Another new thing from me this weekend. I did some analysis at work recently looking at the possible permutations of results for the European Championship qualifiers (e.g. how many different ways are there of a specific nation qualifying etc) and I wanted to try and apply this to domestic leagues.

What I’ve done

I’ve written some code that runs through every possible combination of results from a given round of matches and works out what the league table would look like for each one. It then aggregates these to show what the highest and lowest positions attainable by each club are and how many ways there are of achieving each, to set some expectations around how much the table can change in a given week.

Because I’m interested in what’s genuinely possible (and impossible), I’ve ignored goal difference and just considered three possibilities for each match: home win, draw and away win. This is probably just as well, given that even having just those three possible outcomes for each of the 12 matches in one division represents 3^12 = 531,441 different combinations for my modestly-specced laptop to crunch through. If I wanted to look at individual scorelines then the numbers quickly become obscene. Even if I only wanted to sim every possible result between 3-0 and 0-3, I’d be looking at a completely unmanageable 16^12 = 281,474,976,710,656 different combinations to simulate per division each weekend.

You’ll see that the tables can still change quite a bit this weekend, but as time goes on and three points starts to represent an increasingly small percentage of the average club’s total, we should see the bars getting narrower as a single win makes less and less of a difference. We should also see some patterns as clubs start to cluster into groups and gulfs start appearing in the table.

I doubt that this is something I’ll look at every single week – it’ll probably get wheeled out when there’s an interesting pattern to look at – but I wanted to give it a trial run and show how useful this sort of analysis can be once we get towards the business end of the season.

Championship

For each division I’ve drawn lines under the last play-off spot, mid-table and the last spot above the relegation zone on both “axes” for ease of reference. As I mentioned above, a single win can still make a pretty big difference at this stage of the season, but nonetheless here are some observations.

Only five teams are guaranteed to finish this weekend in the top half of the table, with Brighton‘s strong start meaning that they can’t sink lower than 4th. If they do slip up, only four other clubs are close enough to replace them at the summit.

Even though the four sides in 14th – 17th are three points behind Middlesbrough in sixth, none of them can rise higher than seventh this weekend because Boro are playing MK Dons, who sit between them and those four sides. Whatever the result of that match, one of those two sides will have too many points to be overtaken.

Both Brentford and Derby have made disappointing starts but could find themselves in the top half if they win and other results go their way.

Only four teams are unable to break into the top half this weekend and any one of seven could find themselves bottom, while current bottom side Rotherham incapable of climbing higher than 18th.

League 1

Seven different teams could occupy top spot on Monday, although current leaders Gillingham can’t be dislodged from the play-off places altogether.

Over half of the clubs in the division – the entire bottom half plus 12th-placed Bury – are at risk of finding themselves in the relegation zone next week.

Only the bottom two sides – Colchester and Crewe are mathematically unable to leap into the top half of the table this weekend, but three other teams including managerless Peterborough could also find themselves at the bottom of the pile.

League 2

This division is still so close that even York down in 17th are capable of starting next week in the play-off places and only the current top five are immune from beginning it in the bottom half of the table.

While five clubs are capable of taking top spot – slightly fewer than in League 1 – any of the top eleven could find themselves in the top three if results go their way.

Only the current bottom six are unable to climb into the top half via this round of fixtures, and are also the only six clubs able to finish the weekend in the relegation zone.

National League

Forest Green‘s 100% record after eight matches means that they can’t be overtaken at the division’s summit, although any one of five sides could find themselves tucked beneath them in second place.

Every club outside the bottom five have a chance to start next week in the top half, while only the current top six are immune from sliding into the lower half of the table.

Poor Kidderminster are the only club guaranteed to be in the relegation zone whatever happens this weekend, with Halifax just able to escape if other results go their way.

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Note: there’s also a Premier League version here