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We ran the numbers: here's who will get relegated from the Premier League

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More than 200 scenarios remain for the Premier League run-in. We've run the numbers and here's who is most likely to be relegated.

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As things stand in the Premier League, there are 243 independent scenarios left for the seven teams who are still worried about relegation. That number is lessened a bit by the reality that some of the matches left to be played pit relegation contenders against one another Even with that mitigating factor, though, trying to figure out the three teams that will drop into the Championship at the end of the season is very difficult. But, as I did last year, I've gone ahead and run the numbers on the Premier League run-in to figure out what teams will drop, where safety will be, and how Aston Villa will do.

You can find the methodology of this study below, but I've found that math scares people, so let's get to the results! As things stand, it looks as if 37 points will guarantee Premier League safety this year. For Aston Villa, that means one more win or two draws. Either of those results are very achievable, and it's conceivable that by the time Sunday rolls around we're all breathing easily.

With that in mind, here are the bottom seven teams in order of most to least likely to reach 37 points, and thus be safe:

Team Chance of reaching 37 points
Newcastle United 87%
Aston Villa 86%
Leicester City 80%
Hull City 70%
Sunderland 47%
Queens Park Rangers 0%
Burnley 0%

We already knew this, but Burnley and QPR are essentially already relegated. Unless literally everyone else collapses and they go on a three-match winning streak to end the season they're done. Sunderland, then, are the only remaining team who are more likely to fall short of 37 points than to reach the mark. If we change to 38 points, the order stays the same but Hull join the under-50% crowd.

So, with our first run of the numbers (expect another next week) here's what we can say:

Likely safe: Newcastle, Aston Villa, Leicester, Hull

Likely relegated: Sunderland, QPR, Burnley

The good news is that those numbers-based predictions pass the logical eye test as well Heck, if the table ended up looking exactly like what you saw up there after the final whistle on May 24th, I wouldn't be surprised at all. But now, let's dig into the numbers a bit. If math is not your cup of tea, feel free to skip this bit.

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These calculations are all based on odds and probabilities. In a totally even world we might expect all three potential match outcomes (win, draw, loss) to have an equal chance of happening. But we all know that's not the case. For instance, when Hull played Arsenal on Monday, we all knew that the most likely outcome was an Arsenal win. Because of a dizzying number of variables, though, we have no great way to predict match outcomes and assign probabilities.

This is where bookies come in. Football gambling is an entire industry based on predicting the outcomes of matches and setting the lines such that the bookies will come out ahead. With that in mind, we can use the odds they set as a decent proxy for probabilities. Converting from odds to probability takes some simple algebra (see sidebar).

I grabbed my odds from Bet365.com, but for no other reason than they're easy to get to. As I write this, Aston Villa are 10/11 to win this weekend, 5/2 to draw, and 3/1 to lose. If you plug those numbers into the formula, you'll end up with probabilities that are close to 49.44%, 26.97%, and 23.60% respectively. I say close because all bookies add in a little leeway to their odds to help ensure a profit. In reality they all come out to numbers that add up to about 105%, but that's a quick thing to adjust for.

From there, we just multiply the probabilities of each outcome together to find the probability of a chain of outcomes. So, for instance, Aston Villa have ~50% chance of beating West Ham, ~16% of beating Southampton, and ~45% of beating Burnley. The chance of winning all three? Approximately 3.6%.

Aside from using odds as a proxy for probabilities, there is one additional problem with this method: no one (that I can find) has released odds for the May 24th matches. So for those I was torn between 1) giving everything a 33.3% chance of happening (which is just willfully dumb) and 2) making an educated guess at the probabilities of outcomes. I chose the second option, but tried to base my guess on similar matchups that I do have odds for (for instance, Newcastle hosting West Ham on the last day should be almost exactly the same odds as Villa hosting West Ham this weekend). For the sake of transparency, here are the percentage chances I gave each team's final-day outcome:

Team - Matchup % Chance of W/D/L
Burnley - @Villa 30/25/45
QPR - @Leicester 30/25/45
Sunderland - @Chelsea 20/20/60
Leicester - QPR 45/25/30
Hull - Manchester United 25/25/50
Newcastle - West Ham 50/25/25
Aston Villa - Burnley 45/25/30

You can argue with my choices there, but I think they're fairly reasonable, and unless you drastically change them, it doesn't alter the final numbers too much.

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So! You've now got the results and the methodology. What questions do you have? Do you hate this way of doing things? Do the numbers line up with your gut feelings? Let me know in the comments. I'll be sure to be around to answer anything!