## The Arithmetic of Relegation

When I got back home after yesterday’s concert, I ate some dinner and settled down to have a look through the Sunday papers. Most of the news was as grim as expected, especially the ongoing fiasco of Brexit, and the scandal engulfing Home Secretary former Home Secretary Amber Rudd who obviously lied to Parliament on at least one occasion. Anyway, turning my attention to the Sports pages there was a write-up of Saturday’s disappointing home defeat for Newcastle United against bottom club West Bromwich Albion. I was gloomy enough to wonder whether Newcastle might actually still get relegated, so looked at the Premiership Table:

Neither West Brom (28 points) nor Stoke (30) can catch Newcastle with only two games to play, but Southampton can in principle get 41 points from here if they win all three games. It’s true that they have a worse goal difference but if Newcastle lost all their three remaining games, and Southampton won all theirs that would change. It therefore looks mathematically possible for Newcastle to be relegated.

However, I then glanced at the fixture list and found that Southampton have to play Swansea in one of their remaining matches. If Southampton win that fixture then the maximum number of points Swansea can get by the end of the competition is 39, so Newcastle can’t be relegated. If Southampton lose or it’s a draw then they can’t catch Newcastle.

I conclude, therefore, that Newcastle United are mathematically safe from relegation. Hooray!

But who will go down? I think West Brom and Stoke will probably get relegated, but I’m not sure about the third team. Huddersfield must be very nervous because their recent form has been poor and they have a very bad goal difference. The betting odds are interesting: BetFred are offering 200/1 on West Brom not being relegated and most bookies are about 8/1 on Stoke to stay up. PaddyPower are quoting 4/9 on Huddersfield and even money on Southampton to go down. If you want to bet on Brighton to get relegated your best odds are with BetVictor who are offering 50-1. Few bookies are quoting odds on West Brom to get relegated, so they obviously think that’s the likely outcome.

I expect these odds to change a lot after the next round of matches.

### 6 Responses to “The Arithmetic of Relegation”

1. Nigel Foot Says:

I’m pleased you didn’t mention my team West Ham in your calculations. I am extremely gloomy about their prospects with Manchester United to play (having suffered a 1:4 thumping at the hands of Manchester City yesterday). My feeling is it will go down to the last game of the season for us (home to Everton) and that could end badly! Here’s hoping for the best !

• telescoper Says:

West Ham are about 14-1 to go down at the moment.

• Francis Says:

Bear in mind that betting odds don’t necessarily reflect the actual odds of something happening, but rather what the betting is on that particular outcome. For example England are currently about 16/1 to win the World Cup, but I would say that the actual chance for them to win would be less than 1 in 17….

• telescoper Says:

Well, the bookies do factor in how much money has been wagered but those odds are not totaliser odds; the bookmakers make some judgement about probability in assigning them.

Having said that people do tend to bet on what they want to happen rather than what they think will happen, so odds on England on UK based sites are usually shorter than one would otherwise suppose. I wouldn’t bet on England unless the odds were at least 33-1. On the other hand, Portugal looks an attractive bet at 25-1 as does Russia at 50-1.

2. Anton Garrett Says:

Spare a thought for Brechin City, who have just become the first Scottish pro club since the 1891/2 season to go through the entire season without a league victory.

• telescoper Says:

Quite impressive, and a goal difference of -70 has to be commended. However, they did blot their copybook by drawing four games. With a bit more commitment they could have lost all their matches, which would have been truly spectacular.