviewed journal articles, Dave, Marty and/or I have said this is due to the changes in the population of players in that sport. As we state in our book, this is Steven Gould's argument for the disappearance of the 0.400 hitter in MLB.
So, just how competitively balanced was Major League Baseball in 2011? Using the Noll-Scully competitive balance metric, which calculates competitive balance by taking the standard deviation of actual winning percent and dividing it by the standard deviation of winning percent in an ideal league (i.e. in a league where wins and losses are randomly drawn in a statistical manner) and using the data from the end of the 2011 season, I calculate that the American League's Noll-Scully measure of competitive balance = 1.788 and for the National League the Noll-Scully measure of competitive balance = 1.858. Note if wins and losses are completely random then the Noll-Scully measure of competitive balance equals 1.000.
Thus the American League was about 79% more competitively unbalanced than what we would observe if wins and losses were determined randomly and that the National League was almost 86% more competitively unbalanced than if wins and losses were randomly assigned. So is this high or low? Compared to MLB historically, this year's measure is much more competitive and is much closer to the historical average of the NHL.