Earlier today, I ran the numbers on all 324 scenarios remaining for the bottom six teams in the Premier League. The goal was to figure out what the probability was of each team reaching 36 points, and thus being safe. Graham MacAree, of We Ain't Got No History, pointed out that, with those numbers, there should be some way to figure out how many points each team should end the season with. And he was absolutely right!
As with earlier, I'll give you the numbers first, and then if you're interested you'll find the math a bit further down. If the rest of the season plays out by the odds, here is what the bottom of the table should look like after the last whistle has blown on May 11:
|West Bromwich Albion
Using these numbers, it seems as if 35 points, rather than the 36 I predicted earlier, will equal safety. Sunderland and Norwich City ended up with point differences that are statistically negligible, and re-running the numbers on the chances of reach 35 or more points reveal mostly the same information. It seems as if Norwich actually have a slightly better chance of reaching 35 points than do Sunderland, but not by enough to be significant.
So what can we say from all of this data? Cardiff City and Fulham seem almost certain to join the Championship, while Aston Villa and West Bromwich Albion are almost certainly safe. The two teams left, Sunderland and Norwich City, are essentially a coin flip at this point. Now, let's quickly look at the math for the sake of transparency. As with earlier, beare of the algebra that lies ahead.
If there is a 40% chance of a team getting 34 points and a 60% chance of them getting 36, that means that given 100 runnings, we'd expect to see them get 34 points forty times and 36 sixty. From there, figuring out their expected points is a fairly easy adaptation of the basic averages formula, which you may remember is:
(Sum of all quantities) ÷ (Number of quantities) = Average
Applying that to the scenario above, we can assume the number is 100, and the sum of the quantities is the forty times of 34 and the sixty times of 36, thus getting us:
((40*34) + (60*36)) ÷ 100 = 35.2
Simply do that with all of the possibilities remaining for each club (81 for Sunderland, WBA, Villa; 27 for Fulham, Norwich, Cardiff) and you've got the probable number of points that each will end with.
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