One of the big topics on Twitter today has been whether Chelsea can still qualify for the top 4, and various folks have posted their predictions/simulations on what it will take. Michael Caley predicted 68.6 points, Colin Trainor and Simon Gleave have both agreed at 68 points, and I’m sure there are others out there. My model is a bit lower than the rest of these at 62 points, with 69 being my prediction for the third place team.
These results represent the mean points I expect each team to earn based on the remaining games and their probabilities of winning. For my predicted table I don’t do any simulations, just some simple arithmetic to get there1. Someone else on Twitter asked the question “Don’t models underpredict?” and while the right answer is no, there is some truth to this point, and that truth explains why Chelsea is probably less likely to win that fourth place spot than even the most skeptical models say (and far less than mine).
Right now I have four teams roughly tied for fourth place – Chelsea, Spurs, Liverpool, and Leicester City. Each of those teams is expected to earn between 60 and 62 points, which is a pretty tight race. But logically we’d expect a very different outcome. While we’d expect the teams to cluster around the mean, it’s likely that one team will find a purple patch, and that team will be the one who captures the 4th and final spot in the Champions League. So what do the simulations say?
DISCLAIMER: My model clearly overrates Chelsea so take their numbers with the largest grain of salt you can imagine. However, the model overvaluing Chelsea only means it’s going to be less likely we see these high point values for the 4th place team.
This density plot shows the results of 10,000 simulations, showing the number of points each of the current contenders for the 4th place spot (ignoring those in the expected top 3) earns and the frequency of those outcomes. Chelsea has a decent chance of earning 65 points, and a low chance of earning 69 points, even at their overstated current expectations. The other three teams have a much lower likelihood of each of those outcomes. Spurs seem to have a slight but important advantage over Liverpool and Leicester, but that could change as we get more results. Leicester clearly is the least likely of these teams to make the top 4 but they’d have to be elated to even be in the conversation at this point.
The next plot shows the likelihood of each team finishing with over 65 points. Chelsea about a 43% chance of breaking 65 points (again, see the disclaimer above), while the others are 20% or less. The joint probability of at least one of these teams finishing with over 65 points is 57%, and one of the teams other than Chelsea finishing higher than 65 is about 24%. Even given the idea that one of the teams could hit a hot streak and overachieve, or in Leicester’s case overachieve even more than they already are, we’re looking at an unlikely low point total for the 4th place team.
Finally, I look at the likelihood of finishing at 68 points or higher. Chelsea again leads the pack at about 31% (disclaimer), while the others are pretty unlikely to finish that well. Spurs are a little above 10%, Liverpool at about 7%, and Leicester at about 1%. At least one team will finish at 68 or higher 40% of the time, and a team other than Chelsea will finish at 68 or higher 14% of the time.
My simulations indicate we’re going to see a much lower point total required for the Champions League than we’re used to, and a more competitive race for that spot than we’ve seen in years. Depending on what happens with Chelsea and if Leicester can keep up their pace, it could be a great finish to the season.
- I just do 3*(win prob)+ 1*(draw prob) + 0*(loss prob) ↩