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.


About stevehaake

Steve is Professor of Sports Engineering at Sheffield Hallam University. He has a degree in Physics from the University of Leeds and a PhD from Aston University on the mechanics of golf balls on golf greens. He has over 200 publications, including his first book "Advantage Play: Technologies that changed Sporting History" due out in October 2018.

25 Responses

  1. Scaveed

    True, there are that amount of scenarios, but the question is, which are more likely? Given our (Blackburn’s) current form, and manager, we may greatly struggle against a determained Wolvees, and also a draw is unlkely in any game, so the pie chart does not accurately reflect our, or anyone else’s, survival hopes. The odds, for example, of Rovers going down are not 9 in 81.

    Also, why is scenario 55 any harsher than scenario 1?

  2. Savory

    think of the combinations of bets you could make to soften the blow of us (rovers) goin down..

  3. Nick Rich

    Amazing to know there are 81 scenarios without even throwing goal difference in!

    Unfortunately that’s also a pretty big flaw as only the draw results would keep this as-is; actually, that’d also probably only be strictly true of a single scenario – where all the teams draw. If that doesn’t happen, at least one team will have different GD in any other scenario of the 81.

    What would it look like if a reasonable scoring margin was included – say up to 3 goals – for win/loss? I’m assuming there’d be a whole heap more due to the additional series, but what effect there would be on the outcome is probably the interesting bit – such as the ratio of potential match outcomes to the potential match outcomes that would make a difference, e.g. would blackburn always stay up with a win whatever the win/loss margins in the games?

  4. Savory

    well ive put a few quid on us losing & to draw and the others to win, so if we do go down, at least i’ll be a few quid up to help finance the amount of drink i will need to deal with it 😉

  5. Ben

    I don’t think you are quite right in your goal difference scenario – it affects Birmingham, Blackpool and Wigan if one or more of them lose or win, but involes Wolves and Blackburn if they lose and others draw.

    Goal difference has the biggest effect on scenario 14 and others close to that number. If Blackburn beat Wolves by one goal (the minimum difference possible) and Birmingham draw then Birmingham now have the same goal difference as Wolves, and Wolves may or may not go down (depending on goals scored or whatever). If the difference is two goals then Blackpool can draw and have the same difference (Birmingham stay up), if three goals then Wigan have the same difference, but get relegated on 40 points as well as Wolves if Birmingham and Wigan also draw or win. MY HEAD HURTS!

    Blackburn’s better goal difference is a real boost if it is they rather than Wolves that lose as then they would have to lose by 5 more goals to be in the same situation (i.e. 6:0, 7:0, 8:0) – surely not even Blackburn can manage that…

  6. Ben

    More on the goal difference issue – a quick count says that about 30 of your 81 scenarios involve at least two teams drawing for 17th and 18th places. Goal difference is important for all these except for 41,42,44,50, where the teams in 17th and 18th have both drawn so goal difference doesn’t change.

    This means that 26 scenarios have at least 2 permutations based on goal difference, some more (if three teams are drawn for 17th, 18th and 19th), so the possibilities are well over 100.

  7. Ben

    Following Nick’s suggestion I ran a Monte-Carlo simulation (in Excel) to simulate all game results with each team in each game having an equal chance of scoring 0 to 3 goals. This is a big assumption as it doesn’t take into account the actual probability of each result – e.g. Blackpool’s chance of winning 3:0 at Old Trafford are probably quite slim.

    Ignoring these issues I ran the simulation 100000 times and ranked the teams according to points, then goal difference then goals scored.
    There were no absolute draws (equal points, goal-difference, goals scored).

    The percentage times each team was relegated are given in the second column, with the odds from a well-known bookmaker converted to a percentage and given in the third.

    Blackburn 13% 8%
    Wolves 25% 11%
    Birmingham 47% 62%
    Blackpool 53% 58%
    Wigan 62% 75%
    Sum 200% 214%

    The sum comes to 200% as two teams will be relegated. The bookies’ odds come to more because of their profit margin. On the face of it the bookies seem to underestimate Blackburn’s chances of relegation and quite severely underestimate Wolves chances. I think that just shows the limitations of the assumptions I made earlier, so don’t put your mortgage on it.

  8. damian

    one thing that you have not taken in to consideration and from what i can see is ommited from your various scenarios is you say if wigan and blackpool both lose they are relegated – look again this is not correct

    if all 3 birmingham,blackpool and wigan all lose any 2 from three can go down

    ie wigan lose 1-0 gd – 23, if birmingham lose 3-0 they are down they also would be on -23 but have scored less goals – if blackpool lose by less than 3 goals they are safe they would also be on -23 but have scored more goals than both birmingham and wigan.

    i think there are 9 different permutations here to add to yours

    bottom line is all 3 can lose and any of them can stay up dependant on the goals against.

  9. Sean

    This is an interesting model and outcome. However surely it is overly simplistic, fundamentally flawed and tells us very little about the most likely outcomes on the football pitch this weekend.

    On the positive side, this gives a very crude insight into who is most likely to go down, given the potential outcomes. But this model assumes that all outcomes are equally likely. In reality, they are far from it. To get a more realistic picture, there must be something built in that accounts for differences in quality.

    For example, Blackpool travel to Man United, whereas Wigan are at Stoke. Stoke have a good home record, but where would you rather go needing a win to stay up? This could be done with some kind of points ranking based on league position. Although this would still not become totally accurate, we would end up with a much clearer picture by assigning some kind of likelihood of winning percentages based on the relative strength of the opposition etc? Because at the moment, this model isn’t going to predict anything…..

  10. steve

    Do your sums again. Blackpool can lose and still stay up. So it ain’t ‘pretty obvious’.

    (i.e. Birmingham also loses by quite a few goals making their GD worse than pools. And wigan lose too by either one less than Blackpool or more than one than Blackpool making either their GD worse or losing on goals scored).

  11. GJR

    That is not correct if say Wigan and/or Blackpool lose narrowly say by a single goal and Birmigham lose heavily then Birmingham would br relegated. So Either Wian or Blackpool could lose and stay up on goal difference.

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