Equilibrium in the Champions League

The UEFA Champions League draw took place on Thursday. This wasn't for the knock-out stages, touched on in a previous Massive Blog post, but for the groups.

To create some kind of balance across the 8 groups, UEFA rank all the teams according to their club coefficient system. Much has been written about the system, such as this, with Chris Bevan saying things like “it is likely to preserve the status quo” and it “is stacked in the favour of teams from stronger nations”.

Whatever you think about the system, it rewards teams over a 5 year period for winning and drawing games in Europe and for progressing to later rounds of European competitions. You might think it should weight more recent results more heavily or reward wins against stronger teams more highly, both of which FIFA’s world country ranking does. However, FIFA’s system is often criticised as well, so it would seem that international football governing bodies just can’t win.

Anyway, I’m here to talk about the balance of the groups. At the moment, they rank the 32 teams and then split them into 4 pots: the best 8, 9^th-16^th best, 17^th to 24^th best and the worst 8. Then, to make the groups balanced, each group contains one team from each pot.

Looking for more balance

This only provides a very sketchy level of balance, however, as 8 teams are lumped together in one pot, meaning that Barca, ranked first, are treated just the same as Benfica, ranked eighth, and so on.

If we go into more detail on the ranking, and, instead of just splitting the teams into 4 pots, give each team points according to its ranking, from 1 for Barca down to 32 for Real Sociedad, then we can use these rankings as a basis for finding more balance.

All 32 teams together have (32+1)*16 = 528 points between them. For balance then, each group should have 528/8 = 66 points. And we can still maintain the pots, so that each group also has someone from each of the 4 pots.

To make these groups, the most obvious way would be to put the best teams from pot 1 and 2 with the worst from pot 3 and 4, giving you teams 1,9,24 and 32. You could then work down pots 1 and 2 and up pots 3 and 4, so the next group would have teams 2,10,23,31 and so on. This would give you 8 groups of 66 total points.

However, this very simple method falls at the first hurdle because the first group would be Barca, Atletico Madrid, Leverkusen and Real Sociedad, three of which are Spanish, which isn’t allowed. 

Excel time

I threw a spreadsheet together and did some trial and error and you can get balanced groups which also respect the rule of having maximum one team from each national federation in each group. One way it works is (ranking from 1 to 32 given next to each team):

Group A		Group B
Man U	5	Real	4
Marseilles	13	Schalke	12
Galatasaray	23	Olympiakos	22
Copenhagen	25	Celtic	28
Group C		Group D
Benfica	8	Bayern	2
PSG	15	CSKA	14
Zenit	17	Man City	18
Napoli	26	Sociedad	32
Group E		Group F
Chelsea	3	Arsenal	6
Juventus	16	Atletico	9
Dortmund	20	Basel	21
Anderlecht	27	Plzen	30
Group G		Group H
Porto	7	Barcelona	1
Milan	11	Donetsk	10
Ajax	19	Leverkusen	24
Bucharest	29	Vienna	31

 

In all likelihood, this isn’t the only way the groups could be compiled in a fully balanced way, but it is one way which serves as an example and as proof that it can be done. If you wanted, you could almost certainly let a computer randomly compile balanced groups from all the possible permutations.

Now, given balanced groups, the average strength of your opponents (as defined by the ranking points) is always (66 – n)/3, where n is your ranking. For example, Chelsea’s opponents have an average strength (66-3)/3 = 21, whereas Arsenal’s have an average (66-6)/3 = 20.

This is slightly obvious, but it serves to demonstrate that Arsenal would, if all were balanced, have slightly higher-ranked opponents than Chelsea. And they shouldn’t complain about it because it’s their fault for being worse-ranked than Chelsea.

A look at the actual groups

Now that we’ve established that balanced groups are possible and what they could (in one example) look like, let’s take a look at the actual groups:

Group A		Group B
Man U	5	Real	4
Donetsk	10	Juventus	16
Leverkusen	24	Galatasaray	23
Sociedad	32	Copenhagen	25
Total	71	Total	68
Group C		Group D
Benfica	8	Bayern	2
PSG	15	CSKA	14
Olympiakos	22	Man City	18
Anderlecht	27	Plzen	30
Total	72	Total	64
Group E		Group F
Chelsea	3	Arsenal	6
Schalke	12	Marseilles	13
Basel	21	Dortmund	20
Bucharest	29	Napoli	26
Total	65	Total	65
Group G		Group H
Porto	7	Barcelona	1
Atletico	9	Milan	11
Zenit	17	Ajax	19
Vienna	31	Celtic	28
Total	64	Total	59

 

As better-ranked teams have a lower number ranking, the lower the total, the stronger the group. Going by this, the strongest group turns out as Group H, with a total of 59, and the weakest as Group C, with a total of 72. 

Interestingly, in spite of articles like this one, saying things like “Arsenal have a tricky start” or Phil McNulty saying things like “Arsenal were given the toughest test” and “Jose Mourinho may have silently celebrated how the overblown ceremony treated Chelsea”, the table shows that both groups are equally strong.

This means that Arsenal’s opponents (total ranking 59) are slightly stronger than Chelsea’s (62), but this serves to maintain the balance, as Arsenal are worse ranked. Man City’s opponents are obviously significantly stronger (44), as Man City themselves are only in the 3^rd pot.

Getting lucky

Clearly, if all groups were balanced then no team would be luckier than any other team. To measure the luck of a team, I therefore propose comparing the strength of their group opponents with the strength of their opponents in a balanced group. 

We already have the formula for a team’s opponents’ average strength in a balanced group: (66 – n)/3

For the average strength of a team’s opponents in an actual group, we just replace the 66 with g, the group total: (g-n)/3.

The difference between these two totals then gives us the luck (l) of the team.

l = ((g-n)/3) – ((66-n)/3)

This can be simplified a bit down to:

3l = g-n – (66-n)

3l = g – n – 66 + n

3l = g – 66

l = (g-66)/3

Doing it this way round also means that a team playing lower-ranked opponents will have positive luck, which is nice and intuitive.

Interestingly, perhaps, this shows us that a team’s own rank (n) has no impact on its luck, as there is no (n) in the formula. This means that all teams in any group are all as lucky as each other, which is nice.

Luck of the English

So how does it look for the English teams?

Chelsea and Arsenal both have:

(65-66)/3 = -1/3 = -0.33

Man Utd have:

(71-66)/3 = 5/3 = +1.67

and Man City have:

(64-66)/3 = -2/3 = -0.67

This suggests that Man Utd are the only English side which have really been lucky, Man City have had the worst luck and Chelsea and Arsenal have both been equally (and only slightly) unlucky. 

This would appear to contradict McNulty’s suggestions that “United and Moyes have not been handed an easy group” and that Arsenal have gotten "on the wrong end of the Champions League draw”.

Luck of the Scottish

If we look at Celtic, they have a luck score of:

(59-66)/3 = -7/3 or -2.33

Add that to the fact that they’re the worst team in their group, and you can’t really argue with their manager Neil Lennon’s statement that: “in terms of football it doesn't come any harder”. The worst luck theoretically possible for Celtic would be -3.33 but -2.33 is certainly the unluckiest of all groups in the actual draw.

Given what I said earlier about all group members having the same luck, Celtic’s opponents in Group H, Barca, Milan and Ajax, have also had just as rotten luck as the Scottish champions. This may be of some consolation to them.

To sum up, whether or not you like the way the clubs are seeded, whether or not you agree with the system of club coefficient calculation and whether or not you’d like to see more balance in the draw, I think we can say with some certainty that Lennon probably pays more attention than McNulty to maths.

Coming soon: Tune in to the next blog post for a look at the balance of the groups using the club coefficient points as a basis, not just a simple 1 to 32 ranking.