Points needed for European qualification

It's been 25 days since I last posted this (see here), the numbers haven't changed too much in terms of final points tally v qualification, here's a recap of what's happened since:

• As expected, we didn't come back against Man City (at the time of the last post we were already 2 down going into the away leg) and are out of the EFL Cup

• We beat Qarabag, perhaps also as expected, but got a fairly favourable draw for the following rounds, boosting our chances overall of qualification via winning it

• We picked up 3 points from 4 league games, effectively ending our hopes of Champions League qualification via the league – it's been difficult to know which teams to cheer for in other games this season with it being so open so far, but after today it's become clear that if we want Europa we mainly need Brentford and Chelsea (and to a lesser extent Fulham) to drop points

• We got past Villa in the FA Cup, but all the big boys won as well and then we were drawn against one of them, so we're actually less favoured to win it now, but at least it's good for the number of places falling to next best in the league

There's one interesting permutation which is that if a team wins the Champions/Europa league, and finishes exactly fifth, then the additional UCL place that goes to the Premier League because of European performance will fall to 6th. This doesn't work if they finish in the top 4, has to be 5th. Right now, I make the chances of that happening surprisingly high, about 9.1%. Most of that comes from Villa (6.7%), most of the rest split between Liverpool and Chelsea. Note that even if we don't then come 6th, it can still benefit us, as Europa places subsequently get pushed down.

Note this was generated before today's final game (Leeds v Man City), even if I don't get round to posting it until after it ends.