UCL Quarter Final draw

juanva...@gmail.com

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Mar 18, 2021, 11:12:53 AM3/18/21

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Hello people.

Tomorrow will be the draw for the UCL quarter finals.

Considering the extraofficial resources of UEFA-FIFA, like the cold balls-hot balls technique, Zanetti´s stiff hand, Blatter and Platini disloyal payments and other undisclosed features, bribes, etc., out of 28 possibilities (C8,2) I would pick the following three:

Bayern - Porto
The German club is “el macho” of the draw and Porto is “la hembra” (the female, not politically correct statements, but that´s the way it is in betting). UEFA will try not to upset the last year champions. The road to the final should be open.

Real Madrid - Liverpool
The Spaniards recently won three Cups in a row and guarantee a good TV rating. Liverpool is lagging in midtable.

PSG - Chelsea
The French were runners up last year and have to be cared for and to avoid two English sides clashing this is the only option left.

Manchester City – Borussia D.

or

Bayern - Porto

PSG – Liverpool
UEFA trying to give a good run to the big wallet of Qatari owner of the French side.

Real Madrid – Chelsea

Manchester City – Borussia D.

or

Bayern - Porto

PSG – Liverpool

Real Madrid – Borussia D.

Manchester City – Chelsea
A variant of option 2, considering that the Show Biz Pop club look to me to be at the same level as the Prussians.

Juan Vazquez

The Doctor

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Mar 18, 2021, 3:37:45 PM3/18/21

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In article <1f9ae109-d233-49f8...@googlegroups.com>,

Will be interesting!
--
Member - Liberal International This is doctor@@nl2k.ab.ca Ici doctor@@nl2k.ab.ca
Yahweh, Queen & country!Never Satan President Republic!Beware AntiChrist rising!
Look at Psalms 14 and 53 on Atheism https://www.empire.kred/ROOTNK?t=94a1f39b
Light wants an end to war, but so does darkness. -unknown

juanva...@gmail.com

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Mar 19, 2021, 7:54:23 AM3/19/21

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On Thursday, 18 March 2021 at 16:12:53 UTC+1, juanva....com wrote:
> Hello people.
>
> Tomorrow will be the draw for the UCL quarter finals.
>
> Considering the extraofficial resources of UEFA-FIFA, like the cold balls-hot balls technique, Zanetti´s stiff hand, Blatter and Platini disloyal payments and other undisclosed features, bribes, etc., out of 28 possibilities (C8,2) I would pick the following three:
>
> Bayern - Porto
> The German club is “el macho” of the draw and Porto is “la hembra” (the female, not politically correct statements, but that´s the way it is in betting). UEFA will try not to upset the last year champions. The road to the final should be open.
>
> Real Madrid - Liverpool
> The Spaniards recently won three Cups in a row and guarantee a good TV rating. Liverpool is lagging in midtable.
>
> PSG - Chelsea
> The French were runners up last year and have to be cared for and to avoid two English sides clashing this is the only option left.
>
> Manchester City – Borussia D.
>

Real Madrid - Liverpool - check

Manchester City - Borussia D. - check

Chelsea - Porto
The Russian oligarch offered better conditions than the Qatari Emir to the Board of Representatives of the International Benefactors Establishment (BRIBE).

Bayern - PSG
UEFA has strong feelings against Islam.

Winners of Bayern-PSG meet winners of Manchester-Borussia D.

Winners of Real Madrid-Liverpool meet winners of Chelsea-Porto.

Real Madrid do not meet neither Bayern, nor Manchester City until the final.

Don Florentino has his reward.

Futbolmetrix

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Mar 19, 2021, 8:51:18 AM3/19/21

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On Friday, March 19, 2021 at 7:54:23 AM UTC-4, juanva...@gmail.com wrote:

> Real Madrid - Liverpool - check
>
> Manchester City - Borussia D. - check

Can't be bothered to go through the math, but I'm pretty sure that it's not that difficult to get two out of four pairings right even if you are guessing randomly.

>
> Chelsea - Porto

Lucky Chelsea. Then again, maybe it's better not to underestimate Porto...

>
> Bayern - PSG
> UEFA has strong feelings against Islam.
>
>
> Winners of Bayern-PSG meet winners of Manchester-Borussia D.

The two best teams in the competition will likely meet in the semis, unless Guardiola bottles it again.

> Winners of Real Madrid-Liverpool meet winners of Chelsea-Porto.

It's going to be Real Madrid again, isn't it?

For completeness, the EL draw:

Granada - Manchester United
Ajax-Roma

Dinamo Zagreb - Villarreal
Arsenal - Slavia

ManU vs Villarreal in the final, the Yellow Submarine to win it all.

The Doctor

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Mar 19, 2021, 9:16:39 AM3/19/21

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In article <bc2b6b3b-f716-4d03...@googlegroups.com>,

BMunich and Man C for the semis!

>Winners of Real Madrid-Liverpool meet winners of Chelsea-Porto.
>

Chelsea - RM for the semis!

>Real Madrid do not meet neither Bayern, nor Manchester City until the final.
>
>Don Florentino has his reward.
>
>
>
>

Bruce Scott

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Mar 19, 2021, 11:36:18 AM3/19/21

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On 2021-03-19, Futbolmetrix <daniele....@gmail.com> wrote:

>> Bayern - PSG
>> UEFA has strong feelings against Islam.

No, they don't want us two in the Final again.

>> Winners of Bayern-PSG meet winners of Manchester-Borussia D.
>
> The two best teams in the competition will likely meet in the semis,
> unless Guardiola bottles it again.

I'm glad we avoid Liverpool and Real M until a possible Final. But
getting past PSG will be the hardest task yet this season. We have
the match in Leipzig and the first leg here (in the AA) within 4 days.

>
>> Winners of Real Madrid-Liverpool meet winners of Chelsea-Porto.
>
> It's going to be Real Madrid again, isn't it?

They're most dangerous when no one has them on their shortlist.

(PS Daniele, the book is out now, in case that was you who emailed me)

--
ciao, Bruce

juanva...@gmail.com

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Mar 19, 2021, 11:37:47 AM3/19/21

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Granada is a nice surprise among the quarter finalists. Seventh in La Liga 2019-2020, Qualified for the Europa League second qualifying round.

Currently placed 8th in La Liga.

Beat 4-0 on aggregate Albanians Teuta, 2-0 Lokomotiv Tbilisi and 3-1 Malmö. Second one point behind PSV in the group stage, five points ahead of PAOK and seven of Omonia. Beat Napoli 3-2 on aggregate in round of 32 and Molde also 3-2 in round of 16.

Nice run, but they should be very lucky to beat Manchester United.

President of the club is the 40-year-old Chinese lawyer and entrepreneur Rentao Yi from Wuhan.

Venezuelan international Yangel Herrera (23, 1.84), on loan from Manchester City, has shown consistency as defensive midfielder, even scoring 8 goals in 32 games this year for Granada. Runner up in the U-20 World Cup in 2017, behind England. Bronze Ball in that tournament. Played for New York City in 2017-2018. Valued at 15 million euros according to Transfermarkt.

Another countryman, international Darwin Machis (28, 1.70 m), left wing, has scored 10 goals in 57 games for Granada since 2019. Some of his goals have been really good. Valued at 10 million euros by Transfermarkt.

Futbolmetrix

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Mar 19, 2021, 6:17:50 PM3/19/21

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On Friday, March 19, 2021 at 11:36:18 AM UTC-4, Bruce Scott wrote:

> (PS Daniele, the book is out now, in case that was you who emailed me)
>

I'm afraid I don't know what you are talking about, it must have been some other Futbolmetrix...

MH

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Mar 19, 2021, 9:56:55 PM3/19/21

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>
> (PS Daniele, the book is out now, in case that was you who emailed me)
>

Tell us more about this book. One you wrote ?

juanva...@gmail.com

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Mar 20, 2021, 1:31:50 AM3/20/21

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On Friday, 19 March 2021 at 13:51:18 UTC+1, Futbolmetrix wrote:

> On Friday, March 19, 2021 at 7:54:23 AM UTC-4, juanva... wrote:
>
> > Real Madrid - Liverpool - check
> >
> > Manchester City - Borussia D. - check
> Can't be bothered to go through the math, but I'm pretty sure that it's not that difficult to get two out of four pairings right even if you are guessing randomly.
>

With all due respect:

I made some calculations using “random” numbers in Excel.

You can download it from: https://jmp.sh/LkJ8EiV

Only 12, actually. The low number of sceneries was due to my inability to program the sheet not to repeat numbers. So, I generated random numbers from 1 to 8, copied their values in another column and selected the first eight numbers without repetition.

I matched the first two numbers, 3 and 4, 5 and 6, and 7 and 8.

Each team has a corresponding number.

I could not find a single occurrence out of twelve sceneries of Real Madrid vs Liverpool.

I found three events out of twelve of Bayern vs PSG.

I think my predictions were not that bad.

You have to believe me that I did it bona fide (a sophisticated manner of saying that I did not cheat).

juanva...@gmail.com

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Mar 20, 2021, 1:54:29 AM3/20/21

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On Saturday, 20 March 2021 at 06:31:50 UTC+1, juan wrote:

> With all due respect:
>
> I made some calculations using “random” numbers in Excel.
>
> You can download it from: https://jmp.sh/LkJ8EiV
>
> Only 12, actually. The low number of sceneries was due to my inability to program the sheet not to repeat numbers. So, I generated random numbers from 1 to 8, copied their values in another column and selected the first eight numbers without repetition.
>
> I matched the first two numbers, 3 and 4, 5 and 6, and 7 and 8.
>
> Each team has a corresponding number.
>
> I could not find a single occurrence out of twelve sceneries of Real Madrid vs Liverpool.
>
> I found three events out of twelve of Bayern vs PSG.
>
> I think my predictions were not that bad.
>
> You have to believe me that I did it bona fide (a sophisticated manner of saying that I did not cheat).

Addendum: only one random scenery out of 12 got two predictions right. 8.33 %

Three random sceneries out of twelve got one prediction right. 25 %

Eight out of twelve got zero predictions right. 66.67 %

juanva...@gmail.com

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Mar 20, 2021, 3:23:27 AM3/20/21

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On Saturday, 20 March 2021 at 06:54:29 UTC+1, juan wrote:

> > I matched the first two numbers, 3 and 4, 5 and 6, and 7 and 8.
> >
> > Each team has a corresponding number.
> >
> > I could not find a single occurrence out of twelve sceneries of Real Madrid vs Liverpool.
> >
> > I found three events out of twelve of Bayern vs PSG.
> >
> > I think my predictions were not that bad.
> >
> > You have to believe me that I did it bona fide (a sophisticated manner of saying that I did not cheat).
> Addendum: only one random scenery out of 12 got two predictions right. 8.33 %
>
> Three random sceneries out of twelve got one prediction right. 25 %
>
> Eight out of twelve got zero predictions right. 66.67 %

OTHER FEATURES: Sceneries 4 and 5 are the same

A question to whom it may answer: are there really only 28 possible combinations?

Ion Saliu

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Mar 20, 2021, 6:42:39 AM3/20/21

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On Saturday, March 20, 2021 at 9:23:27 AM UTC+2, juanva...@gmail.com wrote:
>
> A question to whom it may answer: are there really only 28 possible combinations?

Axiomatic:

There is a set of numbers in ‘combinatorics’ named ‘Combinations of N taken M at a Time’ or C(N, M). In this particular case, there are 8 teams and paired. The formula calculates:

‘Combinations of 8 taken 2 at a Time’ = C(8, 2) = (8 * 2) / (1 * 2) = 56 / 2 = 28.

The UCL pairings, however, have restrictions: ‘No teams from the same country can play against one another'.

The English Premier League had three teams; total C(3, 2) = 3 pairings excluded.

The German Bundesliga had two teams; total C(2, 2) = 1 pairing excluded.

Ultimately, only (28 – 4) pairings were possible.

You might want to read more on combinatorics, including the software to calculate all sorts of combinations:

• https://saliu.com/lexicographic.html
• “Lexicographical Order: Index, Rank of Permutations, Combinations”

• https://saliu.com/permutations.html
• “Combinatorics Software: Generate Permutations, Combinations”.

“People call me Parpaluck
Because I wish them good luck
Plus, I give them software
To get lucky with fanfare.”

Best of luck!

Parpaluck

juanva...@gmail.com

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Mar 20, 2021, 7:31:03 AM3/20/21

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On Saturday, 20 March 2021 at 11:42:39 UTC+1, ions

Ta, mait.

Yes, I calculated 28 (see my first post), but was not quite sure and was not sure about the restrictions of same country clubs either. I only have a prediction (the third one) with two English clubs playing against each other.

Intuitively it seemed to me that there were more possibilities. But this was wrong.

Blueshirt

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Mar 20, 2021, 7:35:36 AM3/20/21

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On 20/03/2021 10:42, Ion Saliu wrote:
> On Saturday, March 20, 2021 at 9:23:27 AM UTC+2, juanva...@gmail.com wrote:
>>
>> A question to whom it may answer: are there really only 28 possible combinations?
>
> Axiomatic:
>
> There is a set of numbers in ‘combinatorics’ named ‘Combinations of N taken M at a Time’ or C(N, M). In this particular case, there are 8 teams and paired. The formula calculates:
>
> ‘Combinations of 8 taken 2 at a Time’ = C(8, 2) = (8 * 2) / (1 * 2) = 56 / 2 = 28.
>
> The UCL pairings, however, have restrictions: ‘No teams from the same country can play against one another'.
>
> The English Premier League had three teams; total C(3, 2) = 3 pairings excluded.
>
> The German Bundesliga had two teams; total C(2, 2) = 1 pairing excluded.
>
> Ultimately, only (28 – 4) pairings were possible.

No. That's not correct. There was no seeding or country protection in
the Champions League QF draw yesterday... it was supposedly an 'open' draw.

However, whether people believe that teams from the same country were
kept apart by random or design is another issue...

Blueshirt

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Mar 20, 2021, 7:36:53 AM3/20/21

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On 20/03/2021 11:31, juanva...@gmail.com wrote:
>
> Yes, I calculated 28 (see my first post), but was not quite sure and was not sure about the restrictions of same country clubs either. I only have a prediction (the third one) with two English clubs playing against each other.
>
> Intuitively it seemed to me that there were more possibilities. But this was wrong.

There was no restrictions in the draw.

Ion Saliu

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Mar 20, 2021, 9:27:36 AM3/20/21

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Axiomatics:

Admittedly, I only watched the UEFA drawing for the groups. I thought (or I heard) that country restrictions apply up to and including the quarterfinals. No teams from the same championship have been matched up so far.

But I take your word on it. After all, I am not a soccer hooligan... er, big fan. Just kidding, Skatolchah!

Anyway, my post was about combinatorial calculations. I extended it to restrictions regarding teams of the same flag. Now, you know how to do that as well.

UEFA does take into account the team position in the groups. You might want to read an instructive article on sexual positions in Europe during the pandemic:

• https://saliu.com/bbs/messages/4.html
• "Fines for flagrante delicto".

Watch (if not again) 2020/21 UEFA Champions League quarter-final and semi-final draw:
https://www.youtube.com/watch?v=JvZZXUifoQE

Ion Saliu

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Mar 20, 2021, 10:26:32 AM3/20/21

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On Saturday, March 20, 2021 at 12:42:39 PM UTC+2, Ion Saliu wrote:

> On Saturday, March 20, 2021 at 9:23:27 AM UTC+2, juanva...@gmail.com wrote:
> >
> > A question to whom it may answer: are there really only 28 possible combinations?
> Axiomatic:
>
> There is a set of numbers in ‘combinatorics’ named ‘Combinations of N taken M at a Time’ or C(N, M). In this particular case, there are 8 teams and paired. The formula calculates:
>

Ion Saliu

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Mar 20, 2021, 10:37:19 AM3/20/21

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• https://www.youtube.com/watch?v=ncATonoLmxQ
• We will rock you Queen lyrics Subtitles UPL [HD] Britney Spears, Beyonce & Pink.

Blueshirt

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Mar 20, 2021, 12:56:04 PM3/20/21

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On 20/03/2021 13:27, Ion Saliu wrote:
>
> Admittedly, I only watched the UEFA drawing for the groups. I thought (or I heard) that country restrictions apply up to and including the quarterfinals.

Up to, but not including the QF.

After that they just put the balls in to the freezer to achieve the
required match-ups... allegedly. :-)

juanva...@gmail.com

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Mar 20, 2021, 11:05:57 PM3/20/21

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Apparently my intuition was right

The correct answer seems to be 105.

https://math.stackexchange.com/questions/3147071/champions-league-quarter-final-permutations

I quote:

"You can easily solve this recursively without using any complicated formulas.

Let Sn denote the number of permutations (i.e. possible pairings if there are n teams). For the finals (two teams) there is only one permutation, so S2=1.

For the semi finals (four teams) you can pair A with either B,C or D and the remaining teams are the second pair, so S4=3⋅1.

For six teams you could pair A with any of B,C,D,E or F (5 possibilities). And for the remaining 4 teams there are S4 many possibilities. Hence

S6=5⋅S4=15.

Can you figure out why the answer to your question is

S8=7⋅S6=105."

I found the same answer elsewhere.

https://math.stackexchange.com/questions/2694519/uefa-champions-league-quarterfinals-2018-draw-pairing-of-same-country-teams

I have made a systematic calculation in a spreadsheet and got the same result 105.

Domnule Saliu?

juanva...@gmail.com

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Mar 21, 2021, 1:56:13 AM3/21/21

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Problems with my systematic calculation. Some repetitions found.

My new answer is 70, which coincides with Combinations of 8 taken in 4 by 4. C(8,4).

But I am open to other opinions-results.

Message has been deleted

Ion Saliu

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Mar 21, 2021, 5:06:51 AM3/21/21

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On Sunday, March 21, 2021 at 5:05:57 AM UTC+2, juanva...@gmail.com wrote:
>
> Apparently my intuition was right
>
> The correct answer seems to be 105.
>
> https://math.stackexchange.com/questions/3147071/champions-league-quarter-final-permutations
>
> I quote:
>
> "You can easily solve this recursively without using any complicated formulas.
>
> Let Sn denote the number of permutations (i.e. possible pairings if there are n teams). For the finals (two teams) there is only one permutation, so S2=1.
>
> For the semi finals (four teams) you can pair A with either B,C or D and the remaining teams are the second pair, so S4=3⋅1.
>
> For six teams you could pair A with any of B,C,D,E or F (5 possibilities). And for the remaining 4 teams there are S4 many possibilities. Hence
>
> S6=5⋅S4=15.
>
> Can you figure out why the answer to your question is
>
> S8=7⋅S6=105."
>
> I found the same answer elsewhere.
>
> https://math.stackexchange.com/questions/2694519/uefa-champions-league-quarterfinals-2018-draw-pairing-of-same-country-teams
>
> I have made a systematic calculation in a spreadsheet and got the same result 105.
>
> Domnule Saliu?

Axiomaticule:

I talk mathematics, not baloney... or, er, soccer “hooliganism”! I referred to the pages of true mathematics of combinatorics. The link you referred to calculates (Combinations 8, 2) as 7 * 5 * 3 = 105! That guy must have been mighty DRUNK! Or, perhaps that’s the way he is! BRRRRRRRRAHAHAHAHA!!!!!!!

You saw clearly the list of these year’s pairings of 8 CL quarterfinals. I posted the text file of 8 teams, taken 2 at a time = 28 possible pairings. Show me those 105 pairings, according to the Stackexchange drunkard. Or, show us your... 70 pairings.

I also expanded the calculations from ‘combinations’ to ‘arrangements’: 56 possible pairings. That’s because there are 2 QF legs. The order of the teams in the pairings determines the hosts of the first leg.

Somehow, I get the impression you wanted to also know all possible groups of 4 teams from all 32 CL participants in the group stage. In this case:

C(32, 4) = (32 * 31 * 30 * 29) / (1 * 2 * 3 * 4) = 35960

From those 35960 possibilities, some 1000 8-group lineups can be established. Each 8-group, of course, must consist of unique teams only.

You can generate all possible 4-team groups by running that grandiose piece of software known world-over as PermuteCombine.exe. The output file can be quite large, but you can use team abbreviations to shrink the list. The list is even shorter given the same-country restriction.

Again, I talk mathematics here.

You also sez: “But I am open to other opinions-results.”
Now, that’s you at your best!

Best of luck axiomaticule & axiomaticilor!

Parpaluck,
Axiomatic At-Large

juanva...@gmail.com

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Mar 21, 2021, 7:53:56 AM3/21/21

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On Sunday, 21 March 2021 at 11:06:51 UTC+2, ions... wrote:

Please have a look at my 70 pairings and point out my mistakes.

https://jmp.sh/3HNQ1Nh

A bit difficult to follow with only numbers, but you shouldn't have problems.

Anyway I am going to try to do it with he names.

juanva...@gmail.com

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Mar 21, 2021, 8:11:02 AM3/21/21

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> Anyway I am going to try to do it with The names.

With names:

https://jmp.sh/DswTuUO

Futbolmetrix

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Mar 21, 2021, 8:49:16 AM3/21/21

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On Sunday, March 21, 2021 at 8:11:02 AM UTC-4, juanva wrote:
> > Please have a look at my 70 pairings and point out my mistakes.
> >
> > https://jmp.sh/3HNQ1Nh
> >
> > A bit difficult to follow with only numbers, but you shouldn't have problems.
> >
> > Anyway I am going to try to do it with The names.
>
> With names:
>
> https://jmp.sh/DswTuUO

Man, I created a monster...

Juan, I'm afraid you have some rows missing. For example, you have the combination

12, 34, 56, 78

but not the combinations

12, 34, 57, 68 and 12, 34, 58, 67

It's a more difficult combinatorics problem than I had originally thought, but I think the correct answer is 105.

Now, say that you guessed the draw 12, 34, 56, 78. What is the probability that you got at least two correct pairings?
Well, there are three possible combinations in which the first two pairings are 12, 34:

12,34, 56, 78
12,34, 57, 68
12, 34, 58, 67

But (12, 34) is just one of six possible ways in which you could have guessed two correct pairings (the others are (12,56), (12, 78), (34, 56), (34, 78) and (56, 78)).
So the chances of getting at least two correct pairings are 6x3 = 18 out of 105, or about 17%. Not bad, but not quite enough to convince me of your divinatory powers or of the temperature of balls in the UEFA urn.

Now, given that you actually made *three* guesses in your original post, the probability that at least one had two correct pairings rises to about 43%.

Ion Saliu

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Mar 21, 2021, 10:17:56 AM3/21/21

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On Sunday, March 21, 2021 at 2:11:02 PM UTC+2, juanva...@gmail.com wrote:
> oing to try to do it with The names.
>
> With names:
>
> https://jmp.sh/DswTuUO

BAYERN MUNICH | PARIS SAINT-GERMAIN | *

BAYERN MUNICH | REAL MADRID |
BORUSSIA DORTMUND | CHELSEA FC |

BORUSSIA DORTMUND | PARIS SAINT-GERMAIN |
BORUSSIA DORTMUND | REAL MADRID |

FC PORTO | MANCHESTER CITY | **

FC PORTO | PARIS SAINT-GERMAIN |
FC PORTO | REAL MADRID |

MANCHESTER CITY | PARIS SAINT-GERMAIN |
MANCHESTER CITY | REAL MADRID |

PARIS SAINT-GERMAIN | REAL MADRID | ** ***

The * now represents the actual configuration of the QFs as officially drawn by UEFA, (UEFA stands for “Blood On Your Face” in one of the many languages involved in European football, aka soccer). In alphabetical order:

BAYERN MUNICH | PARIS SAINT-GERMAIN | *
BORUSSIA DORTMUND | MANCHESTER CITY | *
CHELSEA FC | FC PORTO | *
LIVERPOOL FC | REAL MADRID | *

Other QF matchups could have been drawn as well. I marked them by **, ***, (you can do it for more QF possible matchups)...

BAYERN MUNICH | BORUSSIA DORTMUND | **
CHELSEA FC | LIVERPOOL FC | **
FC PORTO | MANCHESTER CITY | **
PARIS SAINT-GERMAIN | REAL MADRID | **

After the ** QF, I have a hard time finding a third 4-match configuration... a unique configuration, without repeating any matchup... If you patient, try other configurations. In my case, I have PARIS SAINT-GERMAIN | REAL MADRID | ** *** twice... Maybe only 2 QF UNIQUE configurations are possible!

This thread started with a lot of confusion. Evidently, mathematics, specifically combinatorics, is NOT the strong suit of most posters. But, then again, methinks it is all about them barrels... as in that Frankish Sinatra song:

“They don’t see the big birdie I am
I fly high to the sky
To plunge hard in that barrel of whiskey
Like a meteor of my God.”

juanva...@gmail.com

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Mar 21, 2021, 10:27:54 AM3/21/21

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These are in row 11 and 12 (14 and 15 rows Excel).

This is difficult to check as there are too many numbers.

I may have made some other mistakes.

It has been interesting, but I am tired of seeing numbers dangling over my head and my bed.

hehe.

Thanks to both of you, anyway.

I say 70 and rest my case.

;-)

juanva...@gmail.com

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Mar 21, 2021, 10:29:43 AM3/21/21

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On Sunday, 21 March 2021 at 16:17:56 UTC+2, ions...wrote:

> On Sunday, March 21, 2021 at 2:11:02 PM UTC+2, juan wrote:
> > oing to try to do it with The names.
> >
> > With names:
> >
> > https://jmp.sh/DswTuUO
> There ain't NO names on either spreadsheet.

The names of the teams are in file C(8,4)-4.xlsx in Tab QF-Teams cells P4 to W108

Ion Saliu

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Mar 21, 2021, 11:27:37 AM3/21/21

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CONTADOR:

Axiomático, I got you! Might have been the proverbial language barrier. We all confused ‘combinatorics’ with ‘probability theory’. What you wanted was:

‘What is the probability to pick correctly the matchups of a quarterfinal (QF; e.g., UEFA Champions League)’?

That is, a QF has 4 matchups made possible by 8 teams. What are the odds of picking all 4 matchups drawn by UEFA?

I just took a look at that grandiose piece of software known world-over as OddsCalc.exe (yup, I wrote it... who else?!)

The odds calculated as EXACTLY in a lotto game '8/4/4':

~ 0 of 4 in 4 from 8 = 1 in 70
~ 1 of 4 in 4 from 8 = 1 in 4.38
~ 2 of 4 in 4 from 8 = 1 in 1.94
~ 3 of 4 in 4 from 8 = 1 in 4.38
~ 4 of 4 in 4 from 8 = 1 in 70

The odds calculated as AT LEAST in a lotto game '8/4/4':

~ 0 of 4 in 4 from 8 = 1 in 1
~ 1 of 4 in 4 from 8 = 1 in 1.01
~ 2 of 4 in 4 from 8 = 1 in 1.32
~ 3 of 4 in 4 from 8 = 1 in 4.12
~ 4 of 4 in 4 from 8 = 1 in 70

No dispute, the probability to pick correctly the 4 QF matchups is ‘exactly’ (and ‘at least’) ‘1 in 70’. That’s a probability value, and has nothing to do with possible combinations of 8 teams taken 4 at a time. You saw what such a list can lead to.

‘1 in 70’ is, mathematically, ‘1/70’ or ‘1.43%’. You can’t generate such combos. It is similar to the paradox of the lotto wheels. But that’s a totally different beast.

Now, I believe this whole matter was elucidated. You was absolutely right about the ‘1/70’ probability. It might take 70 years to get a UEFA quarterfinal correctly (all 4 matchups). But there is an equal chance to get ‘exactly 0 of 4’ matchups! You can guess ‘at least 1 of 4’ matchups with a probability of ‘1 in 1.01’ or ‘99%’! ‘At least 2 of 4’ is 75%. But ‘exactly 2 of 4’ is 52%.

Best of luck to you all axiomatics, axiomatiques, axiomáticas/axiomáticos, assiomatice/assiomatici, axiomatischen!

Parpaluck,
Oddsmaker At-Large
• https://saliu.com/oddslotto.html

Ion Saliu

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Mar 21, 2021, 12:13:54 PM3/21/21

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CONTADOR:

Axiomático, I had a good shot of ţuică (you sez orrojo?) So, I wanted to calculate the probability of getting all 8 matchups of the round of 16 (octavos de finala?)

The odds calculated as EXACTLY in a lotto game '16/8/8':

~ 0 of 8 in 8 from 16 = 1 in 12870
~ 1 of 8 in 8 from 16 = 1 in 201.09
~ 2 of 8 in 8 from 16 = 1 in 16.42
~ 3 of 8 in 8 from 16 = 1 in 4.1
~ 4 of 8 in 8 from 16 = 1 in 2.63
~ 5 of 8 in 8 from 16 = 1 in 4.1
~ 6 of 8 in 8 from 16 = 1 in 16.42
~ 7 of 8 in 8 from 16 = 1 in 201.09
~ 8 of 8 in 8 from 16 = 1 in 12870 *

The odds calculated as AT LEAST in a lotto game '16/8/8':

~ 0 of 8 in 8 from 16 = 1 in 1
~ 1 of 8 in 8 from 16 = 1 in 1
~ 2 of 8 in 8 from 16 = 1 in 1.01
~ 3 of 8 in 8 from 16 = 1 in 1.07
~ 4 of 8 in 8 from 16 = 1 in 1.45
~ 5 of 8 in 8 from 16 = 1 in 3.23
~ 6 of 8 in 8 from 16 = 1 in 15.16
~ 7 of 8 in 8 from 16 = 1 in 198
~ 8 of 8 in 8 from 16 = 1 in 12870 *

* It would take 12870 years to get one correct guess (‘8 of 8’)!!!

How about them 28 combinations of 8 teams taken 2 at a time? No doubt, my list was correct. But in this case, we can calculate the probability of guessing one matchup only: p = 1/28 or 3.6%. If participating with 2 choices, then the probability is double: p = 2/28 = 7% (to guess one matchup).

The important thing is the formulation of the problem...

Ion Saliu

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Mar 25, 2021, 9:25:39 AM3/25/21

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On Sunday, March 21, 2021 at 5:27:37 PM UTC+2, Ion Saliu wrote:
>

Axiomáticas/Axiomáticos, Axiomatics, Axiomatischen, Assiomatice/Assiomatici, Axiomatiques et Al.:

It ain’t done yet! But if we wanted to serve TRUTH, let’s do it through science.

The previous calculations were founded on HYPERGEOMETRIC DISTRIBUTION PROBABILITY: C(8, 4, 4) = 70.

The formula calculates only the combinations, where the order of the elements is ignored. To calculate total sets where the order counts, we must apply the formula of ARRANGEMENTS. Actually, the COMBINATIONS are calculated by dividing ARRANGEMENTS / PERMUTATIONS.

Generating COMBINATIONS C(8, 4, 4) was the easiest way to figure out a solution. But we didn’t get to the bottom of the truth. Just look at the two 4-team sets that lead to the 4 QF matchups.

DOR - CHE | POR - MCI | *
BAY - LIV | PSG - RMA | *

We don’t get the real matchups. The ARRANGEMENTS (A) give us all possible configurations. In this case, A(8, 4) = 1680. Or, C(8, 4) * P (4) = 70 * 24 = 1680. Every 4-team combination is extended by a factor of 24, or P(4) = 1*2*3*4.

I expanded only the 2 combos that form this year’s quarterfinals:

DOR - CHE | POR - MCI | *
DOR - CHE | MCI - POR
DOR - POR | CHE - MCI
DOR - POR | MCI - CHE
DOR - MCI | CHE - POR
DOR - MCI | POR - CHE
CHE - DOR | POR - MCI
CHE - DOR | MCI - POR
CHE - POR | DOR - MCI
CHE - POR | MCI - DOR
CHE - MCI | DOR - POR
CHE - MCI | POR - DOR
POR - DOR | CHE - MCI
POR - DOR | MCI - CHE
POR - CHE | DOR - MCI
POR - CHE | MCI - DOR
POR - MCI | DOR - CHE
POR - MCI | CHE - DOR
MCI - DOR | CHE - POR
MCI - DOR | POR - CHE **
MCI - CHE | DOR - POR
MCI - CHE | POR - DOR
MCI - POR | DOR - CHE
MCI - POR | CHE – DOR

BAY - LIV | PSG - RMA | *
BAY - LIV | RMA - PSG
BAY - PSG | LIV - RMA
BAY - PSG | RMA - LIV **
BAY - RMA | LIV - PSG
BAY - RMA | PSG - LIV
LIV - BAY | PSG - RMA
LIV - BAY | RMA - PSG
LIV - PSG | BAY - RMA
LIV - PSG | RMA - BAY
LIV - RMA | BAY - PSG
LIV - RMA | PSG - BAY
PSG - BAY | LIV - RMA
PSG - BAY | RMA - LIV
PSG - LIV | BAY - RMA
PSG - LIV | RMA - BAY
PSG - RMA | BAY - LIV
PSG - RMA | LIV - BAY
RMA - BAY | LIV - PSG
RMA - BAY | PSG - LIV
RMA - LIV | BAY - PSG
RMA - LIV | PSG - BAY
RMA - PSG | BAY - LIV
RMA - PSG | LIV – BAY

The lines marked by ** show the teams of the actual draws in the actual matchups. Combining the 2 lines we get the entire picture of the QF:

MCI - DOR | POR - CHE | BAY - PSG | RMA - LIV ***

Of course, ultimately, we must separate the 4 matchups:

MCI - DOR
POR - CHE
BAY - PSG
RMA - LIV

So, getting to the actual line *** has a probability of 1/1680.

Of course, we could ignore what teams host the first game. In that case, we would half the total possibilities. Instead of P(4), we apply C(4, 2) = 12. Or, 70 * 12 = 840. 1/840 would be the probability to guess the 4 matchups regardless of who hosts the 2nd-leg game. That has some importance in the case of tied aggregate scores.

Are we done now? Methinks so...

Bruce Scott

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Mar 25, 2021, 12:15:44 PM3/25/21

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On 2021-03-20, MH <MHno...@ucalgary.ca> wrote:
>
>>
>> (PS Daniele, the book is out now, in case that was you who emailed me)

It wasn't you FM. A closer look at the email showed it was spam. Happened
shortly after a colleague told me advance orders were possible...

>>
> Tell us more about this book. One you wrote ?

https://iopscience.iop.org/book/978-0-7503-2504-2

Off topic here though...

--
ciao, Bruce

Jesper Lauridsen

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Mar 25, 2021, 6:35:07 PM3/25/21

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On 2021-03-19, Futbolmetrix <daniele....@gmail.com> wrote:
> On Friday, March 19, 2021 at 7:54:23 AM UTC-4, juanva...@gmail.com wrote:
>
>> Real Madrid - Liverpool - check
>>
>> Manchester City - Borussia D. - check
>
> Can't be bothered to go through the math,

I could.

> but I'm pretty sure that it's not that difficult to get two out of
> four pairings right even if you are guessing randomly.

There's 105 possible combinations (7x5x3). Two given matchups will
show up together in 3 of them (i.e. how many ways you can combine the
remaining 4 teams).

3 matchups will show up all together in one combinations, and for each
matchup pairing, there will be an additional 2 combinations (3 minus
the one with all 3). So that's 1+3x2 = 7. I.e. a 7/105 chance.

But if you pick 3 matchups, the one remaining is a given, so it's
really 4 matchups. And 2 of those will show up in 1+6x2 = 13/105
combinations.

13/105 is less than what I expected.

Ion Saliu

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Mar 26, 2021, 7:33:02 AM3/26/21

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“> Can't be bothered to go through the math,
I could.”

That’s not math; they might call it “drunken maths”.

There are exactly 4 numeric sets: Exponents, permutations, arrangements, combinations (from the most inclusive to the least inclusive).

There are precise formulas for all sets. There is no formula for that weird “7 * 5 * 3”!

Look again at all possible ‘quarterfinal settings’. The total of 1680 is determined by a formula:

Combinations (8, 4) * Permutations (4) = 70 * 24 = 1680.

This total accounts for the hosts of the first leg. If we ignore the order of the teams in a match, then we are in the 2020 unique situation.

The 2020 Champions League quarterfinals were disputed in Portugal. It was one match on a neutral site. The order of the teams did not count. The teams in a match were listed in alphabetical order; e.g., Barcelona – Bayern: 2 – 8.

In this case, the formula reads:

Combinations (8, 4) * Arrangements (4, 2) = 70 * 12 = 840.

I posted the possibilities of the actual QF set.

***

The same procedures are valid for the semifinal (SF) round. But is much easier to follow as we deal with 4 teams only.

1) If the order counts:
Combinations (4, 2) * Permutations (2) = 6 * 2 = 12

2) If the order does not count:
Combinations (4, 2) * Arrangements (2, 2) = 6 * 1 = 6

I took one group of 4 teams as an example. Here are all SF possibilities for both cases.

1)
BAY | LIV |
BAY | PSG | *
BAY | RMA |
LIV | BAY |
LIV | PSG |
LIV | RMA |
PSG | BAY |
PSG | LIV |
PSG | RMA |
RMA | BAY |
RMA | LIV | *
RMA | PSG |

The SF setting:
BAY – PSG | RMA – LIV | **
The first team drawn was BAY; the 2nd team drawn was PSG – they formed the first matchup.
The 3rd team drawn was RMA; the 4th team drawn was LIV – they formed the 2nd bracket.

2)
BAY | LIV |
BAY | PSG | *
BAY | RMA |
LIV | PSG |
LIV | RMA | *
PSG | RMA |

The SF setting:
BAY – PSG | LIV – RMA | **
In this case, either BAY or PSG was drawn first or second; either LIV or RMA was drawn third or fourth.

I took, as an example, the draw of the second bracket of the quarterfinals. There is no matchup missing; there is no duplicate matchup.

That’s how it is done... I mean, mathematically. ALWAYS SHOW DATA!

In the next post, I’ll generate 1000 random quarterfinal sets (i.e. 8 teams). If there were 105 total possibilities, we’ll have at least 9 of the actual QF draw. In any case, we’d have several such occurrences. I can’t find any. You can repeat my event using PermuteCombine.exe, the Arrangements (8, 4) set, Words Randomly; input file must be in one of my previous sets (the 8 QF teams, one team per line).

I tried to make the output file as small as possible. Open Notepad++, select all, copy to a new file, then save it (e.g. Arran8-4.WR.txt). You must find these two brackets exactly:

MCI | DOR | POR | CHE |
BAY | PSG | RMA | LIV |

In this example, doing a search in Notepad++, I found these occurrences:

MCI | DOR | POR | CHE | = 2 times
BAY | PSG | RMA | LIV | = 0 times.

The expectation is to find both strings 9 or 10 times each — IF that absurd 105 number of total possibilities were correct! 1000 / 105 = 9.5.

... to be continued...

Ion Saliu

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Mar 26, 2021, 7:34:20 AM3/26/21

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... continued...

LIV | RMA | BAY | PSG |
LIV | DOR | RMA | BAY |
LIV | MCI | DOR | CHE |
BAY | DOR | PSG | MCI |
RMA | BAY | MCI | PSG |
LIV | RMA | CHE | DOR |
CHE | DOR | BAY | MCI |
RMA | MCI | BAY | LIV |
POR | LIV | DOR | BAY |
POR | RMA | MCI | LIV |
CHE | MCI | LIV | PSG |
PSG | CHE | LIV | DOR |
POR | LIV | MCI | PSG |
PSG | POR | MCI | LIV |
POR | PSG | BAY | RMA |
DOR | CHE | BAY | LIV |
DOR | LIV | BAY | PSG |
CHE | PSG | POR | MCI |
MCI | POR | CHE | LIV |
CHE | POR | PSG | BAY |
CHE | BAY | PSG | MCI |
BAY | RMA | LIV | CHE |
CHE | POR | BAY | DOR |
DOR | MCI | POR | CHE |
MCI | CHE | LIV | POR |
BAY | RMA | POR | CHE |
BAY | DOR | MCI | RMA |
LIV | CHE | PSG | POR |
CHE | PSG | LIV | RMA |
RMA | MCI | PSG | LIV |
PSG | RMA | LIV | DOR |
CHE | RMA | LIV | POR |
LIV | PSG | BAY | CHE |
BAY | RMA | LIV | PSG |
BAY | CHE | RMA | LIV |
RMA | POR | PSG | MCI |
MCI | LIV | BAY | PSG |
RMA | DOR | POR | PSG |
MCI | DOR | LIV | BAY |
CHE | MCI | RMA | PSG |
PSG | DOR | CHE | BAY |
CHE | MCI | BAY | POR |
RMA | PSG | BAY | POR |
MCI | BAY | RMA | PSG |
BAY | LIV | DOR | PSG |
MCI | RMA | BAY | PSG |
PSG | DOR | LIV | BAY |
POR | CHE | BAY | MCI |
RMA | CHE | PSG | BAY |
LIV | POR | DOR | BAY |
POR | RMA | PSG | BAY |
PSG | LIV | DOR | RMA |
CHE | RMA | DOR | LIV |
PSG | POR | BAY | CHE |
CHE | DOR | PSG | RMA |
PSG | RMA | LIV | CHE |
LIV | MCI | PSG | POR |
RMA | POR | MCI | PSG |
MCI | LIV | PSG | CHE |
POR | LIV | MCI | DOR |
CHE | LIV | RMA | POR |
DOR | BAY | CHE | RMA |
DOR | BAY | PSG | CHE |
DOR | BAY | RMA | POR |
MCI | CHE | DOR | BAY |
POR | CHE | DOR | RMA |
POR | MCI | CHE | RMA |
LIV | PSG | BAY | DOR |
PSG | MCI | DOR | LIV |
RMA | DOR | LIV | MCI |
LIV | RMA | BAY | POR |
RMA | PSG | BAY | MCI |
LIV | DOR | RMA | PSG |
CHE | DOR | PSG | BAY |
LIV | PSG | CHE | BAY |
CHE | BAY | PSG | MCI |
CHE | DOR | PSG | LIV |
PSG | RMA | CHE | MCI |
MCI | PSG | POR | BAY |
RMA | POR | BAY | LIV |
PSG | DOR | CHE | POR |
LIV | CHE | BAY | RMA |
PSG | MCI | BAY | RMA |
DOR | PSG | MCI | CHE |
PSG | LIV | MCI | POR |
MCI | PSG | CHE | RMA |
RMA | MCI | CHE | DOR |
CHE | DOR | PSG | LIV |
PSG | LIV | BAY | MCI |
LIV | PSG | RMA | DOR |
LIV | DOR | PSG | RMA |
MCI | PSG | DOR | CHE |
MCI | BAY | CHE | POR |
DOR | MCI | BAY | LIV |
CHE | POR | MCI | DOR |
MCI | PSG | BAY | RMA |
MCI | BAY | DOR | CHE |
PSG | LIV | BAY | DOR |
MCI | DOR | CHE | PSG |
PSG | BAY | POR | RMA |
MCI | BAY | POR | LIV |
PSG | MCI | POR | LIV |
CHE | DOR | LIV | BAY |
MCI | BAY | RMA | LIV |
PSG | BAY | POR | MCI |
RMA | BAY | POR | MCI |
CHE | MCI | LIV | DOR |
CHE | DOR | MCI | PSG |
MCI | CHE | DOR | BAY |
DOR | LIV | BAY | POR |
CHE | RMA | PSG | DOR |
RMA | DOR | MCI | CHE |
MCI | DOR | RMA | LIV |
POR | PSG | DOR | CHE |
PSG | BAY | LIV | RMA |
RMA | DOR | MCI | PSG |
PSG | RMA | CHE | MCI |
POR | RMA | MCI | LIV |
MCI | DOR | PSG | CHE |
DOR | LIV | POR | RMA |
PSG | CHE | RMA | POR |
CHE | MCI | DOR | LIV |
MCI | PSG | LIV | DOR |
MCI | POR | PSG | BAY |
DOR | RMA | MCI | LIV |
DOR | MCI | BAY | LIV |
MCI | LIV | CHE | RMA |
CHE | DOR | PSG | POR |
DOR | MCI | CHE | PSG |
CHE | DOR | MCI | POR |
RMA | POR | LIV | PSG |
DOR | LIV | MCI | RMA |
CHE | BAY | POR | MCI |
RMA | MCI | CHE | POR |
LIV | DOR | RMA | MCI |
DOR | CHE | RMA | LIV |
MCI | RMA | POR | DOR |
POR | DOR | CHE | PSG |
LIV | DOR | BAY | PSG |
BAY | CHE | LIV | POR |
BAY | POR | CHE | RMA |
DOR | PSG | CHE | POR |
PSG | MCI | CHE | RMA |
RMA | LIV | BAY | MCI |
PSG | LIV | BAY | CHE |
RMA | PSG | DOR | BAY |
MCI | LIV | BAY | CHE |
RMA | PSG | CHE | MCI |
BAY | LIV | RMA | MCI |
DOR | LIV | CHE | RMA |
PSG | BAY | MCI | POR |
RMA | PSG | CHE | BAY |
PSG | LIV | CHE | POR |
MCI | CHE | POR | LIV |
DOR | LIV | MCI | CHE |
BAY | RMA | CHE | DOR |
PSG | BAY | MCI | RMA |
RMA | LIV | CHE | POR |
CHE | PSG | POR | LIV |
BAY | PSG | POR | CHE |
PSG | BAY | MCI | RMA |
BAY | PSG | LIV | MCI |
DOR | MCI | PSG | CHE |
RMA | LIV | DOR | POR |
DOR | CHE | RMA | PSG |
CHE | DOR | LIV | BAY |
DOR | LIV | POR | MCI |
BAY | DOR | MCI | RMA |
PSG | MCI | CHE | POR |
POR | MCI | RMA | BAY |
BAY | RMA | MCI | PSG |
POR | PSG | LIV | DOR |
LIV | BAY | CHE | PSG |
RMA | PSG | CHE | MCI |
DOR | CHE | BAY | LIV |
POR | PSG | MCI | RMA |
CHE | LIV | POR | PSG |
MCI | POR | LIV | RMA |
BAY | MCI | DOR | LIV |
BAY | RMA | POR | MCI |
RMA | LIV | DOR | MCI |
MCI | LIV | PSG | BAY |
RMA | DOR | BAY | MCI |
LIV | MCI | RMA | CHE |
POR | LIV | BAY | CHE |
POR | BAY | PSG | RMA |
RMA | CHE | MCI | BAY |
RMA | LIV | POR | PSG |
CHE | BAY | PSG | DOR |
POR | MCI | DOR | RMA |
RMA | PSG | POR | DOR |
RMA | CHE | LIV | DOR |
MCI | LIV | CHE | POR |
DOR | LIV | PSG | POR |
POR | MCI | BAY | DOR |
BAY | CHE | LIV | RMA |
PSG | DOR | CHE | MCI |
DOR | PSG | RMA | LIV |
BAY | POR | DOR | CHE |
POR | BAY | RMA | LIV |
CHE | BAY | MCI | RMA |
CHE | POR | PSG | MCI |
BAY | CHE | PSG | MCI |
POR | PSG | LIV | MCI |
POR | RMA | BAY | DOR |
BAY | DOR | MCI | CHE |
RMA | DOR | PSG | MCI |
MCI | DOR | PSG | POR |
CHE | MCI | LIV | RMA |
CHE | POR | RMA | MCI |
RMA | CHE | DOR | PSG |
PSG | MCI | LIV | CHE |
RMA | DOR | PSG | LIV |
DOR | CHE | POR | RMA |
DOR | RMA | POR | CHE |
LIV | POR | MCI | PSG |
CHE | DOR | PSG | LIV |
CHE | PSG | DOR | MCI |
LIV | CHE | RMA | POR |
RMA | BAY | CHE | PSG |
PSG | CHE | RMA | LIV |
MCI | POR | LIV | PSG |
PSG | DOR | LIV | RMA |
LIV | POR | CHE | BAY |
RMA | LIV | DOR | PSG |
LIV | DOR | BAY | RMA |
CHE | DOR | MCI | BAY |
POR | DOR | RMA | MCI |
MCI | RMA | POR | CHE |
BAY | POR | CHE | DOR |
LIV | DOR | BAY | CHE |
CHE | POR | PSG | MCI |
CHE | BAY | PSG | MCI |
MCI | BAY | RMA | LIV |
PSG | BAY | CHE | MCI |
BAY | POR | PSG | MCI |
DOR | POR | CHE | LIV |
PSG | BAY | LIV | POR |
POR | CHE | DOR | PSG |
MCI | RMA | DOR | PSG |
CHE | DOR | LIV | BAY |
LIV | POR | RMA | BAY |
MCI | BAY | PSG | POR |
CHE | PSG | RMA | LIV |
BAY | POR | MCI | DOR |
CHE | RMA | LIV | POR |
MCI | RMA | CHE | BAY |
POR | LIV | RMA | DOR |
DOR | MCI | RMA | POR |
BAY | PSG | MCI | CHE |
POR | CHE | RMA | PSG |
LIV | PSG | MCI | BAY |
BAY | PSG | DOR | CHE |
LIV | DOR | BAY | MCI |
POR | PSG | RMA | MCI |
POR | DOR | LIV | MCI |
POR | BAY | CHE | DOR |
POR | DOR | PSG | MCI |
PSG | LIV | MCI | RMA |
RMA | POR | MCI | BAY |
POR | CHE | LIV | MCI |
PSG | RMA | LIV | DOR |
CHE | PSG | RMA | BAY |
POR | LIV | RMA | BAY |
DOR | PSG | LIV | RMA |
PSG | BAY | DOR | POR |
POR | DOR | BAY | CHE |
MCI | PSG | LIV | CHE |
RMA | CHE | DOR | BAY |
DOR | RMA | PSG | LIV |
RMA | POR | DOR | BAY |
MCI | CHE | LIV | BAY |
BAY | POR | CHE | LIV |
RMA | CHE | DOR | LIV |
LIV | MCI | DOR | RMA |
RMA | LIV | PSG | POR |
DOR | BAY | POR | CHE |
RMA | POR | BAY | PSG |
LIV | MCI | RMA | CHE |
POR | RMA | BAY | DOR |
MCI | BAY | PSG | POR |
DOR | CHE | LIV | MCI |
PSG | BAY | CHE | RMA |
CHE | MCI | LIV | DOR |
DOR | PSG | CHE | MCI |
DOR | CHE | POR | BAY |
POR | RMA | LIV | PSG |
PSG | BAY | POR | DOR |
PSG | DOR | RMA | BAY |
PSG | POR | CHE | RMA |
BAY | DOR | PSG | MCI |
PSG | MCI | DOR | BAY |
LIV | MCI | CHE | RMA |
MCI | BAY | DOR | POR |
DOR | RMA | LIV | PSG |
MCI | PSG | POR | CHE |
PSG | LIV | DOR | RMA |
MCI | POR | LIV | DOR |
PSG | CHE | LIV | DOR |
RMA | CHE | LIV | PSG |
MCI | DOR | RMA | LIV |
MCI | PSG | RMA | CHE |
CHE | DOR | LIV | POR |
PSG | BAY | POR | RMA |
RMA | BAY | MCI | LIV |
BAY | LIV | MCI | POR |
CHE | RMA | PSG | LIV |
BAY | DOR | LIV | POR |
LIV | DOR | MCI | POR |
POR | BAY | RMA | LIV |
RMA | CHE | POR | LIV |
CHE | LIV | DOR | PSG |
RMA | POR | LIV | CHE |
RMA | CHE | POR | PSG |
RMA | CHE | BAY | LIV |
RMA | LIV | BAY | POR |
CHE | DOR | MCI | POR |
DOR | RMA | PSG | MCI |
PSG | RMA | LIV | BAY |
CHE | RMA | POR | MCI |
PSG | CHE | BAY | MCI |
LIV | DOR | MCI | RMA |
PSG | LIV | RMA | MCI |
RMA | MCI | CHE | PSG |
CHE | PSG | POR | DOR |
CHE | PSG | POR | LIV |
MCI | BAY | POR | LIV |
PSG | POR | BAY | LIV |
RMA | PSG | BAY | POR |
MCI | RMA | CHE | LIV |
CHE | LIV | MCI | PSG |
LIV | BAY | MCI | RMA |
BAY | MCI | LIV | CHE |
MCI | PSG | BAY | LIV |
PSG | MCI | LIV | POR |
CHE | DOR | POR | BAY |
BAY | DOR | PSG | LIV |
MCI | DOR | LIV | BAY |
MCI | RMA | PSG | DOR |
MCI | PSG | BAY | CHE |
LIV | RMA | DOR | MCI |
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CHE | BAY | RMA | POR |
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DOR | POR | RMA | LIV |
MCI | POR | LIV | DOR |
CHE | RMA | DOR | PSG |
BAY | PSG | LIV | DOR |
POR | DOR | CHE | BAY |
BAY | MCI | PSG | DOR |
CHE | MCI | DOR | PSG |
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RMA | BAY | MCI | POR |
PSG | CHE | POR | LIV |
RMA | POR | MCI | CHE |
RMA | MCI | BAY | DOR |
DOR | MCI | LIV | CHE |
BAY | PSG | CHE | MCI |
LIV | MCI | POR | RMA |
LIV | BAY | RMA | CHE |
RMA | DOR | BAY | MCI |
RMA | MCI | POR | CHE |
LIV | DOR | RMA | PSG |
MCI | PSG | DOR | CHE |
CHE | MCI | DOR | RMA |
CHE | RMA | DOR | LIV |
DOR | LIV | BAY | CHE |
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CHE | MCI | PSG | POR |
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DOR | CHE | BAY | LIV |
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PSG | MCI | RMA | LIV |
MCI | RMA | POR | CHE |
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PSG | POR | DOR | BAY |
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CHE | LIV | POR | MCI |
DOR | RMA | MCI | PSG |
RMA | CHE | PSG | DOR |
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DOR | CHE | LIV | POR |
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POR | PSG | LIV | MCI |
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PSG | DOR | MCI | CHE |
CHE | BAY | MCI | PSG |
MCI | PSG | CHE | LIV |
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POR | LIV | CHE | MCI |
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POR | RMA | BAY | CHE |
POR | RMA | BAY | CHE |
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POR | PSG | MCI | BAY |
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RMA | LIV | CHE | PSG |
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PSG | BAY | MCI | CHE |
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RMA | BAY | MCI | CHE |
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DOR | PSG | BAY | MCI |
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DOR | CHE | PSG | LIV |
PSG | BAY | CHE | RMA |
PSG | CHE | BAY | DOR |
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LIV | MCI | PSG | BAY |
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DOR | MCI | BAY | CHE |
RMA | BAY | CHE | PSG |
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RMA | DOR | PSG | CHE |
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MCI | POR | DOR | CHE |
CHE | DOR | RMA | PSG |
LIV | RMA | CHE | DOR |
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PSG | POR | MCI | BAY |
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MCI | BAY | POR | RMA |
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MCI | DOR | PSG | RMA |
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POR | RMA | BAY | MCI |
RMA | CHE | POR | MCI |
MCI | RMA | BAY | POR |
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MCI | RMA | CHE | BAY |
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CHE | LIV | DOR | MCI |
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POR | DOR | LIV | MCI |
CHE | POR | BAY | PSG |
LIV | RMA | MCI | CHE |
LIV | BAY | MCI | PSG |
MCI | POR | CHE | BAY |
LIV | CHE | BAY | DOR |
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RMA | PSG | BAY | DOR |
CHE | DOR | LIV | MCI |
POR | BAY | RMA | DOR |
BAY | PSG | POR | MCI |
PSG | DOR | CHE | RMA |
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POR | RMA | BAY | DOR |
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PSG | RMA | MCI | DOR |
DOR | POR | RMA | BAY |
POR | RMA | CHE | MCI |
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LIV | BAY | MCI | POR |
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DOR | POR | BAY | MCI |
DOR | BAY | MCI | PSG |
CHE | DOR | RMA | BAY |
CHE | DOR | POR | BAY |
DOR | RMA | LIV | MCI |
POR | LIV | MCI | DOR |
DOR | BAY | LIV | MCI |
RMA | MCI | BAY | DOR |
MCI | PSG | LIV | RMA |
POR | DOR | LIV | MCI |
PSG | POR | BAY | LIV |
DOR | CHE | RMA | PSG |
CHE | MCI | RMA | PSG |
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MCI | CHE | DOR | POR |
LIV | PSG | BAY | MCI |
MCI | BAY | PSG | DOR |
MCI | CHE | BAY | PSG |
BAY | MCI | PSG | CHE |
RMA | LIV | CHE | DOR |
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CHE | MCI | RMA | PSG |
DOR | MCI | BAY | PSG |
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BAY | DOR | POR | PSG |
CHE | POR | LIV | MCI |
LIV | MCI | RMA | BAY |
PSG | LIV | MCI | DOR |
MCI | POR | BAY | LIV |
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RMA | BAY | MCI | CHE |
PSG | RMA | MCI | LIV |
PSG | POR | BAY | RMA |
PSG | POR | BAY | LIV |
LIV | POR | DOR | RMA |
POR | LIV | PSG | BAY |
DOR | RMA | BAY | MCI |
RMA | PSG | LIV | MCI |
CHE | MCI | LIV | PSG |
POR | PSG | MCI | RMA |
CHE | RMA | BAY | POR |
DOR | PSG | MCI | BAY |
LIV | MCI | POR | CHE |
DOR | PSG | POR | MCI |
MCI | DOR | POR | PSG |
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POR | PSG | CHE | LIV |
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DOR | POR | PSG | CHE |
MCI | PSG | DOR | BAY |
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LIV | DOR | BAY | MCI |
BAY | POR | MCI | RMA |
LIV | POR | MCI | RMA |
DOR | MCI | RMA | BAY |
LIV | DOR | BAY | MCI |
CHE | PSG | MCI | DOR |
LIV | DOR | PSG | MCI |
BAY | DOR | CHE | LIV |
RMA | CHE | MCI | PSG |
RMA | MCI | DOR | POR |
BAY | PSG | POR | DOR |
DOR | BAY | RMA | CHE |
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DOR | LIV | RMA | PSG |
DOR | CHE | PSG | POR |
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POR | BAY | MCI | DOR |
POR | RMA | CHE | LIV |
PSG | BAY | CHE | LIV |
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DOR | POR | LIV | MCI |
DOR | PSG | BAY | RMA |
POR | DOR | MCI | RMA |
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DOR | CHE | LIV | POR |
POR | RMA | LIV | CHE |
POR | CHE | DOR | PSG |
PSG | CHE | MCI | BAY |
BAY | MCI | POR | CHE |
POR | BAY | DOR | PSG |
DOR | PSG | BAY | MCI |
LIV | POR | RMA | MCI |
MCI | CHE | DOR | BAY |
RMA | CHE | DOR | BAY |
DOR | CHE | RMA | LIV |
RMA | CHE | PSG | POR |
POR | LIV | BAY | DOR |
RMA | POR | DOR | PSG |
MCI | LIV | POR | RMA |
BAY | CHE | LIV | POR |
PSG | DOR | LIV | RMA |
MCI | LIV | PSG | BAY |
RMA | MCI | PSG | DOR |
BAY | DOR | PSG | POR |
POR | RMA | BAY | CHE |
BAY | LIV | PSG | MCI |
BAY | RMA | LIV | POR |
MCI | POR | CHE | DOR |
MCI | RMA | PSG | DOR |
PSG | CHE | MCI | RMA |
PSG | RMA | POR | BAY |
DOR | RMA | POR | PSG |
DOR | POR | LIV | RMA |
CHE | PSG | RMA | DOR |
BAY | LIV | MCI | RMA |
DOR | RMA | MCI | PSG |
MCI | CHE | LIV | PSG |
MCI | RMA | LIV | POR |
PSG | POR | MCI | RMA |
RMA | DOR | POR | LIV |
MCI | CHE | LIV | PSG |
CHE | LIV | PSG | MCI |
PSG | BAY | MCI | LIV |
PSG | POR | RMA | MCI |
RMA | CHE | POR | LIV |
LIV | BAY | POR | DOR |
POR | BAY | PSG | CHE |
LIV | CHE | POR | BAY |
RMA | PSG | POR | LIV |
RMA | POR | BAY | MCI |
POR | BAY | LIV | PSG |
BAY | DOR | RMA | CHE |
POR | DOR | PSG | CHE |
POR | PSG | LIV | DOR |
PSG | RMA | BAY | DOR |
CHE | LIV | MCI | POR |
BAY | CHE | DOR | RMA |
MCI | LIV | DOR | RMA |
MCI | DOR | CHE | POR |
LIV | DOR | POR | BAY |
BAY | POR | CHE | PSG |
POR | MCI | BAY | PSG |
LIV | DOR | POR | RMA |
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PSG | LIV | MCI | RMA |
POR | DOR | RMA | PSG |
POR | BAY | CHE | PSG |
CHE | POR | RMA | PSG |
DOR | CHE | PSG | RMA |
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MCI | PSG | LIV | BAY |
RMA | PSG | BAY | POR |
DOR | LIV | MCI | RMA |
LIV | CHE | PSG | DOR |
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MCI | CHE | LIV | DOR |
POR | CHE | RMA | PSG |
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POR | MCI | CHE | DOR |
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MCI | POR | CHE | PSG |
PSG | CHE | RMA | BAY |
DOR | LIV | MCI | CHE |
MCI | LIV | POR | BAY |
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POR | PSG | CHE | LIV |
POR | LIV | BAY | CHE |
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POR | PSG | RMA | MCI |
DOR | RMA | LIV | POR |
POR | DOR | LIV | MCI |
DOR | CHE | LIV | MCI |
CHE | MCI | PSG | POR |
LIV | PSG | CHE | RMA |
BAY | CHE | PSG | MCI |
POR | MCI | BAY | RMA |
CHE | RMA | LIV | MCI |
DOR | BAY | PSG | RMA |
PSG | DOR | RMA | LIV |
LIV | PSG | RMA | BAY |
PSG | POR | BAY | RMA |
LIV | PSG | POR | CHE |
MCI | DOR | PSG | CHE |
PSG | CHE | MCI | DOR |
CHE | LIV | BAY | DOR |
CHE | MCI | BAY | LIV |
DOR | CHE | POR | LIV |
PSG | RMA | DOR | POR |
DOR | PSG | MCI | LIV |
LIV | PSG | RMA | MCI |
POR | CHE | LIV | PSG |
CHE | MCI | POR | BAY |
POR | CHE | RMA | PSG |
DOR | MCI | RMA | BAY |
PSG | MCI | BAY | RMA |
MCI | DOR | CHE | LIV |
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DOR | RMA | CHE | MCI |
LIV | RMA | PSG | MCI |
PSG | RMA | DOR | CHE |
DOR | CHE | PSG | RMA |
POR | DOR | LIV | MCI |
BAY | MCI | PSG | DOR |
RMA | BAY | LIV | MCI |
DOR | RMA | PSG | LIV |
POR | PSG | DOR | CHE |
CHE | LIV | PSG | DOR |
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MCI | RMA | PSG | BAY |
DOR | PSG | POR | BAY |
DOR | PSG | LIV | BAY |
POR | DOR | CHE | RMA |
DOR | LIV | RMA | BAY |
PSG | LIV | CHE | RMA |
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MCI | DOR | BAY | RMA |
MCI | LIV | CHE | POR |
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DOR | BAY | MCI | CHE |
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CHE | PSG | BAY | DOR |
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DOR | MCI | RMA | LIV |
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POR | MCI | BAY | RMA |
LIV | POR | CHE | RMA |
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POR | RMA | BAY | LIV |
DOR | POR | BAY | LIV |
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DOR | MCI | LIV | PSG |
DOR | PSG | RMA | CHE |
POR | PSG | DOR | RMA |
PSG | RMA | CHE | POR |
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POR | LIV | MCI | CHE |
MCI | POR | BAY | PSG |
MCI | LIV | BAY | DOR |
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POR | MCI | DOR | BAY |
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CHE | PSG | RMA | LIV |
LIV | RMA | CHE | MCI |
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CHE | MCI | DOR | PSG |
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DOR | LIV | MCI | POR |
CHE | DOR | MCI | LIV |
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POR | MCI | LIV | RMA |
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PSG | CHE | MCI | POR |
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PSG | RMA | DOR | BAY |
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POR | LIV | CHE | MCI |
DOR | BAY | PSG | MCI |
DOR | CHE | MCI | PSG |
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MCI | BAY | DOR | LIV |
DOR | RMA | LIV | BAY |
RMA | DOR | PSG | BAY |
BAY | MCI | CHE | DOR |
RMA | BAY | CHE | POR |
BAY | DOR | RMA | POR |
MCI | CHE | BAY | RMA |
BAY | RMA | LIV | MCI |
RMA | POR | BAY | CHE |
MCI | RMA | LIV | BAY |
DOR | LIV | PSG | BAY |
PSG | CHE | DOR | RMA |
PSG | CHE | POR | BAY |
PSG | BAY | POR | DOR |
RMA | MCI | LIV | POR |
BAY | PSG | MCI | DOR |
DOR | BAY | POR | RMA |
CHE | DOR | BAY | PSG |
BAY | MCI | LIV | POR |
MCI | PSG | POR | DOR |
RMA | LIV | CHE | MCI |
RMA | BAY | POR | MCI |
LIV | CHE | RMA | MCI |
MCI | POR | CHE | RMA |
POR | PSG | MCI | DOR |
BAY | POR | RMA | DOR |
RMA | DOR | CHE | POR |
PSG | RMA | BAY | LIV |
POR | LIV | RMA | DOR |
CHE | PSG | RMA | DOR |
POR | RMA | MCI | BAY |
PSG | CHE | RMA | DOR |
RMA | POR | LIV | BAY |
CHE | MCI | PSG | POR |
MCI | LIV | POR | DOR |
BAY | CHE | POR | MCI |
PSG | RMA | LIV | MCI |
BAY | CHE | LIV | RMA |
LIV | DOR | PSG | MCI |
MCI | PSG | DOR | POR |
BAY | CHE | RMA | PSG |
DOR | BAY | POR | RMA |
POR | CHE | MCI | RMA |
RMA | POR | PSG | DOR |
LIV | PSG | MCI | RMA |
LIV | POR | CHE | PSG |
CHE | RMA | LIV | DOR |
RMA | POR | CHE | DOR |
POR | PSG | BAY | DOR |
POR | PSG | LIV | MCI |
MCI | DOR | POR | CHE |
CHE | MCI | DOR | LIV |
POR | DOR | MCI | RMA |
POR | DOR | BAY | PSG |
LIV | BAY | PSG | MCI |
LIV | CHE | POR | BAY |
POR | DOR | MCI | PSG |
POR | LIV | DOR | PSG |
POR | LIV | PSG | RMA |
PSG | BAY | CHE | LIV |
RMA | BAY | POR | MCI |
RMA | DOR | POR | BAY |
BAY | MCI | PSG | POR |
LIV | RMA | CHE | POR |
MCI | DOR | POR | CHE |
LIV | BAY | PSG | RMA |
MCI | CHE | LIV | PSG |
RMA | LIV | MCI | PSG |
MCI | DOR | CHE | LIV |
PSG | LIV | BAY | RMA |
PSG | POR | BAY | DOR |
POR | MCI | DOR | PSG |
PSG | POR | LIV | DOR |
CHE | POR | LIV | RMA |
BAY | PSG | RMA | MCI |
PSG | BAY | RMA | CHE |
RMA | MCI | BAY | DOR |
RMA | CHE | DOR | PSG |
CHE | MCI | BAY | POR |
MCI | BAY | DOR | LIV |

Ion Saliu

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Mar 26, 2021, 7:58:39 AM3/26/21

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To generalize total possibilities when matching elements 2 at a time; e.g., a round of a competition as UEFA Champions League.

The quarterfinal round consists of 8 teams and 4 matches.

1) Total possibilities where the team order counts:
Arrangements (8, 4) = 8 * 7 * 6 * 5 = 1680 or

Combinations (8, 4) * Permutations (4) = 70 * 24 = 1680.

2) Total possibilities where the team order does not count (as if all 8 teams play on a neutral site):

Combinations (8, 4) * Arrangements (4, 2) = 70 * 12 = 840.

For the round of 16, total possibilities are represented by a huge number — over 500 million!

The computer can generate quite fast random sets. See just how difficult it is to get the right round setup (all matchups as drawn by the “lottery” commission). Some people might speculate that the commission “fixes” the draw on different considerations. Sometimes they might record a higher success rate than choosing absolutely randomly. But that’s another story, not related to maths...

Jesper Lauridsen

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Apr 4, 2021, 4:17:23 PM4/4/21

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On 2021-03-21, Futbolmetrix <daniele....@gmail.com> wrote:
>
> It's a more difficult combinatorics problem than I had originally thought, but I think the correct answer is 105.
>
> Now, say that you guessed the draw 12, 34, 56, 78. What is the probability that you got at least two correct pairings?
> Well, there are three possible combinations in which the first two pairings are 12, 34:
>
> 12,34, 56, 78
> 12,34, 57, 68
> 12, 34, 58, 67
>
> But (12, 34) is just one of six possible ways in which you could have guessed two correct pairings (the others are (12,56), (12, 78), (34, 56), (34, 78) and (56, 78)).
> So the chances of getting at least two correct pairings are 6x3 = 18
> out of 105, or about 17%.

I believe you're double counting combinations here. Yes, each of the
six matchup pairs appears in 3 combinations, but one of those 3 is the
compination where *all* 4 matchups are present. So that one is counted
6 times.

Ion Saliu

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Mar 18, 2022, 7:00:18 AM3/18/22

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The 2022/21 edition is discussed in this thread:

• https://groups.google.com/g/rec.sport.soccer/c/pnA8pSVJKrs
• UCL 2022/23 R16 2nd Legs [R]