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 lowerranked 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 132 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
worstranked 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 adjacentlyranked 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 132 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 = (g66)/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 = (h306.815)/3
However, as we want good luck to be positive, we need to
switch this around to take into account the fact that a highnumbered
coefficient, unlike a highnumbered ranking, is given to a strong team. So we
can make it:
k = (306.815h)/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 topranked 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.
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