Since the English Premier League has "draws" or ties, the Noll-Scully competitive balance measure must be calculated with the trinomial distribution, which as Richardson shows in his Eastern Economic Journal article, the idealized standard deviation is [(1-p)4n]^(1/2); where n is the number of games played and p is the probability of balanced teams tying. The number of games played is simple, its 38. The calculation of p is not as simple. Here, I have to make a determination. What I did was to look at the last (approximately) 20% of the season, and calculate the number of games teams that finished 9th, 10th, 11th and 12th in the EPL final table, in which those teams tied. Then I took the average of those four teams to calculate p.
Using data from [https://datahub.io/sports-data/english-premier-league#resource-season-1819], the Noll-Scully Competitve Balance measure reveals the following:
As you can see, the English Premier League has been becoming less competitive since the 2015/16 season. Yet, is it a problem? That is much harder to definitively answer. Overall, it seems to me that an economic problem exists if the league becoming less competitive results in a significant decrease in attendance, revenues and viewership. That doesn't seem to be the case, so even with the EPL recently becoming less competitive, it is not a problem.
For those interested in the actual numbers, see below.
| Season | Noll-Scully |
| 2009/10 | 3.104 |
| 2010/11 | 2.469 |
| 2011/12 | 3.178 |
| 2012/13 | 3.141 |
| 2013/14 | 3.808 |
| 2014/15 | 3.066 |
| 2015/16 | 2.826 |
| 2016/17 | 3.507 |
| 2017/18 | 3.584 |
| 2018/19 | 4.086 |
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