Premier League permutations: 30 Dec – 1 Jan

What’s possible

Here are the highest and lowest possible positions that each club can occupy after the forthcoming round of fixtures. I’ve drawn lines under the Champions League places, mid-table and the last spot above the relegation zone on both “axes” for ease of reference.

These graphics are explained here, but in a nutshell I crunch through every possible combination of results to work out how far it’s mathematically possible for each club to rise and fall.

pl-permutations-2016-12-29

While Arsenal are just three points off second place, they can’t reach it in this round of fixtures due to Liverpool playing Man City: one of these two will remain ahead of the Gunners whatever happens.

Man Utd’s recent resurgence has opened up a seven-point gap between them and seventh-placed Everton, but there’s plenty of movement possible beneath the Toffees.

At the bottom, both Swansea and Hull are stuck in the relegation zone for now thanks to Palace’s four-point cushion, but Sunderland can send either the Eagles or Leicester into the bottom three if they win at Burnley.

What’s likely

The above shows what’s mathematically possible but doesn’t make any allowances for what’s likely to happen, so I’ve come up with a second graphic that uses my E Ratings prediction model (used to simulate the forthcoming round of games thousands of times) to assign some probabilities to all these potential changes.

It’s structured very similarly to the one above: the clubs are still listed in the same order as the current league table down the side and the dividing lines are all in the same place, but now across each row is the percentage chance of them moving to other positions in the table. As above, green indicates a rise, red a drop and grey staying put. The darker the red or green, the higher the probability. If there’s no number in a square, it means that the club didn’t fill that position in any of the thousands of simulations I ran and is therefore very unlikely.

pl-probabilities-2016-12-29While Arsenal can’t claim second this weekend, their home game against Palace gives them a good chance of overtaking whoever comes off worse out of Liverpool v Man City.

While Man Utd are just three points behind Tottenham, the swing in goal difference they’d require to move above them is so large that it didn’t happen in any of the simulations I ran.

With Sunderland having a similar goal difference disadvantage compared with Crystal Palace and Leicester, the Black Cats can only realistically move out of the bottom three at the expense of the former – and even then only by winning and hoping that the Eagles lose (a 32% chance multiplied by a 63% chance gives roughly 20% of both happening).