Premier League permutations: 21 May 2017

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 automatic promotion and play-off spots, 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.

The only remaining drama is around the battle for a place in the top four, with Arsenal able to displace one of Liverpool or Man City. Plenty can change in lower mid-table, with Leicester particularly mobile: they can end the season anywhere between a respectable eighth and a disappointing 15th.

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.

So Arsenal only have a 15% chance of sneaking into the top four, with Man City seemingly all but assured of Champions League football. West Brom and Bournemouth look marginally likelier to fall than rise, giving Leicester a decent chance of a top half finish.