The Premier League: predicting who will go down (and the strange case of scenario no. 55)

As a Blackburn Rovers season ticket holder I can’t believe that it’s come down to the last game of the season.  By 5.45pm on Sunday 22nd May 2011, two of five teams currently separated by only a single point will have been relegated from the Premier league (Table 1).  Comments from mates like “you’ll be safe” or “you’re too good to go down” don”t help when it comes down to a single game that can make or break your season.  So what are the chances of Blackburn – or indeed any of the bottom teams – joining West Ham by going down on Sunday?

Table1. The Premier League Table 2010/11.
What is unusual about this season is that five teams could be relegated and that it is possible to be relegated with 41 points – the accepted safety number.  For comparison, only 31 points were needed to be safe in 2009/10 and there was a difference of 5 points between third and fourth from bottom. What is even more interesting about this year is the large number of  different scoring scenarios – 81 of them.
How can we predict who will join West Ham in relegation?

What every fan wants to know is, what are the permutations that affect my team, and what is the probability of them going down?

The first key thing is that the game between Wolves and Blackburn affects all others – if either of these teams win then they automatically stay up.  What is also pretty obvious is that if Wigan or Blackpool lose, then they automatically get relegated.  But there are a lot of other combinations.

How to predict who will get relegated

There are 3 scenarios in the game involving Wolves and Blackburn, i.e. a Wolves win, a draw or a Blackburn win.  For each of these options there is the possibility of a Birmingham win, draw or loss making 9 scenarios in all.  Similarly, for each of these 9 there are 3 in the Blackpool game – making 27 – and for each of the 27 there are 3 Wigan options.  This makes for 81 scenarios in all (3x3x3x3) shown in Table 2 which can be used to see who would be relegated in any specific scenario (with the assumption that goal difference remains the same).

Table 2. The 81 different scenarios that could take place on the last day of the 2010/11 Premier League season and the total points gained by each team (the teams relegated are in red).

Figure 1 shows the number of senarios in which each team is relegated. For Blackburn, there are 9 scenarios out of 81 (11%) where they get relegated while for Wolves there are 13 (16%).  It gets worse for the bottom three with Blackpool being relegated in around half of all scenarios and Wigan two thirds.

Figure1. The number of scenarios on 22nd May in which each team could be relegated.

Bizarre scenario no. 55

What would be the bizarest scenario we might see on Sunday?  If Wolves and Blackburn draw and all the others win, then they will both get relegated (scenario no. 28).  The one that appears to be the harshest, however, is scenario no. 55.  In this case, Blackburn loses and all other teams win. Blackburn go down with 40 points and Wigan with 42 points.  The only way out for Wigan in this scenario is for them to score lots of goals so that one of the others go down instead.  For Blackburn, there is no way out.

Am I happier now?  Well, a little.  My team, Blackburn, is not relegated in 72 of the 81 scenarios.  However, that does leave the other 9 where they are.  There’s only one thing for it.  At 4pm on Sunday 22nd May 2011, I will be going for a run that lasts around 2 hours.

Update 20th May 2011

Given the number of comments who wanted to know about goal difference and how this would affect each teams chances, please see the new article on Survival Sunday in the Premier League: how to escape relegation.