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Which is more balanced- NFL or Champions League?

Even a competitive balance sceptic like myself would grudgingly admit that the NFL is more balanced, so I thought I would check what the market was saying by looking at some betting odds. If you go to internet betting sites such as "odds checker" you can compare what the bookies are offering for each of the clubs (as you would expect, the bookies are all pretty much in line with each other).

So, I looked at the odds on winning the Superbowl and the Champions League last week just before competitions started, imagining that I would see much more balance in the odds on the former. But not a bit. According to Sporting Odds, the probabilities of winning for the three favourites in the Champions League are 15%, 11% and 10% (Chelsea, Barcelona and AC Milan). The odds of the three Superbowl favourites are 14%, 12%, and 11% (Indianapolis, New England and Philadelphia). Each competition has 32 teams, and the odds on the top three are almost identical. If we look at the bottom, then the Champions League outsiders are FC Thun and Artmedia Bratislava - each quoted at 500/1- but how much worse is that than Cleveland and San Francisco, each quoted at 200/1? In probability terms there is little difference.

Now, if a competition were perfectly balanced, the odds would be 31/1, or roughly 3% for each team. However, in the NFL there are 10 teams with odds better than this, and the joint probability that one of these teams will win is 68%. In the Champions League there are 11 teams with better odds than 31/1, and they account for 81% of the total probability. Overall, the distribution of probabilities between the two competitions looks remarkably similar.

Now, all this does not mean that NFL socialism is not working, just that the balance it creates is not markedly greater than that of the Champions League. The ratio of income of the top to the bottom teams in the NFL is about 2:1, while in the Champions League exceeds 100:1 (Manchester Utd £171m last year, Artmedia Bratislava £1.5m). If the NFL had similar income disparities then it would probably not be safe for teams to play. Moreover, the technology of soccer is such that results are much more uncertain (As England can testify after losing to Northern Ireland the other week, despite a gap of 109 places in the FIFA rankings prior to the game). And of course, the 49ers have won Superbowls before and probably will again while, without wishing to sleight Artmedia Bratislava or FC Thun, these teams have never won much in Europe and probably never will.