In my last post on the two-leg format in soccer (MLS Cup Playoffs vs. UEFA Champions League), I determined that in a typical two-leg series, the club hosting the second leg has a 60% chance of winning (3:2 on in betting parlance).  I was wondering if that probability held up during each elimination round in either the preliminary or knockout phase.  My initial expectation was that the stronger teams in the preliminary round do not always host the second leg, so the probability of the second leg host advancing would drop closer to 50%.  In the knockout stage, the group winners host the second leg of the first knockout round and the group results are used to determine seeding in subsequent rounds, but the teams in the knockout phase are more even, so the probability might drop as the competition progressed to the final. 

I discussed in my last post on the subject how I tabulated the data, which were collected for the 2002-03 to 2008-09 European seasons; it was just a matter of summing the number of occurrences over seasons and computing the individual probabilities and then conditional probabilities. 

It's interesting to see how the performance of the first leg host changes as the Champions League progresses from the qualifying rounds to the post-group stage rounds.  Below are the cumulative statistics of home wins, draws, and away wins in the first leg of the series.

One thing that is worth noting is that the statistics for the qualifying rounds are roughly in line with the win-draw probabilities over the entire tournament.  That's not too surprising since there are almost twice as many qualifying ties as knockout round ties.  The other statistic to notice is the high percentage of draws in the knockout stage.  At this point in the competition, the teams are more evenly matched and the penalty for failing to win the home leg is steep, so it's likely that the competing sides play more of a safety-first style, which would be reflected by the high rate of drawn matches. 

Now, the total probability of a series win by either team, along with the probability of a tie decided by penalties:

While the series probabilities by either team match closely the probability over all the matches of the tournament, the percentages do drop in the 3rd qualifying round as the teams become more closely matched.  However, this is also the round in which the teams from the top European leagues enter the competition, so those sides that host the second leg have a distinct advantage.  In the first knockout stage, there's a sharp swing in the advantage toward the group winners, which host the second leg.  But in the quarterfinal and semifinal rounds the field is reduced to the teams with minimal differences in quality, which is reflected in the series win probabilities at or near 50%.

I guess the surprise for me was the close match between the series probabilities for the first two preliminary rounds and the overall tournament, but perhaps that should not be such a surprise given the large number of matches in those two rounds.

So for those of you outside the USA, now you know how to bet in the two-leg matches!