Monday, April 14, 2014

NHL Competitive Balance

With the 2013-14 NHL regular season in the books, let's take a look at how competitively balanced the season was (using the Noll-Scully measure of competitive balance) and compare this with recent seasons.

There are two ways of measuring competitive balance in hockey since unlike baseball or basketball, hockey games can end up tied at the end of regulation.  So I will report both the binomial and the trinomial Noll-Scully measure.  Additionally, there are two ways of reporting both the binomial and trinomial Noll-Scully measure:  one using the standard deviation of a sample and the other using the standard deviation of the population.  Again, I will report both.

Additionally, I will have to compute (for the trinomial distribution) the probability of a tie under equal playing strength.  In the past, I used Richardson's estimate from Stanley Cup playoff games.  In this case I will change and just assume that the probabilty of games that go into overtime occurs among teams with equal playing strength.  Feel free to quibble with this, as this is simplification of the estimated probability.  For transparency, I will also report for each season this probability estimate.

OK, with the measurement details noted, here are the Noll-Scully competitive balance numbers for the last NHL season.  The first table used the binomial measure and the second table uses the trinomial measure.    The first column of numbers uses a sample standard deviation and the second column uses the population standard deviation. 

Binomial Distribution Sample Population
Standard Deviation of Winning Percent = 0.093023 0.091459
Average of Winning Percent = 0.5624 0.5624
Square root of Games Played = 9.055385 9.055385

Noll-Scully Measure of Comp. Balance = 1.497792 1.472617

Trinomial Distribution Sample Population
Richardson EEJ 2000

Idealized Standard Deviation= 0.047192 0.047192
Probability of a Tie = 0.269512 0.269512
Number of Games Played = 82 82
Noll-Scully Measure of Comp. Balance = 1.971147 1.938017

Compared to recent years, this year was less competitive balanced, but overall the level of competitive balance in the NHL is still rather similar to recent historical numbers.

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