Monday, April 29, 2013

2013 NHL Competitive Balance

Now that the NHL regular season has finished, let's take a look at how competitive balanced the NHL has been this season.  I have written about NHL competitive balance last year, and concluded using the Noll-Scully measure of competitive balance concluded that the NHL was fairly balanced last season.  So what about this lock-out shortened season?  Does competitive balance change all that much with fewer games played?  The quick answer is no, let's see how using the Noll-Scully competitive balance measure.

As I mentioned 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 over the last few NHL seasons.  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.  The probability of a game ending in regulation tied is given in the far right of the second table.

Binomial STD  Sample STD Population

Noll-Scully Noll-Scully
2013 1.2503 1.2293
2011-2012 1.1380 1.1175
2010-2011 1.3065 1.2838
2009-2010 1.2081 1.5284
2008-2009 1.3690 1.3459
2007-2008 0.8845 0.8666
2006-2007 1.5990 1.5722

Trinomial STD  Sample STD Population Probability

Noll-Scully Noll-Scully
2013 1.5800 1.5535 0.2250
2011-2012 1.4528 1.4267 0.2448
2010-2011 1.6704 1.6414 0.2405
2009-2010 1.5284 1.4998 0.2421
2008-2009 1.7381 1.7089 0.2293
2007-2008 1.1031 1.0808 0.2234
2006-2007 2.0281 1.9940 0.2285

While the NHL was slightly less competitively balanced than the previous season, there is not much difference over the last few NHL regular seasons, and I would conclude that the NHL lock-out shortened regular season was not significantly different in terms of competitive balance as compared to other NHL regular seasons since 2006-2007.