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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