Premier League permutations: 2-4 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-2017-01-02

Chelsea remain safe in top spot but Arsenal can snatch second from Liverpool if they win while the Reds lose.

The two Manchester clubs are outside the top four at the moment but both are capable of breaking into it, with neither able to fall lower than sixth thanks to the nine-point gap between United and seventh-placed Everton.

At the bottom, only Swansea are guaranteed to remain in the relegation zone for now: even if they beat Palace on Tuesday they’d still be a point behind them and with a far inferior goal difference.

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-2017-01-02

Arsenal’s chances of overtaking Liverpool are pretty slender at 4% – they’d need to win at Bournemouth while their rivals lost at Sunderland, and with a sufficient goal difference swing to move them past the Reds.

The huge goal difference swing that Man Utd would need to move up the table during this round of fixtures didn’t occur once in any of the simulations I ran, so it looks like they’re effectively stuck in six barring an unprecedented combination of scorelines.

With Burnley visiting Man City, the model doesn’t think much of the Clarets’ chances of remaining in, or bettering, their current 11th position after this round of games.

The Black Cats themselves look unlikely to move out of the relegation zone thanks to the task ahead of them combined with Palace – the only team they can catch for now – hosting struggling Swansea.