Equilibrium in the Champions League II

This post is the sequel to the previous post, hence the II in the title. So you should probably read that first, if you haven’t already done so

Anyway, the previous post ranked the Champions League qualifiers from 1 to 32 according to their UEFA club coefficients and used these rankings as a basis for analysing the balance of the groups and measuring each team’s luck in the draw.

There are two other obvious ways of measuring the strength of the teams:

- Using the UEFA club rankings;

- Using the club coefficient points.

Using the UEFA club rankings

The UEFA club rankings seem like a good idea, because they keep the numbers as nice manageable integers and they add some detail as the gaps between teams aren’t all the same, thereby taking into account that some teams are significantly lower-ranked than others. For example, the top 6 ranked teams in the Champions League are also ranked 1 to 6 overall, but Austria Wien, 31^st in the Champions League, are ranked 114 overall. 

The problem with using this ranking system is that Real Sociedad, the team ranked 32^nd and worst of all the Champions League qualifiers, don’t have a UEFA ranking at all, because they haven’t been in Europe in the last five years. As there are 450 teams with a UEFA ranking, this would make Sociedad joint 451^st. 

Unfortunately, this massive leap to the 32^nd team (all other 31 teams are in the top 114) skews the entire system. In the same way as, with a 1-32 ranking system, we had a total 528 points and 66 per balanced group, this system gives us 1,328 and 166 per balanced group. 

However, the group with Sociedad will automatically be far worse than average and most groups will be far better, with the only way to get a balanced group being to have Vienna (114) and three other teams with a total 52 between them, such as Bayern (2), PSG (19) and Dortmund (31). Even the third worst-ranked team, Plzen (74) cannot be put in a balanced group, with the most balanced scenario having a total 145, with Benfica (9), Juventus (20) and Leverkusen (42) completing Plzen’s group.

This is clearly unsatisfactory and, as such, I reject the use of the UEFA club rankings as a workable system for looking to achieve balance. They may be useful next year, if there is not such an anomaly, but, for 2013/14, they must be set aside.

What about using the club coefficient points?

Using the club coefficient points avoids the problem with Sociedad. Although they have zero points, this is only 16.575 fewer than Vienna, which does not represent such a dramatic and exaggerated drop as 114^th to 451^st in the ranking. In fact, this is not even the largest difference between two adjacently-ranked sides, as Arsenal have  17 fewer than Man U.

So this system seems to be workable. And it takes into account larger and smaller gaps between teams than the more simple ranking system. So it could be worth a look. 

Balance using the coefficients

Following an equivalent methodology to the one for the rankings, we have a total 2454.519 points, so balanced groups would each have 2454.519/8 = 306.815 points. 

It is unlikely that we will be able to get 8 groups with this exact score but we could consider them fairly balanced if we had no group with more than 306.815+(306.815/32) and none with less than 306.815-(306.815/32). 306.815/32 is 9.588 so this means groups between 297.227 and 316.403.

The choice of 32 is fairly arbitrary, basically being used because there are 32 teams. If anyone has a better suggestion for something more suitable, they are welcome to comment.

Anyway, let’s start out by looking at the 8 groups which were balanced with the ranking system. These have scores of:

Group	Total coefficient	Difference to balanced group
A	310.932	+4.117
B	316.865	+10.050
C	292.228	-14.587
D	295.280	-11.535
E	315.223	+8.408
F	301.727	-5.088
G	299.211	-7.604
H	323.053	+16.238

Based on what I’ve said above, this would make suggest that groups A, E, F and G are fairly balanced, whilst B, C, D and H are either too strong (B and H) or too weak (C and D).

By making two simple swaps:

• CSKA (D, 77.776) with Donetsk (H, 94.951
• PSG (C, 71.800) with Schalke (B, 84.922)

we redress this imbalance and come out with 8 balanced groups.

Of course, making these two changes brings about imbalance according to the 1-32 ranking system. However, if we fiddle about with the spreadsheet for long enough, then we can come up with the following groups:

Group A			Group B
Man U	130.592	5	Real	136.605	4
Schalke	84.922	12	Juventus	70.829	16
Basel	59.785	21	Zenit	70.766	17
Celtic	37.538	28	Bucharest	35.604	29
Totals	312.837	66	Totals	313.804	66
Group C			Group D
Benfica	102.833	8	Bayern	146.922	2
CSKA	77.766	14	Donetsk	94.951	10
Man City	70.592	18	Olympiakos	57.800	22
Napoli	46.829	26	Sociedad	0.000	32
Totals	298.020	66	Totals	299.673	66
Group E			Group F
Chelsea	137.592	3	Arsenal	113.592	6
Marseilles	78.800	13	Atletico	99.605	9
Dortmund	61.922	20	Leverkusen	53.922	24
Plzen	28.745	30	Anderlecht	44.880	27
Totals	307.059	66	Totals	311.999	66
Group G			Group  H
Porto	104.833	7	Barcelona	157.605	1
Milan	93.829	11	PSG	71.800	15
Galatasaray	54.400	23	Ajax	64.945	19
Copenhagen	47.140	25	Vienna	16.575	31
Totals	300.202	66	Totals	310.925	66

Now it took quite a long time for me to get such a distribution which suggests that there aren’t all that many possible draws which offer balance according to both ways of measuring. This is not, however, by any means to say that this is the only way.

Whilst it is nice to see that it is possible, given the fact that 1/32^nd deviation from the average was chosen rather unjustifiably, I could have chosen something less stringent and achieved balance with that more easily, if I’d wanted to.

And what about lady luck?

As we saw in the previous post, you can measure the luck of a team by comparing its actual draw, that is the strength of its actual opponents, with the strength its opponents would have in balanced groups. In the previous post, the luck (l) was calculated as:

l = (g-66)/3

where (g) was the total ranks of the group and 66 the rank of an average group.

The equivalent formula with the club coefficients, if we say k is now luck and the group total is h, would then be:

k = (h-306.815)/3

However, as we want good luck to be positive, we need to switch this around to take into account the fact that a high-numbered coefficient, unlike a high-numbered ranking, is given to a strong team. So we can make it:

k = (306.815-h)/3.

Luck (k) of the English

We saw in the previous post that, contrary to the claims of the BBC and, in particular, Phil McNulty, Arsenal and Chelsea were equally (and only slightly) unlucky, Man City had the worst luck and Man Utd were the only English side to get lucky.

If we measure luck (k) of the English teams, as formulated above, we get:

Man City with -5.74

Arsenal with +1.89

Chelsea with -3.70

Man Utd with +9.11

Clearly, whilst Man City and Man Utd retain their positions from the previous post as most unlucky and luckiest respectively, we see a significant change with Arsenal and Chelsea. 

Chelsea stay unlucky but Arsenal emerge as being a little bit on the lucky side of balanced. This is perhaps not a surprise as Arsenal’s, though ranked 6, are a long way behind the 5 top-ranked teams in terms of coefficient points. So measuring by coefficient points, they deserve, as it were, to get somewhat stronger opponents. 

Luck (k) of the Celtic

In the last post, Celtic were very unlucky. When measuring according to coefficient points, this doesn’t change much, as they come out with a luck (k) score of -15.70, making them 2.73 times more unlucky even than Man City, the unluckiest of the English sides. And, as with luck (l), Celtic (and the other teams in group H) have the most rotten luck (k) of all teams in the competition.

Arsenal, however, prove to be much more fortunate than a lot of pundits would have us believe.