The Arsenal Society VI

Posted a very small part of this in the CL thread, but I think it warrants more discussion.

Going from 1984-1985 to last season in the Champions League, I determined the percentage of the time each team went through in a knockout stage based on the result of the first leg.

The first column is score, second is the percentage of the time that the team playing the first leg at home wins the tie, thrid column is the number of times that happened. BTW if any matches were forfeited, I excluded them. I also excluded any matches where either team scored more than 3 in the first leg. There weren't that many of these, and the overwhelming majority were matches where one team just killed the other team and the loser scored no goals. I also have included all observations where teams were seeded by performance in group stage and so the better teams were playing away in the first leg. This isn't all that many observations, but there is the problem that the away teams in the first leg will be better on average. For the statistically inclined, the standard errors are about 5%, so a lot of things are significantly different from .5.

score HW% n
0-0 33.33 78
1-0 55.56 81
2-0 89.83 59
3-0 88 50
0-1 10.71 56
0-2 3.13 32
0-3 0 14
1-1 38.46 65
1-2 11.11 27
1-3 0 13
2-1 53.7 54
2-2 12.5 24
2-3 0 11
3-1 78.79 33
3-2 35.29 17
3-3 11.11 9

Overall there were 623 matches and the team playing first at home won just over 43% of them (268 times the home team went through versus 355 for the visitors). I'm sure if we removed the seeding issue, it would still be about the same - maybe 44 or 45%.

It's a small sample for them, but the most surprising thing is that when the first leg was a nil-nil draw, the home team went on to win a third. When it was a 1-1 draw, the home team actually did better winning 38.46%. These aren't statistically different, but it's surprising because I expected the home team in the 0-0 case to do better due to having not conceded the away goal. My thinking here is that maybe the 0-0 draw at home will often come when the away team is much better than the home team. It's much more likely that the teams are about evenly matches when each team scores a goal. If you are not as good as your opponent it is easier to get a goalless draw than any other sort. 2-2 and 3-3 however, are much worse than either as the home team has only won three times out of 24 for 2-2 and one time out of 9 for 3-3.

Overall you have to keep in mind that while the scores in the first leg are somewhat random in that there is going to be variance in outcomes when two teams play each other, the same factors that affect the outcome are present in the second leg. Basically what I'm trying to say is that if team A wins the first leg, that indicates that they are likely better than B so it shouldn't be surprising if they win the tie. This is similar to the observation that when running back X gets over 100 yards, his team usually wins the game. In reality, him gaining that yardage is mainly due to the team winning than the other way around. To get the true advantage of just being in a situation we would need to have UEFA just randomly state the scores for the first leg and not actually play the games.

Similarly, if the home team has won the first leg 1-0 then they won over 55% of the time (45/81). It dropped less than 2 percent for a 2-1 win (29/54). A 3-2 win happened 17 times and the home team only won 6 of them. So historically a 1-0 win isn't much better than a 2-1 win, but both are much better than a 3-2 win. Again, I think it's a lot more a signal of team quality. A team that wins 3-2 likely has problems at the back. Given that teams tend to be less potent away, their attack isn't likely to make up for it when they play the second leg.

Since I didn't go up to 4 goals (there wouldn't be much of a sample here anyway), I only have 2 2 goal difference scores. Teams that win 2-0 went through just under 90% of the time (53/59), those that won 3-1 went through less often, just under 79% of the time (26/33). This makes sense given the away goal advantage. With this sample size they aren't quite significantly different, but I think they very likely are.

Home teams are in deep [censored] if they lose. For one goal losses, teams losing 0-1 went through just 6 times out of 56 (10.71%), teams losing 1-2 went through 3 times out of 27 (11.11%), teams losing 2-3 lost the tie all 11 times it happned. Teams losing by 2 were obviously in even worse shape. Only one team of 32 went through after losing 0-2 while none of the 13 teams that lost 1-3 went through. The 14 times a team lost 0-3 they didn't advance.

Ignoring the actual score (though excluding the few matches, most all of which were blowouts, where a team scored more than 3 goals), if the home team won the first leg they went through 69% of the time (203/294), if the first leg was a draw then the home team won 31.25% (55/176) of the ties, winning just 6.53% of the time that they lost the first leg (10/153).

Jared