# Points needed to steer clear of relegation in the Premier League

The Premier League is England’s highest football league. Each of the 20 teams play each other twice. A win gains 3 points, a draw 1 point and a loss gains nothing. Teams that a drawn on points are sorted according to ‘goal difference’ (the number of goals scored subtracted by the number conceded) and after that the number of goals scored are used.

The team that finishes top wins the league title, whilst the bottom three teams are relegated to the Championship (the second highest football league). This begs the question: How many points do you need to win the league, and how many will the team with the most points achieve?

The following graph shows the values for every year that the Premier League has run in its current format:

Points achieved in the Premier League across different seasons

On average about 85 points have been required to win the Premier League. On average, 36 points will still get the team relegated.

Mathematically, anything less than winning every game (114 points) can see you losing out on the league table, for the team you lost or drew against can win all their other games and thus either win straight out or on superior goal difference. In reality nobody has ever got higher than Manchester United’s 91 points though, and it has been won with as few as 75 points (again by United).

The highest number of points that can be achieved whilst still being relegated is when everybody else in the league except the two teams below you are drawn on points (and so you go down on goal difference). Thus everybody wins both games against the two bottom teams and wins one of the games against everybody else. Thus gives 6+17×3 = 57 points. In this situation 58 points will win you the Premier League! In fact the most points a relegated team had was West Ham United’s 42.

Is there any reason to assume this year might be any different? I’ve taken the Christmas standings from the last few seasons and calculated the average number of points per game the top and 3rd bottom teams had:

Points per game at Christmas in the last few years

So far this year doesn’t look like it is significantly different.