How 11 Premier League clubs could qualify for Europe -- but not this season

Each European titleholder is guaranteed a place in Europe. As above, if any team finishes in a European place domestically, there is no additional place. However, if a team does not qualify from domestic competition, it's an extra spot for the titleholders on top of the league allocation -- even if all three were to do so.

So that means it's possible, though highly improbable, for the Premier League to have 11 teams in Europe, including the EPS.

Champions League: 1-5, UCL winners, UEL winners
Europa League: 6, FA Cup winners, UCoL winners
Conference League: Carabao Cup winners

Realistically the maximum in Europe is 10 this season?

Yes, because it would be quite the collapse for Arsenal not to finish in a domestic European place. Or in fact the top four.

For 10 to qualify, it would require Man United or Tottenham to win the UEL, plus Chelsea the Conference League and finish outside the top six:

Champions League: 1-5, Man United/Tottenham as UEL winners
Europa League: 6, FA Cup winners, as Chelsea as UCoL winners
Conference League: Newcastle United as Carabao Cup winners

If Newcastle were to finish in the top six, or the FA Cup winners do so, that shifts the places down by one or two.

How eighth could qualify for the Europa League by league position

For clubs hovering around eighth in the table, the performance of Chelsea is going to be very important. They are the only team who could win a European title and finish in a position to cause this drop down.

We need to assume Newcastle United and Man City as winners of the FA Cup have finished inside the top six.

This is the allocation before the EPS:

Champions League: 1-4
Europa League: 5, 6
Conference League: 7

Chelsea win the Conference League and finish seventh -- they sit three points ahead of this place right now. Chelsea would play in the Europa League, and the Premier League would give up Chelsea's place in the Conference League.

Champions League: 1-4
Europa League: 5, 6, Chelsea as UCoL winners (7)
Conference League: -

Add the EPS, and everything moves down one place -- but the Europa League place for 6th position jumps over Chelsea and is given to eighth.

Champions League: 1-5
Europa League: 6, Chelsea as UCoL winners (7), 8
Conference League: -

Hypothetical: How ninth, 10th and 11th could qualify for Europe

This is like the previous scenario, the difference being the European titleholder finishes in the first place outside the European positions.

For this to happen a European title winner would need to finish eighth. This cannot happen this season.

So, the Conference League winners finish in eighth place -- one below the Conference League spot. Chelsea play in the Europa League as Conference League winners, and the Premier League has eight teams in Europe.

Champions League: 1-4
Europa League: 5, 6, UCoL winners (8)
Conference League: 7

Now the EPS is applied with fifth in the UCL, and as this creates the plus-1 in all scenarios there are now nine teams in Europe. The European places drop down one, but as Chelsea already have a place in the Europa League, the Conference League spot "jumps" over them and goes to ninth.

Champions League: 1-5
Europa League: 6, 7, UCoL winners (8)
Conference League: 9

The same EPS logic can be applied to push the allocation down two or three places in the league.

It requires multiple European titleholders to be in consecutive places outside the domestic spots, to create two or three "jumps."

This is the effect of two teams winning European titles and finishing eighth and ninth -- 10th gets the Conference League spot after the EPS is applied.

Champions League: 1-5, UEL winners (9)
Europa League: 6, 7, UCoL winners (8)
Conference League: 10

Add in the UCL winners finishing in a consecutive place, and 11th gets the Conference League.

Champions League: 1-5, UCL winners (8), UEL winners (10)
Europa League: 6, 7, UCoL winners (9)
Conference League: 11