If you'd like to get a grip on the possible relegation scenarios remaining in the Premier League, it will take a dizzying amount of math. Trust me, I spent most of yesterday doing it so that you don't have to! First, let's give you the good news that you want so badly to hear: by all accounts, Aston Villa should likely be safe regardless of what happens in the rest of the season. Some other teams may have a bit more to worry about though.
For the sake of having a firm line to look at, I've assumed that 36 points will absolutely equal safety this year and that 35 will be the cut line. It may change in the coming days, but as things stand now that seems to be the wise choice. With that in mind, here are the bottom six teams in order of most-to-least likely to reach 36, and thus be safe:
|Chance of reaching 36 points
|West Bromwich Albion
From this, we can also assume that the three teams most likely to be relegated to the Championship next year are Cardiff, Norwich, and Fulham. By beating Chelsea last weekend, Sunderland may have miraculously saved their season and their standing in the top flight of English football.
Now, a few words on the math and assumptions that went into those numbers. Beware: beyond here is algebra!
Let's take Norwich, for example. With three matches remaining, they have 27 possible unique outcomes (unique meaning that Win-Loss-Loss is different than Loss-Win-Loss despite the fact that they will net the same amount of points). In 16 of their remaining 27 scenarios, Norwich reach that magical number of 36. If we don't weight anything, that would give them a 59.25% chance of getting there.
The problem with that, though, is that we all know that Norwich are far more likely to lose to Manchester United at Old Trafford this weekend than they are to win. Not weighting assumes that a win, draw, and loss all have an equal probability of 33.3%.
Well, there isn't a really great way to figure out what a team's probability of winning are scientifically, but thanks to the huge gambling industry, we do have plenty of very smart people working to figure out the odds of the remaining matches this season. You can convert odds to probability using a fairly simple formula (see sidebar), and from there weight things pretty easily.
To finish the Norwich example, they have -- according to the odds -- a 10.84% chance of beating Manchester United this weekend. To figure out their chance of that followed by them beating Chelsea at Stamford Bridge in the following weekend, we simply multiply 10.84% by the 7.8% chance they have of winning there. To see if Norwich can win out, we multiply their odds of beating Manchester United, Chelsea, and Arsenal to get a 0.33% chance of that happening.
Do this for all of the possible scenarios, and you can then add together the chances of all scenarios in which Norwich reach 36 points to get the 23.34% number above.
There is, of course, some margin for error here. For instance, for teams with four matches remaining (Sunderland, WBA, Villa), the odds for the final match of the season are not quite as accurate as those for this weekend. Betting websites build in a little wiggle room to assure themselves of a profit. For this weekend, the probabilities of all three outcomes pretty uniformly add up to 106% (that 6% helps give the companies a bit of a margin of error). That's easily corrected for by saying that if a win is (for instance) 55% out of 106% then it's 51.8% out of 100%.
As the matches get further away, though, the oddsmakers build in more cushion. The probabilities for Villa's last match of the season end up adding to around 150%. In reality, this makes a lot of sense, since it's hard to tell how both Villa and Tottenham will be playing by then.
Nevertheless, given the information we have at hand, I'm confident that these are the best numbers available. With four teams unlikely to get 36 points, Villa should be safe if they can get just one more. And realistically, given goal differential, they are probably safe even if they don't. Still, a draw would be pretty nice tomorrow.