Does Defense Wins Champions Leagues?

An old saying, at least for American sports, is that "offense wins games, but defense wins championships". In soccer the claim is often made that in cup competitions, particularly those like the Champions League that use the away-goals rule, strong defense is more important than the ability to score. The argument, which I've used myself, is that it's tough to advance if you can't win the home leg 1-0. There is an obvious flaw in this - advancing in the knockout stage is a zero-sum game. If you are very good at scoring then it's going to be tough for the other team to beat you 1-0 when they are at home. If keeping the other team from scoring an away goal is vital then a team that is very rarely held scoreless should have a similar advantage as one that is rarely scored on. Like a lot of cliches and common wisdom, this can be tested with data.

My work on this is preliminary. There is much more that I can and will do on this in the future, but I thought I'd share my findings thus far.

To test for this, I created a points system similar to the one used by FIFA for World Cup seeding. I awarded 32 points to the champion, 31 for the runner-up, 29.5 to the semifinal losers, 26.5 for those who busted out in the quarterfinals, 20.5 to the teams that were eliminated from the first knockout round, 12.5 to those finishing third and 4.5 for those finishing last in their group. I did not look at teams that were eliminated before the group stage. This scoring system may not be perfect, it's just meant to give a numerical representation of how well a team did in the Champions League for the season. Starting with the 2003-2004 Champions League, the first that featured 32 teams and 16 teams in the knockout round, I recorded Champions League points according to my system and points, goals for, goals against and goal differential per match for each team in their domestic league that season. I recorded this info for the 5 biggest leagues - English Premier League, Spanish Primera Division, Italian Serie A, German Bundesliga and French Ligue 1.

To test whether strong offense or defense is more important, I used the correlation coefficient as I did in the previous article on the role of luck in close matches. Here are the correlations:

Correlation coefficient between Champions League points (as defined above) and:
League points per match: 0.512
Goal difference per match: 0.567
Goals for per match: 0.390
Goals against per match: -0.501

All correlations are significantly different from zero and go in the expected direction. Teams that performed better in their league a given year, whether defined by league points or goal difference, tended to perform better in the Champions League than teams from these leagues that did worse domestically. Teams that scored more goals domestically tended to do better in the Champions League and those that conceded fewer also did better.

By using the results from a different competition, I'm essentially using domestic results as a proxy for skill. Teams that concede a lot of goals domestically will tend to be worse than those who allow fewer. It's not perfect, but it's a good way to represent offensive and defensive skill with a number.

Unfortunately, because the data set isn't large enough I can't say that correlation between Champions League results and goals against is larger than that for goals for. The 95% confidence intervals for correlations not only overlap, but actually contain the other value. Having said that, it appears to be larger. I would say based on these results that it is likely that defense is in fact more important than offense when it comes to getting results in the Champoins League, but further study is needed.

Correlation and Causation

A quick word about correlation. A common mistake people make in looking at data is believing that correlation implies causation. Two sets of numbers A and B can be correlated if A causes B, B causes A or some other thing causes both A and B. As an example, team goals scored and conceded tend to negatively correlated - teams that score a lot of goals tend to give up few. This is because overall difference in quality cause good teams to both score more goals and concede fewer goals than their weak opponents. It would be incorrect to say that they are negatively correlated, therefore playing open all-out attacking football would lead to conceded fewer goals than playing in a more balanced way. Similarly, packing 11 guys in the box isn't going to have you scoring 5 goals per match.

In this case though, I think correlation implies causation, if anything underestimating it. There is no reason to think that performing well in the Champions League would cause a team to become better or worse defensively. However, doing well in the Champions League could negatively affect league results since teams going deep will likely have to rest their best players in league matches more often.

Conclusion

This is a preliminary study that shows conclusively that both scoring and defending skill are important in the Champions League. There is nothing surprising there. They also indicate, though not conclusively, that defense is more important than offense. Similarly, goal difference appears to be a better indicator for how well a team will do in the Champions League than league points.

In the future, I will study this further. I will expand the points system to include previous editions of the Champions League. Also, in addition to looking at correlations I will run regressions that will take into account country effects, which I ignored here. Finally, at some point I hope to incorporate the Poisson model and use the scoring and conceding ranks it gives instead of just using league results.