# UEFA Champions League: The Value of a One Seed

by Barrett Hansen and Brendan Kent

In the final phase of the 2013-2014 UEFA Champions League Group Stage, Manchester City beat Bayern Munich 3-2 at the Allianz Arena in Munich. As stunning as Cityâ€™s defeat of the reigning Champions was, City Manager Manuel Pellegrini came under criticism for misunderstanding the mathematical situation that determined whether City or Bayern would be the one-seed in Group D. Pellegrini removed David Silva 20 minutes before the final whistle while the score was 3-2 and neglected to bring on Sergio AgĂĽero, believing that City needed a nearly impossible 5-2 win to top the group. They only needed to win 4-2.

But in quantitative terms, how potentially costly was Pellegriniâ€™s error? In other words, what is the value of being the one-seed going into the knockout rounds, all else being equal? To answer this, we ran a logistic regression that predicted success in the Round of 16 based on, among other things, whether or not a team was a one-seed following the Group Stage.

It is important to note that in the Round of 16, the 8 one-seeds from the Group Stage play the 8 two-seeds in two-legged ties. The two-seed hosts the first leg while the one-seed hosts the second leg. While there is no technical advantage, it is often thought that playing the second leg at home provides some kind of advantage.

Using data from the 2008-09 through the 2013-14 Champions Leagues, we ran a regression that used success in the Round of 16 as the dependent variable (1 if the team moved on from the Round of 16, 0 if it didnâ€™t). We controlled for the strength of the clubs and their opponents using the UEFA Coefficient. The UEFA Coefficient gives clubs a rating based on success in European play over the previous 5 years; this isnâ€™t a perfect measure of present skill, but also isnâ€™t overly sensitive to one yearâ€™s performance.

We also controlled for the country that each team was from. There are two motivations for this. First, competing squads from different nations arenâ€™t necessarily of the same caliber. Second, teams cannot play teams from their own country in the Round of 16; therefore, it may be beneficial to be an English team because there are fewer really good teams (i.e. other teams from the Premier League) that are potential opponents in the Round of 16.

We also included each club and its opponentâ€™s domestic success in the current season, using the proportion of points taken out of those available in each clubâ€™s domestic league through the New Year (because the Group Stage ends before the New Year and the Knockout Rounds begin after). This hopefully captures current form, which also dictates whether the club will play hard in the Champions League or is more focused on the domestic season. Our final variable was, of course, a dummy variable that indicated whether or not a team was a one-seed.

As it turned out, the only variable with a strong predictive power was whether or not a team was the one-seed. With a p-value of .0055, our one-seed variable holds up at the 1% significance level, where no other covariate hold up even at the 10% level. We also note that the majority of country dummies are negative; since Englandâ€™s dummy is the one omitted, it is clear that Premier League teams have outperformed their peers over the past several years.

The takeaway? Apparently there is an advantage to being a top seed going into the Round of 16. This could be due to the material advantage of playing the second leg at home. It could also be due to some sort of â€śChampions League formâ€ť that can be acquired in the group stage. Finally, there could be some way in which the one seeds are superior teams to the second seeds not captured in our data, a distinct possibility given the tough task of comparing teams across leagues. Regardless, perhaps it is fair to criticize Pellegrini because, considering Cityâ€™s routinely poor form in the Champions League, they need any help they can get.