Tuesday, April 10, 2012

2011-2012 NHL Competitive Balance

Now that the 2011-2012 NHL regular season is over, let's find out how competitively balanced the NHL was over the 2011-2012 regular season. In order to do this we need a measure of competitive balance, and while there are a number of measures, I am going to choose the Noll-Scully measure of competitive balance. Noll and Scully were looking at basketball and baseball respectively and in each case, there are two outcomes for each game, you win or lose. In some sports that is not always true; hockey being an excellent example. It is possible in hockey to end up with three outcomes: a win, a loss or a tie. Typically, I get around the possibilities of a tie by just calculating each team's winning percentage (# of wins * 2 + # of ties)/(# of games played *2) and use the typical Noll-Scully approach to measure competitive balance - such as we did in our book, The Wages of Wins. If I do that I end up with a Noll-Scully for the 2011-2012 NHL regular season equal to 1.15, which would indicate that the NHL is fairly competitively balanced last year. (If you use the standard deviation of a population instead of the standard deviation of a sample the Noll-Scully is now equal to 1.13).

Yet, what about the possibility of ties and how does that change the competitive balance measure under the Noll-Scully assumption of equal playing strength? Well, David Richardson in a paper "Pay, Performance, and Competitive Balance in the National Hockey League" published in the Eastern Economic Journal in 2000 addressed exactly that question and reports that the formula for calculating the idealized standard deviation of the Noll-Scully measure of competitive balance under a trinomial distribution is: [(1-p)/4n]1/2, where p is the probability of a tie under the equal playing strength assumption and n is the number of games played. Richardson estimates that the probability of a tie (using Stanley Cup playoff series that went 6 or 7 games and ended up tied during regulation to be equal to 0.162). So let's use that for now as our probability of teams with equal playing strength in the NHL of tying to calculate the ideal standard deviation. When doing so, now the Noll-Scully measure of competitive balance is equal to 1.414 - or less competitively balanced than by not including the probability of a tie occurring. (Using the standard deviation of the population results in the Noll-Scully now to be equal to 1.391).

Update: Step-by-step guide to calculate the Noll-Scully Competitive Balance Measure.

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