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Author: bert.kassies
Date: 25-06-2004, 14:50

The list of UC qualifiers displays the first results of the new team ranking calculation (with the 33% rule) published by UEFA. There are some rounding differences with the rankings at this website.

Does anybody have any idea what kind of rounding UEFA applies? E.g.
ARM 0.93423 is rounded up to 0.935,
SWE 5.51628 is rounded down to 5.516,
UKR 7.30125 is rounded down (?) to 7.300.

Usually I could figure their calculation method by reverse engineering. But now I'm lost. Please help.

Author: LBlanco
Date: 25-06-2004, 15:10

A possible idea (not necessarily the right one):

They calculate each year coefficient on its own, and then round up to three decimal figures.
Then they add the five year coefficients with three decimal figures.

Looking at your tables, that procedure would explain Armenia's coefficient, but would give for Ukraine 7.299, so I believe I am not right at all, but this can may be a hint for our detectives.

Author: Jos_Van
Date: 25-06-2004, 21:10

I think they take the total cumulative coefficient of the last five years and they calculate the 33%, then the coefficients are rounded down from four tenths of thousandth of a point downwards
and rounded up from five tenths of thousandth of a point upward (e.g. 13.6554 = 13.655
or 21.8449 = 21.845).
It seems valid for armenia (2,831*0.33=0.93423) and sweden (16,716*0.33=5.51628) and not for Ukraine (22,125*0.33=7.30125) , but it is possible that uefa commit an error (is not the first time!!!).
Howewer,in my ranking list the coefficient of ukrainian teams is .,301 too.

UEFA europeancups

Author: viulo
Date: 26-06-2004, 01:08

I've gone round and round and round and can't seem to get 7,300 for Ukraine.

Armenia ok. If you calculate 33 per cent for each year, you get 0,110 + 0,220 + 0,000 + 0,385 + 0,220, which adds up to 0,935, different from calculating 2,831 * 0,33, which equals 0,93423, that wouldn't round up to 0.935.

With Sweden, you get 5,51628, that is rounded up, because if you do the calculations for each year you'll get 5,516 anyway (1,430 + 1,584 + 1,265 + 0,742 + 0,495).

But doing the same with Ukraine, you get 1,774 (1,77375), 1,320, 1,196 (1,19625), 1,402 (1,4025) and 1,609 (1,60875). Go figure...

Author: bert.kassies
Date: 28-06-2004, 11:41

Hmm, still no satisfactory explanation. I'm quite sure that UEFA takes the country ranking of 2004 to calculate the contribution to the team ranking. And not the yearly country coefficients. But even if they did it cannot explain the differences. E.g. for the country with the largest difference, Switzerland, it amounts to exactly the same difference.

I cannot believe the difference is random. E.g. countries with 4 teams tend to have a negative difference which is a multiple of 0.25. And countries with 3 teams tend to have a positive difference which is a multiple of 0.33 (or 0.11).

What mechanism can be the source of these differences? See below for a complete list with differences:


country             rank2004     33%        uefa  diff*1000
------------------  --------  ---------  -------  ---------
Switzerland           22.375    7.38375    7.382      -1.75
Poland                21.750    7.1775     7.176      -1.50
Scotland              32.125   10.60125   10.600      -1.25
Ukraine               22.125    7.30125    7.300      -1.25
Austria               21.125    6.97125    6.970      -1.25
Norway                21.900    7.227      7.226      -1.00
Portugal              42.333   13.96989   13.969      -0.89
Spain                 79.851   26.35083   26.350      -0.83
Czech Republic        33.075   10.91475   10.914      -0.75
Croatia               17.375    5.73375    5.733      -0.75
Belgium               28.875    9.52875    9.528      -0.75
France                48.326   15.94758   15.947      -0.58
Denmark               17.450    5.7585     5.758      -0.50
Finland                5.874    1.93842    1.938      -0.42
Italy                 59.186   19.53138   19.531      -0.38
Germany               49.489   16.33137   16.331      -0.37
Sweden                16.716    5.51628    5.516      -0.28
Russia                19.916    6.57228    6.572      -0.28
Israel                21.249    7.01217    7.012      -0.17
Belarus                3.582    1.18206    1.182      -0.06
Turkey                32.291   10.65603   10.656      -0.03
Liechtenstein          2.000    0.66       0.660       0.00
Greece                34.748   11.46684   11.467       0.16
Netherlands           34.081   11.24673   11.247       0.27
Hungary               15.290    5.0457     5.046       0.30
Romania               14.790    4.8807     4.881       0.30
Bosnia-Herzegovina     5.499    1.81467    1.815       0.33
Georgia                4.999    1.64967    1.650       0.33
Moldova                6.832    2.25456    2.255       0.44
Iceland                3.332    1.09956    1.100       0.44
Wales                  2.332    0.76956    0.770       0.44
Faroe Islands          0.832    0.27456    0.275       0.44
Slovakia              12.832    4.23456    4.235       0.44
England               62.153   20.51049   20.511       0.51
Lithuania              4.165    1.37445    1.375       0.55
Azerbaijan             1.165    0.38445    0.385       0.55
Slovenia               9.165    3.02445    3.025       0.55
Northern Ireland       1.665    0.54945    0.550       0.55
Estonia                1.665    0.54945    0.550       0.55
Serbia-Montenegro     20.165    6.65445    6.655       0.55
Bulgaria              19.998    6.59934    6.600       0.66
Latvia                 5.998    1.97934    1.980       0.66
Luxembourg             1.498    0.49434    0.495       0.66
Cyprus                 8.998    2.96934    2.970       0.66
Albania                1.831    0.60423    0.605       0.77
Armenia                2.831    0.93423    0.935       0.77
Malta                  3.331    1.09923    1.100       0.77
Ireland                3.164    1.04412    1.045       0.88
Macedonia              4.830    1.5939     1.595       1.10

Author: Ricardo
Date: 28-06-2004, 13:20

If you turn things around: what is the Country ranking when 33% is the Uefa number, it showns for Bosnia 5.500 and for Georgia 5.000 in stead of 4.499 and 4.999.
Can it be that all year coefficients are re-calculated because of this? That there is no roudning for ht 5 year total anymore?
I have not checked other countries, but these two were striking.
Anyone?
All other countries below these two(except England) also have nice figures, all ending on .333333, .833333, .166667, .666667, .000000 and .500000

Author: Ricardo
Date: 28-06-2004, 13:33

Looking at the other countries:What I dd is the following:
I took the list of Uefa (out of this thread) and devided this number by .33. SO i got the expected Uefa Country Ranking. Then you get a lot of numbers behind the decimal.
The bottomhalf are, like I said before ending on 3333 or 666667(actualy not rounded!)
the others are also strainge, but groupable: When you multiply them by 11, you get a nice figure again! At least 1 decimal+ 0000 or 3333 or 666667.

I don't know yet why they do it, and what this 11 stands for, but I think it is part of the solution of this riddle.
Good luck!

Author: duncshine
Date: 28-06-2004, 14:53

Consider Ukraine.

Because they have had four teams in Europe in each of the last five seasons, their figures are

Year     Teams      Pts       Average
2003/4   4          19.5      4?ı (exactly 4.625)
2002/3   4          17        4?ù (exactly 4.250)
2001/2   4          14.5      3?ı (exactly 3.625)
2000/1   4          16        4  (exactly 4)
1999/0   4          21.5      5?ü (exactly 5.375)

Now, none of these fractions need to be rounded to three decimals, as they form exact thousandths anyway.

So, the total of these numbers must be exactly 22?û, or 22.125.

So, there can be no rounding before we multiply by 0.33. That calculation MUST give us 7.30125, which could be rounded down to 7.301, or maybe even up to 7.302.

But it definitely cannot go to 7.300.

Or, you can look at it another way. If you divide 7.300 by .33 to get the total for five years, you must get a figure between 22.119696969... and 22.122727272727....

However, since all five years contained 4 teams only, the Ukraine total must end with

.000, .125, .25, .375, .5, .625, .75, or .875

(ie, all the eighths)

It is therefore impossible for a coefficient of 7.300 to be achieved by Ukraine, no matter how you slice the maths.

My conclusion is that UEFA have got the maths wrong, or they have added a hidden variable. I suspect the former...

Cheers

Duncan

Re: UEFA roundings
Author: duncshine Date: 28-06-2004, 14:54	Sorry, the system couldn't cope with eighths The table for Ukraine should look like Year Teams Pts Average 2003/4 4 19.5 4 5/8 (exactly 4.625) 2002/3 4 17 4 1/4 (exactly 4.250) 2001/2 4 14.5 3 5/8 (exactly 3.625) 2000/1 4 16 4 (exactly 4) 1999/0 4 21.5 5 3/8 (exactly 5.375) The point is still the same... Cheers D

Author: anita
Date: 28-06-2004, 15:23

Have to agree with Dunc and others. Tried for too long time tonite finding a system. And there is, like Bert mentions. (0,11, 0,25, 3 teams, 4 teams). But it make no sense.

And funny enough, Dunc, I tried with Illichivets and Ukraine as well (because of four teams every year). No chance in hell you can get 7.300. So UEFA must be out cycling here, but where and how do they use the wrong parameters? Because even if UEFA is wrong, they have used an equation that I'd like to detect.

By the way, very nice site, Jos. It's placed on Favorites.

Author: Ricardo
Date: 28-06-2004, 15:39

You prabably mean 4 7/8 on the first line (19.5/4).
I also don't get it.
Even if I round it down after each year (year total/4 *0.33) I get a total of 7.299 and not 7.300.
For Poland this is OK, for Switzerland and Ukraine I get .001 to low. This is getting frustrating.
Looking at the .333 it looks like calculation is done without rounding or with rounding at the end.

P.S. where were these Uefa numbers published?

Re: UEFA roundings
Author: bert.kassies Date: 28-06-2004, 15:44	here

Author: VadimUK
Date: 29-06-2004, 09:15

One way for Ukraine to get 7.300 would be out of assumption that different rounding rules where applied for different years. For example, if all seasons except the last are rounded down to 3 digits (ROUNDDOWN() in Excel), and the last one is rounded to 3 digits as mathematicians do (ROUND() in Excel), it gives the desired 7.300 (1.774+1.320+1.196+1.402+1.608).

Macedonia is the only other country I tried as well. It worked actually, but more checks are required of course.

Author: Ricardo
Date: 29-06-2004, 10:38

How did you get Macedonia working?
I dont get it. Only when all 5 years are rounded up I get the required 1.595:
0.21978, 0.21978, 0.21978, 0.38478, 0.54978
becomes 0.22, 0.22, 0.22, 0.385, 0.55 together 1.595.

No I can not explaint it. Except for NOT using the rounded yearly country coefficient, but an unrounded, coefficient.

To make a split between the last year and the 4 years before might be necessary!
just having 2 numbers
1 for 4 years(UKR:17.25)
1 for last year(UKR:4.875)
multiply by 0.33
rounddown
add up: you get 7.300

For Macedonia to get this working you will have to use the NOT rounded year coefficients.

Author: VadimUK
Date: 29-06-2004, 11:33

Hey Ricardo:
Below are my cal's:

Ukraine (4 teams each year)
2000 2001 2002 2003 2004 (year)
21.5 16 14.5 17 19.5 (points)
1.77375 1.32 1.19625 1.4025 1.60875 (points/#teams*0.33)
1.774 1.320 1.196 1.402 1.608 (rounding) ===> 7.300

Macedonia (3 teams each season)
2000 2001 2002 2003 2004 (year)
2 2 2 3.5 5 (points)
0.22 0.22 0.22 0.385 0.55 (points/#teams*0.33)
0.220 0.220 0.220 0.385 0.550 (rounding) ===> 1.595

And here is another way to get 7.300 for Ukraine. Take the country coefficients calculated by 50% rule and rounded up to 3 digits (that is what UEFA kept up to the coming season). Multiply them by 0.66 (that'll give the new 33% rule). Round down and sum up. Or, instead of rounding down it's enough to round 0.0005 to 0. Both ways work for Macedonia as well.

Actually, my only claim that there are many ways to get 7.300. It's far from been impossible.

Author: seol
Date: 29-06-2004, 19:28

I've checked something for two countries (Ukraine and Luxemburg), and it works. Unfortunately, I don't have the time to check this for every country. Maybe someone of you could do it? This is it:

1.sum of points per country
2.divide by number of teams
3.round down (=ignore fourth decimal and further)
4.take 50% of that
5.round down
6.multiply by 0.66 (=>33%)
7.normal rounding on third decimal

This gives for:
UKR: 7.300
LUX: 0.495

But still the question remains: why is UEFA not calculating in a normal way? As the overview here a bit higher shows, there are some deviations, and you never know that this could cost you a CL place...

Re: UEFA roundings
Author: macaskil Date: 29-06-2004, 23:11	I suspect they had a spreadsheet calculated on 50% and just created another column based on 66% of those coefficients!

Re: UEFA roundings
Author: jpcccc Date: 30-06-2004, 01:35	But if they multiply by 66% then the 33% rule becames the 34% rule ! Is that it ? By the way, what is the exact phrasing of this rule: 33% or a third or something else ? Can anybody paste that piece of text in this topic ?

Re: UEFA roundings
Author: Ricardo Date: 30-06-2004, 09:53	Do you mean by step 1 and 2 to 'recalculate the coefficients' again? It is one of the only ways to explain the positive difference with Macedonia and the other 3-countries??

Re: UEFA roundings
Author: VadimUK Date: 02-07-2004, 03:01	viulo: I checked the method you proposed for all european countries. It worked for many, but not for Austria, Belgium, Croatia, Czech Republic, Denmark, England, Greece, Portugal, Spain, Turkey.

Author: viulo
Date: 02-07-2004, 18:20

Some of you were right on the money.

UEFA had calculations with the 50 per cent rule for the previous four years. So, instead of calculating each year * 0,33, they calculated each year / 2 * 0,66.

The exception is last year, which hadn't been calculated in advance, so they used the normal proceeding (total * 0,33).

I'm pretty sure this was how it was done. I haven't had time to calculate everything, but I tested it with the following examples:

Ukraine
5,375 * 0,50 = 2,687 * 0,66 = 1,773
4 * 0,50 = 2 * 0,66 = 1,320
3,625 * 0,50 = 1,812 * 0,66 = 1,196
4,250 * 0,50 = 2,125 * 0,66 = 1,402
4,875 * 0,33 = 1,609 (this is where you can see last year was done different, because 4,875 * 0,50 = 2,437 * 0,66 = 1,60842, which would be rounded down to 1,608, thus making impossible the total of 7,300)

Armenia
0,333 * 0,50 = 0,166 * 0,66 = 0,110
0,666 * 0,50 = 0,333 * 0,66 = 0,220
0
1,166 * 0,50 = 0,583 * 0,66 = 0,385
0,666 * 0,33 = 0,220
Total: 0,935

Switzerland
4,125 * 0,50 = 2,062 * 0,66 = 1,361
4,375 * 0,50 = 2,187 * 0,66 = 1,443
6,125 * 0,50 = 3,062 * 0,66 = 2,021
5,875 * 0,50 = 2,937 * 0,66 = 1,938
1,875 * 0,33 = 0,619
Total: 7,382

Poland
3,250 * 0,50 = 1,625 * 0,66 = 1,072
3,625 * 0,50 = 1,812 * 0,66 = 1,196
4,125 * 0,50 = 2,062 * 0,66 = 1,361
6,625 * 0,50 = 3,312 * 0,66 = 2,186
4,125 * 0,33 = 1,361
Total: 7,176

Macedonia
0,666 * 0,50 = 0,333 * 0,66 = 0,220
0,666 * 0,50 = 0,333 * 0,66 = 0,220
0,666 * 0,50 = 0,333 * 0,66 = 0,220
1,166 * 0,50 = 0,583 * 0,66 = 0,385
1,666 * 0,33 = 0,550
Total: 1,595

Ireland
0,333 * 0,50 = 0,166 * 0,66 = 0,110
1,666 * 0,50 = 0,833 * 0,66 = 0,550
0,666 * 0,50 = 0,333 * 0,66 = 0,220
0,166 * 0,50 = 0,083 * 0,66 = 0,055
1,666 * 0,33 = 0,550
Total: 1,045

The rounding, up or down, is done by the usual UEFA way. So, is the system fair? Of course not. They were just too lazy or too stupid... But in four years time you will have the normal numbers - each year * 0,33

It clearly seems to work. One day I'll calculate all of them, because there are few coefficientes whose result is different if you multiply by 0,33 or if you multiply by 0,50 and then by 0,66.

Hope it helped. It has been bugging me for ages...

Re: UEFA roundings
Author: duncshine Date: 03-07-2004, 10:41	Viulo, and all other contributors to this thread... Genius! Absolute genius! I've been through the spreadsheet, and it seems to work in every case. Bert, this perfectly illustrates your point made on another thread about information found here but nowhere else. Funny how a bit of European cooperation can make sense even of UEFA's impenetrable 'logic'. Cheers Dunc

Re: UEFA roundings
Author: anita Date: 03-07-2004, 14:49	Indeed Dunc. Thx to all of you. I don't think I would have got the time, energy, phantasy or brains to solve this mystery. But changing parameters in my team/nation ranking, I will continue double book-keeping for a while in case UEFA change their mind. Presume that thought have struck you all. regards

Author: anita
Date: 03-07-2004, 17:12

Viulo (and others).

I need some tutoring (or rounding up...). So you mean that previous four years UEFA round down to three decimals, but last season they round up? This is not according to their own rules. Ukraine give last five years (with Viulos method):

1,77375 (not rounded up)
1,320
1,19625
1,4025 (not rounded up)
1,60875 (rounded up to 1,609)

OK, you get 7,300, but seems totally inconsistent. Or is it me missing out something?

Author: bert.kassies
Date: 03-07-2004, 17:34

anita, I noticed the same kind of problem. If you always round down (UEFA method), and do that more then once (every year or even twice a year), then the ranking can only diminish. In that way you never get the correct ranking for Macedonia.

I observed some fairly good results by using the UEFA method (round down) for calculation of the 50% in the first 4 years, but using usual rounding (Excel ROUND(..;3)) for the 66% and 33%. That gives correct results for the two max/min countries Switzerland and Macedonia. But not for all other countries.

Well, I still don't know. It should be some combination of rounding up and down. But which?

Re: UEFA roundings
Author: anita Date: 03-07-2004, 17:41	I still think UEFA has messed it up and has to recalculate. According to Annexe II, Coefficient Ranking Calculation System, point 8., coefficients are always rounded down to the thousandth. And these are this years UEFA rules. But all credit to contributors on problem. And to jpcccc, its 33%, not 33 or something.

Re: UEFA roundings
Author: anita Date: 03-07-2004, 17:49	Yes, bert, I use Excel myself and get curious results up and down. And I think we all can agree that slandering and bantering other and others on this forum is not wanted or polite or suitable, with one major exception: UEFA

Author: viulo
Date: 03-07-2004, 19:27

Anita and Bert, according to my calculations the rounding is done the usual way. First thing you have to take in account is that the coefficient is obtained by the sum of 33 per cent for all five years.

It's hard to make myself perfectly clear using a language that isn't mine, but I'll try.

Take Ukraine's example and Bert's Team Ranking for 2004 (the one in question):

for each year you have the 33 per cent for each coefficient: 1.773 - 1.320 - 1.196 - 1.402 - 1.608

The sum of all five is 7,299, but in the total you have 7,301, because you assumed that UEFA would calculate 33 per cent for the total.

They don't, they sum each year's 33 per cent individually. Now I don't know how you got 1,608 for the last year, because 4,875 times 0,33 results in 1,60875, which, using UEFA's rouding system, would be rounded up to 1,609.

The problem is that, if you do that to every year, you would get 1,77375 for 99/00, which would be rounded up to 1,774. Curiously enough, on Bert's page we have 1,773.

I figure that Bert's page works the same way as UEFA's for the first four years: you had a previous result with 50 per cent, so instead of calculating the total times 0,33, you calculated the previous result times 0,66.

Hence the difference: for 99/00, you have a total for the country of 5,375.

Multiplying by 0,33 you get 1,77375, which is rounded up to 1,774.

Multiplying by 0,50 you get 2,6875. The question here is that they round (up or down) twice. So this result is rounded down to 2,687. Then you multiply 2,687 by 0,66. And you get 1,77342 which is rounded down to 1,773.

In Bert's page this is done for all five years. But UEFA doesn't do their calculations as often as Bert.
So for last year they had no previous result with 50 per cent, so they calculated directly the result times 0,33, thus getting 1,609, which allows the total of 7,300.

I've started calculating all coefficients both ways to see where we can find differences between one system and the other. But I've had little time, so I only have the following:

18,571 = 6,128
16,611 – 5,481/5,482
15,928 = 5,256
15,500 = 5,115
14,857 – 4,902/4,903
14,500 = 4,785
14,312 = 4,723
14,166 = 4,675
12,571 = 4,148
12,000 = 3,960
11,571 = 3,818
11,250 = 3,712
10,666 = 3,520
9,812 = 3,238

Obviously, all coefficientes ending with an even digit will have the same result.

In the coefficients where you have different results, the first column is for * 0,50 * 0,66 and the second for * 0,33.

Obviously, also, the result for the first will never be higher, because by multiplying by 0,50 you will, in case of odd numbers, get a number with four digits after the coma ending in five, which is always rounded down. Most cases, by multiplying by 0,66, you still get a result which rounded (up or down) is equal to multiplying by 0,33. But there are exceptions.

Author: viulo
Date: 03-07-2004, 19:50

Sorry, it seems to be wrong. Only now did I see VadimUK's post (it is strangely before mine) and he's right, I tried it for Austria and I get:

3,875 * 0,50 = 1,9375 – round down to 1,937 – multiply by 0,66 = 1,27842 – round down to 1,278

7,750 * 0,50 = 3,875 – multiply by 0,66 = 2,5575 – round down to 2,557

3,375 * 0,50 = 1,6875 – round down to 1,687 – multiply by 0,66 = 1,11342 – round down to 1,113

4,000 * 0,50 = 2,000 – multiply by 0,66 = 1,320

2,125 * 0,33 = 0,70125 – round down to 0,701

Sum 1,278 + 2,557 + 1,113 + 1,320 + 0,701 = 6,969

And UEFA has 6,970.

Oh well, it was a nice try...

Re: UEFA roundings
Author: viulo Date: 03-07-2004, 19:52	Could it be that the second rounding when multiplying by 0,50 and then by 0,66 is being done up when the fourth digit is finishing in 5? I'll try it later if I can.

Author: viulo
Date: 03-07-2004, 20:01

Couldn't wait till longer.

Tried it for Portugal. You have two multiplications ending with five.

The last one: 10,250 * 0,33 = 3,3825
The one before: 10,750 * 0,50 = 5,375 * 0,66 = 3,5475

Assuming that when you have two multiplications you round up and when you have only one you round down (which doesn't make much sense in this case, because 10,750 * 0,33 would also be 3,5475, but let's not try to make sense of UEFA, just figure their devious way of calculating...), the first one is rounded down to 3,382 and the other one is rounded up to 3,548.
Adding 1,925 + 2,021 + 3,093 you get the desired 13,969.

As you could see before, it also worked for Austria.

Re: UEFA roundings
Author: viulo Date: 03-07-2004, 20:55	Nope, doesn't work either. Tried it for Spain, but there is no year ending with 5.

Re: UEFA roundings
Author: anita Date: 03-07-2004, 22:51	Hi viulo Strange way to spend a Saturday evening. As you may see on my former reply, Ukraine (your method) goes as follows: 1,77375 (not rounded up) 1,320 1,19625 1,4025 (not rounded up) 1,60875 (rounded up to 1,609) So your theory about the fifth digit(5) doesnt cope either.

Author: viulo
Date: 03-07-2004, 23:53

True, Anita.

Although in my teory I had 1,77342 for the first year, not 1,77375.

Although that's hardly the point now. Neither is the 5th digit theory - as you have pointed out, Ukraine's fourth year should then be rounded up. But I had already noticed with Spain that it wasn't working.

As for the way I'm spending my evening on a saturday... well, I'm allegedly working but can't be bothered... But it would be too much to leave the computer or to surf music and movie pages... This is something I can disguise as work, actually...

Re: UEFA roundings
Author: anita Date: 05-07-2004, 00:22	Maybe the unknown parameter is a logaritm on Lennart Johanssons shoe-size-number. Where do UEFA hide their nation ranking? And to bert, comparing sheets, any particular reason why you add wrong on Team Ranking 2005. Real Madrid and other Spanish teams should have .503, not.505. ManU .007, not .008. Suppose you have an intention? regards

Author: bert.kassies
Date: 05-07-2004, 10:12

anita,

My team rankings are NOT calculated as the sum of the yearly coefficients, but as the number of individual team points added to 33% of the country ranking.

And yes, before you ask, I do use some "parameter that must be a logaritm on Lennart Johanssons shoe-size-number". In order to produce exactly the same team rankings as published by UEFA before 2004, I did use the following (Excel style) formula for the country contribution:

ROUNDDOWN(0.50 * country_ranking + 0.00025; 3)

where the parameter 0.00025 is Johansson's constant

Since a few weeks I'm totally confused. Not able to reproduce the UEFA team rankings of 2004 exactly. But until further knowledge has arrived I will use the following:

ROUNDDOWN(0.33 * country_ranking + 0.00025; 3)

Re: UEFA roundings
Author: duncshine Date: 09-07-2004, 10:45	Hi all, (I thought I'd revive this thread as A Word from Codemasters seemed the wrong title!!) Ricardo, thanks for your analysis on that thread. You, Bert, Viulo, Anita and others all seem to have exhausted every mathematical permutation. But we shall not give up! D

Author: anita
Date: 09-07-2004, 14:41

Lot of football journalists in Norway holidaying now after Euro2004 and the silly summer break in Nor PL. But I have contacted some per e-mail, and referred them to this thread (those grown-up football journalists in Norway not being acquainted with berts site, are not serious). I have contacted Nor FA as well. Not that they may have any answers, but they in their turn may contact UEFA. The vice-president in UEFA is Norwegian, and "all" football journalists in bigger newspapers kmow him socially. It's a shot to nothing, but some of my contacts in newspapers are genuinely interested in the rankings and coefficients.

This may seem desperate, but it seem that all of us on this forum are missing a parameter or a "twitch". Or - and thats why I lately have been so reluctant trying solving this problem - UEFA is wrong. No point trying to solve a problem that is unsolvable, i.e mathematically inconsistent.

And - and here is maybe the catch - UEFA should have an interest for everyone to understand their ranking. Well, that's the catch. I'm not sure, knowing UEFA's - close to stupid - secrecy in other matters.

regards

Author: duncshine
Date: 09-07-2004, 16:54

So if we go back to basics...

If we take each country's average for each of the last five years, multiply each by .33, add them numbers together and then do just one ROUNDDOWN (x,3) at the end, then all of the countries reflect UEFA's number, except for the following, each of which are .001 too high

Country     1999/0   2000/1   2001/2   2002/3  2003/4   Total  UEFA
-----------|--------|--------|--------|-------|-------|------|------|
Switzerland|1.36125 |1.44375 |2.02125 |1.93875|0.61875| 7.383| 7.382|
Poland     |1.0725  |1.19625 |1.36125 |2.18625|1.36125| 7.177| 7.176|
Austria    |1.27875 |2.5575  |1.11375 |1.32   |0.70125| 6.971| 6.97 |
Scotland   |1.69125 |1.85625 |2.18625 |2.43375|2.43375|10.601|10.6  |
Ukraine    |1.77375 |1.32    |1.19625 |1.4025 |1.60875|7.301 | 7.3  |
Spain      |6.12857 |5.48167 |4.90286 |5.115  |4.72312|26.351|26.35 |
Germany    |3.65357 |3.65062 |4.455   |3.01714|1.55571|16.332|16.331|
France     |3.39429 |3.135   |2.35125 |2.6125 |4.455  |15.948|15.947|
Portugal   |1.925   |2.02125 |3.09375 |3.5475 |3.3825 |13.97 |13.969|
Norway     |1.716   |1.52625 |1.0725  |0.891  |2.02125| 7.227| 7.226|
---------------------------------------------------------------------

Every other country returns the right .XXX number.

So all we need to do is to work out whether these ten nations are a mathematical error, or whether some form of rounding has gone wrong.

HELP!!!

Dunc

Re: UEFA roundings
Author: mark Date: 09-07-2004, 19:42	Pedantic people do not go to hell when they die, Satan is to afraid of them I guess that since the issue of rounding to the .001 do not bother me, I will go to hell

Author: duncshine
Date: 09-07-2004, 20:00

Hi Mark,

Just to correct you, I'm not a pedant, I'm a perfectionist. There's a subtle difference.

Actually, the .001 probably won't matter (Bert, Anita, Ricardo, Viulo and I have the same seeded teams as UEFA, allowing for the regional groupings), except that if we are .001 out, it shows that we may not be using the right formula, which may mean we get the seedings wrong (or that UEFA do!!).

Also, we have had countries less than .001 apart, so the seedings actually could be affected.

Look at Israel and Switzerland. They start 2004/5 on exactly the same coefficient (6.022). If either country is miscalculated by just .001 (esp. by UEFA), it could mean the difference between seeding and not, between reaching the next round or not.

Since we actually do think Switzerland is miscalculated, you can see how this .001 may be crucial.

OK, maybe we are being a bit obsessive, but there is a chance that it will actually matter.

Cheers

Dunc

Author: anita
Date: 09-07-2004, 20:37

I don't think you have to be neither a pedant or perfectionist. You just want to do what you do the right way. Before knowing the UEFA rules, I rounded up in my sheets. Couple of years. Discovered the difference after spotting Berts site, and then rounded down. Had no impact for my personal life, just wanting to get the correct sum.

We may all go to hell, but I wanna go there with my calculations and formulas in the right order. I find football calculation more interesting than calculating the exact distance to Mars, but try to miss out 0.001 there, and see where you end up

What a silly comparison.

regards

Re: UEFA roundings
Author: bert.kassies Date: 09-07-2004, 21:40	Well, by missing Mars you might end up in the Asteroid Belt. Look in the BBC version of the Hitchhiker's Guide (h2g2) for that subject and notice the basics of the Bode-Titius Law. And the similarities to the UEFA rounding problem. Using a pure mathematical approach to explain an unknown phenomenon. Coincidence? Or is anita leading a new way?

Author: mark
Date: 10-07-2004, 10:50

Talking about the Hitchhikers guide, my own rounding theory is that like in one of the Hitchhikers books (the restaurant at the end of the universe ?) in which a space navigation calculations are made in a restaurant because numbers in a restaurant behave differently then normal numbers, the numbers in UEFA HQ behave differently than in any other place in the world. I think that from time to time we see evidence to this, and then UEFA try to cover up by calling them mistakes

Author: anita
Date: 10-07-2004, 12:38

Since we're in there, Bode-Titius law doesn't work in this case. Was one of the first things I tried. Mark has a point with Chaos theory. But I have been through lot of that stuff, with no success. Calculated fractals, intermittence, bifurcations, periodicity, diffeomorfisms, using Lorenz' attractor, Koch curves, Mandelbrot and Cantor quantities.

I have been close, but not knowing the Johansson constant, I miss a factor. So I rest my case.

So long, and thanks for all the fish

Author: jpcccc
Date: 16-07-2004, 02:09

Well, still with the hitchiker's guide and the roundings.

I've been around the restaurant at the end of the universe and took with me the table posted by dunc in 9 july (with the countries gone wrong). I've done some maths between meals - in fact, practising my excel.

Suddenly, while some meat was cooking itself and everybody awaited the second coming of a prophet, i found a curious sequence of roundings that corrects those countries errors in the table posted by dunc. Could anybody with the full table, check if it works for all other countries, please ?

The sequence is : take the country ranking multiplied by .33 for each year, let it be x, and round it as follows. In seasons ending in an even year (99/00, 2001/2002, etc) perform a ROUNDDOWN(x,4). For seasons ending in odd years perform a ROUNDDOWN(x,3).

Finally, sum all five seasons after rounding, let it be X, and perform a last ROUNDDOWN(X,3).

I find it very weird, but since i'm in a restaurant that goes back and forth in time, it should be obvious. Right ?

If this works, this restaurant should be named 'UEFA's diner'.

Re: UEFA roundings
Author: jpcccc Date: 16-07-2004, 03:54	Well, don't you bother testing that. I found a full list and remade all the maths. It doesn't work for other countries. With England it works really bad... So, i'll just pay my way out of this place and go to sleep. Maybe there's a pattern for this elsewhere in the universe...

Re: UEFA roundings
Author: anita Date: 16-07-2004, 08:40	Hi jpcccc Since noone else bother to answer you, I'm in the restaurant myself. Nice try, and a cow is coming up to me now asking me what part of her I want to eat. No, I think most of the probable "rounding downs" has been tried. And "rounding ups". But keep on with ideas. Nowadays every innovation is welcome. We are out in the "deep blue" all of us. Lost in UEFA's space. regards from anita

Re: UEFA roundings
Author: macaskil Date: 17-07-2004, 12:59	I think this explains it all http://www.earthstar.co.uk/bistro.htm Since UEFA are used to eating at restaurants on expenses I think this is how they calculate the coefficients.

Re: UEFA roundings
Author: Ricardo Date: 19-07-2004, 08:24	I'm afraid I am giving up. Tried rounding up, rouding down, first 50%, then 66%, or straight 33%, for every year a different strategy. There is no logic in the result. Maybe they changed somewhere halfway the year. I have not tried to divide the last year into 2 parts, with each a different strategy. Anybody??

Author: jpcccc
Date: 20-07-2004, 01:55

Well, i'm still trying but i'm hinting the problem is with mere round, not up nor down, just the way they solve the halfway point. The ROUND in Excel works different from the rounding in Euro currency, for instance.

This means they performed some other rounding besides a single final one. Probably, they compute the 33% on pre-rounded values from an old software version. This means there can be more than one or even two intermediate roundings, and the exact rounding function used is still to be found.

Anyway, i'm going to sleep. From tomorrow on i'll try reverse computation (from which set of initial values can we reach final UEFA values ?) to get other hints.

And, by the way, this beats my late night crosswords to help me sleep. Problem is i dream of floating commas...

Nightmare !

Author: jpcccc
Date: 23-07-2004, 00:53

Finally, i think i got it (or a really, really nice try, if Spain's values are ALL confirmed).

The rounding used by UEFA works like this:

XXX,xxxyy will be rounded to XXX,xxx if yy is from 0 to 50. It will be rounded to (XXX,xxx + 0,001) if yy is above 50+ (anything slightly above 50)

Problem: EXCEL ROUND is NOT like this. It rounds up from 50 and not 50+

However, this rounding can be performed by the following combination of EXCEL functions:

ROUNDDOWN(0,5 * ROUNDUP((value * 2);3) ; 3)

Now, for the second part: UEFA performs its maths (and roundings) based on season results that are added, and not the 2004 ranking. It works like this:

For each country, take each season's points (Pi) and

1) Compute Ai = (Pi + Pi) * 0,33 ( OR 2*Pi*0,33 OR Pi*0,66 BUT the first one keeps the spirit of the formula, i'll tell why afterwards)

2) Round Ai (with Ai as value formula above)

3) Divide the rounded value of Ai by 2, getting Ci

4) For all five seasons, sum all Ci to get the sum value C

5) Finally, round the sum C to get the country 33% contribution according to UEFA.

On step 5, rounding with a mere ROUNDDOWN(R;3) achieves the same results as using the rounding formula above. However, i think the formula above keeps the roundings coherent.

This works for countries 2 down to 53. However, it gets 26,351 for Spain instead of 26,350.

So, before believing i failed, can someone assure me about which are the real (meaning, according to UEFA) Spain's points for last two seasons ?
Bert, is there any official UEFA confirmation on these values ? A slight 0,001 reduction on Spain's points is enough to make it all work.

Anyway, if this is right i reach a curious conclusion, besides the rounding formula UEFA uses.

When the contribution was 50%, the process in 1-5 steps (except step 3) could be used to compute each team ranking. Simply replace one of the Pi in step 1 with the team season's points (and use 0,5 instead of 0,33, of course).

Now, the trick: to compute the country contribution, UEFA used the same formula by "averaging" the country season's points with itself. By adding step 3) you reversed the "mirror averaging" and got a 50% contribution. So, IMO UEFA realised it could adapt that same process by replacing 0,5 with 0,33 in step 1.

For me, this is it and Spain's points for 2003/2004 should be slightly below 14,312. 14,311 is fine for me.

Or the previous season could have been 15,499 instead of 15,500. Works nice too.

But can anybody (Bert included) prove me what are the real Spain values ? From which source ?

Even if 15,500 and 14,312 are oficially confirmed i quit and start getting some nice sleep, so please just check it...

Regards

Re: UEFA roundings
Author: Ricardo Date: 23-07-2004, 09:21	jpcccc, Do you want a confirmation of the club-coefficiants, or the team coefficiants? team coefficients can be found in the particiapntlist of the UefaCup: here For the country-coefficients see this article on uefa.com

Author: arti
Date: 23-07-2004, 19:30

Yep, but these are last years coeffs. I still wonder why is it still on their site, instead of new one. And I have strong believe, that in Nyon they have some problems with multiplying and dividing - in previous seasons they were putting coeffs all over on the site - before round matches and so on and so on. This year it's hidden somewhere, and I believe, that even before draw for CL qualifying stages they didn't reveal it, only giving the pots and the seeded-unseeded division. Hence the conclusion, that they are not sure if they got it right or wrong.

Author: jpcccc
Date: 24-07-2004, 01:02

Thanks for the info. It was the countries' points that i wanted.

In fact, right now i only need to check this: Spain's points for 2003/04 are 14,312 (as in Bert's site) or is the official value slightly smaller ?

If it is 14,311 or smaller, my proposed solution for roundings (and UEFA's maths) works and is coherent with UEFA's values posted early by Bert on this thread.

If Spain's value is 14,312, it works for every country BUT Spain. A very strange approximation...

So, right now i'm betting that the "Johansson's constant" Bert uses is not right (or, in the words of Anita, the man has no exponential shoe size that we can use a logarithm on).

I'm betting Spain's value for 2003/04 is not 14,312 but smaller. It would mean the type of rounding i propose is what UEFA really uses. Not the one Bert said he uses by reverse engineering and trial-and-error (although producing the same result in most cases).

So, it all comes down to this: what is the official UEFA saying on 2003/04 points? Have they appeared anywhere ? I cannot rule out my solution on my previous post until i get that confirmation.

But, hey, you all can take a spreadsheet, take Bert's site ranking and the UEFA values for country 33% contribution he posted, do the maths i propose and see it for yourselves. It all works nicely, and when changing Spain's 03/04 value for 14,311 it becomes perfect.

Re: UEFA roundings
Author: anita Date: 24-07-2004, 02:08	Actually, jpcccc, I think you are close. You are "nagging" me, so I have used some week-end-time to check up your theories. Some deviations on teams, but I think you have something. To say it with Kipling, :"When Ricardo and Bert and Anita and Duncshine and Forza give in, and you stay on, you're a man". Sorry if I lost someone on the way.

Author: duncshine
Date: 24-07-2004, 11:22

Hey Anita!

Who said I?d given in??!! I?m just on holiday in Spain, that?s all...

Jpccc, I can?t check the maths over here (the water from the pool would make my spreadsheets soggy) but I think your theory sounds very close indeed.

I?ll have a go when I get back and see if we can?t solve the mystery of Spain (and I don?t mean the one about how to get the @ sign on their keyboards

)

Go Shelbourne!!

Re: UEFA roundings
Author: anita Date: 24-07-2004, 11:37	Seriously, dunc, you don't go on holiday when it is unsolved problems to work out. Irresponsible. Typical "youngins" today. Yes, I think jpcccc is into something. Innovative ideas at least, and closest so far. Have a nice time in Lloret de Mar(?)

Re: UEFA roundings
Author: duncshine Date: 25-07-2004, 12:19	Anita! Costa Dorada actually, Birdwatching on the Ebro Delta, but thanks anyway. Now, I need to check those Intertoto results...

Re: UEFA roundings
Author: Ricardo Date: 28-07-2004, 18:06	Dunc, I hope you're having a great vacation. I am having it too in Szcecin. Almost wetn to see Pogon-Hertha. unfortunately I was just ill that day. I got my sheets at home, and will try these calculations there for sure. Sounds strange but promising.

Author: jpcccc
Date: 30-07-2004, 01:35

Well, i have some news but not that good.

Although i still would like to check the official values UEFA confirms, i'm pretty much convinced Spain's value for 03/04 is 14,312. Not less.

So, this means the reason for the difference lies somewhere else.

Digging further into this, i have made changes on step 1) of my proposal. As i changed things around i noticed that it is just a minor detail that is missing. For instance, when computing step 1) for the season 01/02 with 0,329995 instead of 0,33 (a rounding of five digits, below any relevance), Spain's final value gets into 26,350. Of course, i don't propose this as solution. It is just to show the level of detail missing for a correct solution...

I'm also convinced that the way i previously interpreted the proposed solution is not the correct one: step 1) is not a "double" average. It is a mere average. What happens is that, before rounding, values are doubled and, after rounding, halved.

So, my current interpretation is:

1) compute 0,33 * season_ranking

2a)Double the value obtained in 1)
2) Round it (with the rounding method proposed earlier)
3) halve the rounded value in 2)

4) sum all seasons' contributions obtained by repeatedly doing steps 1-3)

5) Round final sum (as in 2) without doubling/halving)

So 2a-3 is a full rounding procedure for intermediate results, with no special meaning regarding the doubling and halving. Probably not related to previous 50%.

So, i could let this go if there was no Spain, but then where would dunc go for holidays ? By the way, can dunc be the "extra weight" in Spain ?

Just kidding...