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Comparing balance in the Champions League and NFL

For many years the NFL has boasted of the competitive balance of its competition -- "on any given Sunday any team can win." By contrast European soccer leagues are well known for being dominated by a small number of teams such as Barca and Real Madrid in Spain; Juventus, Inter and AC Milan in Italy; and Bayern Munich in Germany. The start of the new season in each sport provides an interesting opportunity to compare the competitive balance of the two footballs.

Thirty-two teams will compete for this year's Lombardi trophy (awarded to the Super Bowl winner), the same number as will compete for the Champions League trophy. The NFL kicked off on Sept. 4 and the Champions League group stage on Sept. 16.

Some might say that the two competitions are not comparable -- the closed nature of the NFL means that the same teams compete every year and must operate within a salary cap, while in the Champions League different teams qualify every year and, theoretically, can spend as much as they wish.

However, the Champions League is more stable than most people think. This year's participants account for almost half of all appearances in the Champions League over the past decade and four teams have played in every season. Two thirds of the teams in this year's competition played in it last season.

The best indicator we have of the likely outcome of the season right now is the betting odds, which you can download from many websites. You can convert these odds into implied probabilities.

Real Madrid are favourites to retain the Champions League crown they won in May.

The bookies currently have Real Madrid as favourites with a 19 percent probability of winning and Malmo the biggest outside, with a 0.05 percent probability (2000 to 1). In the NFL the Seattle Seahawks are favourites with an implied probability of 25 percent, while the biggest outsiders are the Jacksonville Jaguars with a 0.4 percent probability.

On the face of it, then, the NFL does appear more balanced: four teams alone account for 50 percent of the probability in the Champions League (Bayern Munich, Barcelona and Chelsea along with Real Madrid), compared to six in the NFL (Denver, San Francisco, New England, Green Bay, New Orleans and Seattle). The cutoff is sharpest among the top 16 (those likely to reach the playoff stage of the Champions League) -- there is a 92 percent probability the winner will come from the top 16, but in the NFL the probability is the top 16 winning the Superbowl is only 76 percent.

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From the point of view of attracting broader interest, the problem for UEFA is that the teams playing in the group stages may generate huge national pride -- Ludogorets Razgrad will be followed intensely in Bulgaria whatever the results -- but the odds of 2000 to one or so suggest that they are in line for some heavy defeats which will not make the game that exciting to watch for the neutral. By contrast, the last 16 will produce many close games and almost anything could happen.

But the NFL is not that much more even. Almost no one thinks it conceivable that a Champions League winner will emerge from outside the elite of the league. For teams outside of the top 10 the average probability of winning is just over one percent. But the Super Bowl winner is also expected to be drawn from only a small subset of teams -- for those outside the top 10 in the NFL the probability is just under three percent. That's three times larger than the Champions League equivalent, but supporting a team with a probability of winning of three percent doesn't seem a whole lot better than just one percent. Once a century or once every 33 years, well, neither prospect is likely to set the pulse racing.

It's possible to compare the degree of inequality graphically. Rank the teams from those with lowest probability to the highest, and then calculate the cumulative probability of the weakest teams winning. If all teams were equally likely to win, the resulting chart would produce a diagonal line from the bottom left to the top right of the chart. Because the weaker teams have lower probability of winning, the actual lines start out being less steep and then get much steeper once you reach the high probability teams.

In short, the more bowed out is the curve, the more unequal. The chart above illustrates that the Champions League is more unequal than the NFL, which is itself quite unequal.

We can also summarise the inequality in a single number, called the "Gini" coefficient. The Gini is a measure of the gap between the line of theoretical equality and the actual inequality curve. If the actual and theoretical coincide then the Gini coefficient is zero. Maximum inequality (which in this context would mean that one team alone had a 100 percent probability of winning), the Gini coefficient would equal one. The Gini coefficient for the NFL is 0.44 and for the Champions League is 0.69.

So on this measure the Champions League is about 50 percent more unbalanced than the NFL.

The Champions League has a competitive balance problem -- it is wildly out of sync with the prevailing image of equality that Europeans like to promote. By comparison the NFL is more egalitarian, but not by as much as the NFL would like us to think.

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