Parity Pooper

If you listen to the CFL commissioner long enough, the probability of hearing the word "parity" approaches 100%.  As far as the media is concerned, just searching for "CFL parity" in my browser history yields 3 results for articles with those words in the title.  There are probably even more articles whose body contains the word, even though it doesn't appear in the title.  In these contexts, the word means that teams are roughly equal in ability, that any given match could be won by either team (or, rarely, end in a tie), and it's almost always considered a good thing.  Other leagues and the journalists that cover them do it too, though possibly using different terms such as "competitive balance".

This article on parity gives some history to the concept and some explanation to why it might not be all that it has been cracked up to be (although it doesn't mention the CFL at all).  While I was reading it, a couple of other reasons crossed my mind.

First of all, it is hard to know with certainty whether or not parity really exists in a particular season.  Ignoring the possibility of a tie, we can run some simulations to show that even when every team is exactly as good as every other team, there still is a roughly 23% chance that the team with the worst record will have only 5 wins.  It should be emphasized that, despite the dismal record, this does not mean that it's the worst team.  We are assuming that all teams are equally good, so there is no best team and there is no worst team.  It is simply the team that won the fewest games.

Of course, it is possible that a team that wins only 5 out of 18 games is just bad.  But the fact that a team could be exactly as good as every other team yet still have a relatively high probability of finishing the season with the same record makes it hard to tell whether team is bad or just unlucky.

We could run a similar analysis for the other teams.  The numbers would be different, of course, but similar results would hold.  A league with parity would have some teams with poor records even if they are just as good as those with winning records.  So there's reason to be skeptical when the commissioner of your favourite league talks about it.

Secondly, there is a psychological reasons why we might not even want parity.  Surely, if your favourite team posts losing records year after year or hasn't won a championship in more than a decade, parity would be an improvement.  But is it still desirable if your team is the one that won the championship?  Under parity, each team is as good as every other team, so each team has an equal probability of coming away with the win.  Thus, the outcome of the game is essentially just the result of a physically demanding coin toss.  Each victory earned by your team, from the first regular season game, all the way through to the final playoff game, was not due to skill, but to chance.  Your team won the championship not because it was better than other teams but because of a 20 or 21 game lucky streak (well, a luckier streak than all of the other teams).

Thus, parity essentially does away with one of the things that keeps people invested in their team: the belief that it's better than all of the other teams (or the hope that it one day will be) [1].

At best, parity could give consolation to fans of those teams with losing records.  Rather than being forced to admit that their teams are no good, they can simply claim that the teams were the hapless victims of probability.  Then again, parity is often billed as the thing that gets your team wins, not the thing that causes losses, so it's not really much consolation at all.

---------------

You might be wondering why I ignored ties in my analysis.  It was because it's not clear how to account for ties.  We would expect more when there is parity, but it's not obvious how frequent they would be.  Some seasons have none at all, and those that do tend to have only one, so we might guess that the probability is at most 1 in 72 (the total number of games played in the regular season -- playoff games cannot end in a tie).   In any case, they seem to be rare events, so ignoring them probably doesn't change the analysis by much.

[1] That being said, I'm sure there are people who could simultaneously believe that there is parity and that their championship winning team is better than the others without seeing the contradiction even after being told.