Champions League Math Explained

You may be surprised to learn that being a PSG Talk contributor doesn’t exactly pay the bills. My actual job is being a teacher, so, with that being said, I decided to give a mini-tutorial on Paris Saint-Germain’s UEFA Champions League draw scenarios. The draw takes place on Monday, December 17 at 6 AM EST. Follow along kids because today’s topic is all about percentages. Bear in mind the permutations are far more complicated and intricate than I’m about to describe, but I’ll give you the basic things to keep in mind.

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Let’s start with the beginning. The eight first-place group winners are seeded and picked first. Then, their opponent—a second-place group finisher—is picked based on some basic criteria:

1. The first place team cannot draw a team they played in the group stage.
2. The first place team cannot draw a team from their own domestic league until the quarter-final.

So, what that means is that first-place PSG cannot draw Liverpool FC (same group) or Olympique Lyonnais (same domestic league). Therefore, Paris can only draw one of six teams.

Atlético Madrid
Tottenham Hotspur
Schalke 04
Ajax
AS Roma
Manchester United

If PSG were to be drawn first, they would have a 16.66 percent chance of drawing either of these six teams and a 1/3 chance of drawing a team from England (either Tottenham Hotspur or Manchester City).

Now, if PSG is not drawn first that is where things start to get complicated.

If any of the eight teams, but Manchester City, are selected first and draw a non-English side, the odds change. That’s the key in all of this—the order in which the first place teams are drawn. So, let’s say the first first-place team drawn is Borussia Dortmund. They can draw any team except Schalke and Atlético, which gives them a 50/50 chance of drawing an English squad. Let’s say that squad is Liverpool FC. PSG’s draw percentages would be the exact same as they were if they were drawn first.

Now, let’s say Borussia Dortmund draw Olympique Lyonnais. The situation still remains the same.

However, if Dortmund draws Ajax (Scenario 1), PSG’s potential opponent list drops from six to five. The percentages look something like this:

Atlético Madrid: 20%
Tottenham Hotspur: 20%
Schalke 04: 20%
AS Roma: 20%
Manchester United: 20%

So, in this scenario, PSG’s chances of drawing an English team jump from 33 percent to 40 percent.

But, if Dortmund draws Tottenham or Manchester United (let’s say Spurs), the percentages remain the same except PSG’s odds of drawing an English team drop from 33 percent to 20 percent and Ajax goes back in the pot at 20 percent.

This basic scenario holds for every possible team being drawn first (except PSG) and except for Manchester City, who can only draw Atlético, Schalke, Ajax, and Roma, which would automatically increase PSG’s odds of drawing an English team from 33 percent to 40 percent without even having to be drawn. Let’s for this sake say they drew Roma (Scenario 2).

Keep in mind there are so many different permutations that going through them all would be insane. So, let’s keep to a hypothetical three draws (the third upcoming. Let’s start with Dortmund drawing first with Ajax. The next hypothetically drawn team will be Bayern Munich. Bayern can only draw Atlético, Tottenham, Liverpool, Roma, Lyon, and Manchester United. Let’s say they draw a non-English team, Lyon for example. Here are PSG’s draw percentages in that situation:

Atlético Madrid: 20%
Tottenham Hotspur: 20%
Schalke 04: 20%
AS Roma: 20%
Manchester United: 20%
(Odds don’t change)

The chance of drawing an English team increases to 50 percent. Let’s see what happens if Bayern were to draw Manchester United (Scenario 3).

Atlético Madrid: 25%
Tottenham Hotspur: 25%
Schalke 04: 25%
AS Roma: 25%

Now, let’s say we go with the scenario of Manchester City drawing first. In this hypothetical, Juventus FC draws second. They can only draw Atlético, Tottenham, Liverpool, Schalke, Ajax, and Lyon. Hypothetically, they draw Atlético. Here are PSG’s draw percentages:

Tottenham Hotspur: 25%
Schalke 04: 25%
Ajax: 25%
Manchester United: 25%

However, if Juventus were to draw Tottenham…

Atlético Madrid: 25%
Schalke 04: 25%
Ajax: 25%
Manchester United: 25%

(Reminder these odds are for if PSG were to be picked next in the draw order).

So far three of our hypothetical draws look like this:

1. Borussia Dortmund vs. Ajax // Bayern Munich vs. Olympique Lyonnais

2. Manchester City vs. AS Roma // Juventus FC vs. Atlético Madrid

3. Borussia Dortmund vs. Ajax // Bayern Munich vs. Manchester United

Let’s start with situation one and say the next team drawn is Real Madrid and they draw Tottenham. Here is what the PSG scenario looks like:

Atlético Madrid: 25%
Schalke 04: 25%
AS Roma: 25%
Manchester United: 25%

Now, what if Real Madrid drew Schalke?

Atlético Madrid: 33%
Tottenham Hotspur: 33%
Manchester United: 33%
(66 percent chance of drawing an English club)

On to hypothetical draw two. Real Madrid gets drawn and receives Manchester United.

Tottenham Hotspur: 33%
Schalke 04: 33%
Ajax: 33%

If Real Madrid draws Liverpool FC:

Tottenham Hotspur: 25%
Schalke 04: 25%
Ajax: 25%
Manchester United: 25%

(Notice PSG can still draw four different teams in this scenario).

Scenario three will see Manchester City be drawn third and receive Roma:

Atlético Madrid: 33%
Tottenham Hotspur: 33%
Schalke 04: 33%

Here is an update on our hypothetical draws so far:

1. Borussia Dortmund vs. Ajax // Bayern Munich vs. Olympique Lyonnais // Real Madrid vs. Tottenham Hotspur

2. Manchester City vs. AS Roma // Juventus FC vs. Atlético Madrid // Real Madrid vs. Manchester United

3. Borussia Dortmund vs. Ajax // Bayern Munich vs. Manchester United // Manchester City vs. Roma

In Scenario 1 (head hurting yet?) the next team drawn is Juventus. They can now only receive Atlético, Liverpool, and Schalke. They receive Schalke. What are PSG’s percentages now?

Atlético Madrid: 33%
AS Roma: 33%
Manchester United 33%

In Scenario 2, the next name is FC Barcelona. They can only select Liverpool, Schalke, and Ajax. In this hypothetical they select Ajax. What are PSG’s percentages then?

Tottenham Hotspur: 50%
Schalke 04: 50%

In Scenario 3, the next team selected is the Portuguese team FC Porto. They select Liverpool.

Atlético Madrid: 33%
Tottenham Hotspur: 33%
Schalke 04: 33%

(Notice in the third scenario three choices remain)

Halfway through the draw and here is where our hypotheticals stand:

1. Borussia Dortmund vs. Ajax // Bayern Munich vs. Olympique Lyonnais // Real Madrid vs. Tottenham Hotspur // Juventus FC vs. Schalke 04

2. Manchester City vs. AS Roma // Juventus FC vs. Atlético Madrid // Real Madrid vs. Manchester United // FC Barcelona vs. Ajax

3. Borussia Dortmund vs. Ajax // Bayern Munich vs. Manchester United // Manchester City vs. Roma // FC Porto vs. Liverpool FC

The next team drawn in Scenario 1 is Manchester City. They can only draw Atlético Madrid in this circumstance. Meaning that PSG can now either draw Roma or Manchester City.

In Scenario 2, it is Porto out of the pot next and they, like in Scenario 3, draw Liverpool. This leaves PSG’s odds in Scenario 2 untouched.

Scenario 3 sees Barcelona pulled out of the pot. They draw Schalke. The percentages change:

Atlético Madrid: 50%
Tottenham Hotspur: 50%

Here are our scenarios through five matchups:

1. Borussia Dortmund vs. Ajax // Bayern Munich vs. Olympique Lyonnais // Real Madrid vs. Tottenham Hotspur // Juventus FC vs. Schalke 04 // Manchester City vs. Atlético Madrid

2. Manchester City vs. AS Roma // Juventus FC vs. Atlético Madrid // Real Madrid vs. Manchester United // FC Barcelona vs. Ajax // FC Porto vs. Liverpool FC

3. Borussia Dortmund vs. Ajax // Bayern Munich vs. Manchester United // Manchester City vs. Roma // FC Porto vs. Liverpool FC // FC Barcelona vs. Schalke 04

Scenario 1 sees Porto picked next and they draw Manchester United, which means PSG will
automatically receive Roma.

Scenario 2 sees Dortmund come out of the pot. They cannot draw Schalke (same domestic league), so they are left with Tottenham or Lyon. If they draw Lyon, PSG’s odds remain the same, but in this case, Dortmund draws Tottenham, which means PSG are drawn with Schalke.

Scenario 3 has Real Madrid’s name drawn. At this point they can only draw Tottenham or Lyon. Let’s drag this out and say they draw Lyon. PSG’s odds remain constant in this scenario.

Here are our updated scenarios through six matchups (one and two are complete):

1. Borussia Dortmund vs. Ajax // Bayern Munich vs. Olympique Lyonnais // Real Madrid vs. Tottenham Hotspur // Juventus FC vs. Schalke 04 // Manchester City vs. Atlético Madrid // FC Porto vs. Manchester United // Paris Saint-Germain vs. AS Roma // FC Barcelona vs. Liverpool FC

2. Manchester City vs. AS Roma // Juventus FC vs. Atlético Madrid // Real Madrid vs. Manchester United // FC Barcelona vs. Ajax // FC Porto vs. Liverpool FC // Borussia Dortmund vs. Tottenham Hotspur // Paris Saint-Germain vs. Schalke 04 // Bayern Munich vs. Olympique Lyonnais

3. Borussia Dortmund vs. Ajax // Bayern Munich vs. Manchester United // Manchester City vs. Roma // FC Porto vs. Liverpool FC // FC Barcelona vs. Schalke 04 // Real Madrid vs. Olympique Lyonnais

Almost done. The only two names that can be pulled now are PSG and Juventus. Both have equal chances of receiving either Atlético or Tottenham. Juventus draws and gets Tottenham. PSG in this scenario draws Atlético Madrid.

Leaving our final two matches in Scenario 3 as:

Juventus FC vs. Tottenham Hotspur
Paris Saint-Germain vs. Atlético Madrid

If you’ve stayed to the end of this you are an absolute trooper. But for those who did you learned a lot. What you learned was that the odds constantly shift as a team is drawn later and later in the draw. And that even though we only fleshed out three scenarios there and hundreds of these we could do. And finally, the most important lesson of all is that we’re probably going to draw Atletico Madrid no matter what so get used to it.

Thank you as always for reading and if you would like to show your appreciation for PSG Talk, we invite you to visit our Patreon page. Thank you and Allez PSG!

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Posted by Marc

Marc is PSG Talk's man in New York. A PSG fan since a trip to Paris in 2008, his fandom ratcheted up when a BeIN sports came to America in 2013. He one day hopes to celebrate a champions league victory with a lot of adult beverages. What he doesn't want you to know is that he actually likes the new 2017-2018 PSG home kit.