“I think that usually with 10 points all the teams go through always, 99 percent” – The Champions League Group Stage

Manchester City failed to qualify from their group in the Champions League despite getting ten points, prompting their manager, Mancini, to say what is quoted in the title of this post.

A group in the Champions League has 4 teams in it. Each team player each other twice. There are three points for a win, one for a draw, none for a loss. Since 1999-2000, the top 2 teams (ordered by points, then in the case of ties head-to-head goal difference, and then general goal difference) in each group quality to the next round.

Is it true that ten points has guaranteed qualification 99% of the time? Well, it’s not too far out at 2.5%. On 158 occasions has a team achieved 10 or more points, since the 1999-2000 season (but excluding this season). Only four of those teams failed to qualify, and each of those got exactly 10 points.

These were:

• Werder Bremen in 2003-4 (Barcelona got second play with 11 points)
•  Olympiacos and Dynamo Kyiv in 2005-6 (Liverpool and Real Madrid went through in second place with 10 and 11 points respectively)
• PSV Eindhoven in 2006-7 (Deportivo had 10 points but went through instead of them).

Whilst in practice no team has ever failed to go through with 11 points, it is in fact possible to still miss out with 12 points. Imagine three teams A, B and C who win all their home games against each other (and so lose all their away games against each other), but all beat D both home and away. Then you get the following table, where C misses out on qualification:

13 points does ensure you qualification. As suppose you fail to qualify with 13 points. Then another two teams must get at least 13 points, and so there are at least 39 points on the board. But it is only possible to get 36 points on the board, as there are 12 games and each game can add up to three points on the board.

In reality, no team has qualified with less than 7 points. However, teams have qualified with exactly 7 points. Werder Bremen in 2005-6 and Lokomotiv Moscow in 2002-3 both came runners up to a high-scoring Barcelona. In theory, it is possible to get four points and still qualify. Imagine team A wins every game and teams B, C and D draw against each other. Then you get the following table: