Survival Sunday is almost upon us and my earlier post on the number of scenarios appears to have stirred up feelings – see The Premier League: predicting who will go down (and the strange case of scenario no. 55). To recap, there are 5 teams separated by only one point who could all get relegated to the Championship. I calculated that there are 81 possible scenarios based on a simple win, draw or lose. I then worked out the percentage of the scenarios in which the teams went down (see Figure 1 below) such that overall the chances of relegation are Rovers 11%, Wolves 24%, Birmingham 48%, Blackpool 58%, and Wigan 67%.

The main criticism of this approach was that it didn’t take into account goal difference or the number of goals scored. In particular, it was easy to point out that Wigan, say, could significantly improve their chances by scoring a couple of goals at demoralised Stoke. So I decided to have a look at potential scores in the games on Sunday to answer the basic question:

**What does my team have to do to escape relegation?**

### The Rules of the Game: Monte Carlo or Bust

So firstly, what are the Premier League rules for Sunday? In the case of a tie in the number of points, then position in the table is decided on goal difference and then on goals scored. If there is still a tie then the two teams play a further game at a neutral venue.

This information allowed my colleague Dr Ben Heller to create a spreadsheet which used the Monte Carlo method to calculate the potential position of all 5 teams based upon any score in any game (NB: the Monte Carlo method was created by two nuclear scientists at Los Alamos in the 1940s as they worked on the Atomic Bomb project).

The simulation here used 500,000 random scores with a maximum of 3 goals per team to get a feel for what was the likeliest to happen. The games looked at were the following: Man Utd-Blackpool, Stoke-Wigan, Tottenham-Birmingham and Wolves-Blackburn. The maximum score in the any of the games was 3-3 and the most a team could win by was 3 goals.

### How to avoid relegation

Table 1 shows the chances of relegation for each team depending upon whether they draw, win, or lose by the goals specified. If Blackpool win by 1 goal then they will only have a small chance of relegation and if they win by 2 are more or less likely to stay up (remember we only go up to 3 goals scored for any team). The following sections identify what each team has to do to stay up within the assumptions of our model.

Blackburn have it easiest of all teams because of their superior goal difference (minus 14). Even if they lose by 3 goals they still only have a 32% chance of relegation. A draw – probably the likeliest outcome from a Rovers point of view – gives them only a 5% chance of relegation while if they win by any margin they are safe. **Rovers tactic – do not lose.**

The chances of Wolves going down if they lose depends upon how many goals they concede – the larger the margin the higher their chance of getting relegated. Even a draw has a 31% chance of relegation. Any win guarantees them safety so they should go all out to beat Blackburn. *Wolves tactic – go for the win.*

Birmingham are in a tricky position – if they lose by any margin then they are highly likely to go down. Even a draw isn’t much good with more or less a 50/50 chance of relegation. Birmingham really have to win to stay up but even a win by 1 goal has a very small chance of relegation (because the teams below them could still in a few circumstances overtake them if they score enough goals).* Birmingham tactic – win by at least one goal, two should do it.*

Probably the neutral supporters favourite team, Blackpool are in the position where a draw at Manchester United gives them a two thirds chance of relegation and any loss rapidly approaches 100%. A win is a must but even then, a win by 1 goal still has a tiny chance of relegation (for instance, Wigan could overtake them by scoring enough goals). **Blackpool tactic – win by at least one goal, two should do it.**

As the bottom team, it’s no surprise really that Wigan have the greatest chance of relegation and even a draw has an 86% chance of relegation. Winning by 1 or 2 goals at Stoke reduces the chance of a drop to 11% and even a win by 3 still has a 3% chance of relegation. *Wigan*** tactic – win by at least one goal and hope for the best.**

**What about a tie?**

It seems that the chances of a tie are nil since there is no combination where there can be the same goal difference and the same number of goals scored. So not this year.

### The dynamics of Survival Sunday

The probabilities here show what the teams need to do to survive the relegation battle based upon the assumption that winning by more than 3 goals is unlikely. Of course, at 4pm on Sunday, everyone is on 0-0 and if nothing changes Wigan and Blackpool go down. If Blackpool score, say, then they swap places with Birmingham and all the probabilities change. I might attempt to do a blog on the dynamics of what happens on Sunday, but this probably depends upon whether my team (Rovers) go down or not.

In the meantime – good luck everyone!

**Update: 3.30pm Survival Sunday**

My mate Lee Hickey at Games Faction has written a computer programme to do a rather complex analysis involving home and away form. His current take on the overall chances of relegation:

Blackburn (4.6%)

Wolves (6.3%)

Birmingham (48.4%)

Wigan (69.8%)

Blackpool (70.9%)

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Nick RichNow that’s one hell of a way to respond to comments/critique…Fantastic job gents!

stevehaakeThanks Nick – enjoy the games (if you can!)

Arjun KatroSteve

Just came across this searching to an answer to a different question. Fantastic analysis.

What I wondered was whether it was practically possible for someone to do an MCS for the EPL to work out the probability distribution and likely points requirement to avoid relegation (to finish 17th). You’d need some simplifying assumptions like wins are 1-0 and draws 0-0, etc to avoid complicated GD scenarios. There is a finite (though very large – 1.8bn?) number of scenarios so it may be extremely difficult to actually run but it would show the number of points needed and also the probability distribution (e.g. 90% of the time 39pts is enough, etc). You could also then take a snaphot mid-season as that EPL table would be identical to one of the scenarios (omitting GD discrepancies to actual positions)

I just get infuriated with pundits talking vaguely about 42pts being the “magic number” so it would be nice to have some numbers!

What are your thoughts?

Arjun