Even though these results are the most likely, the odds that I predicted each match correctly are absurdly small, i.e., one out of the number of particles in the universe sort of small.
What I would really like is to estimate the probability that the top 5 positions will be what I have predicted.
Unfortunately, we can't compute this probability exactly. The number of possible outcomes to consider is 3^82, which is another "number of particles in the universe" sort of number.
Fortunately, we can compute this probability approximately, via random sampling. And of course, I couldn't stop myself from wasting a half an hour doing just that. So I will now describe the results.
The five most likely outcomes are the following:
- 15% — Man United, Arsenal, Chelsea, Man City, Tottenham
- 13% — Arsenal, Man United, Chelsea, Man City, Tottenham
- 8% — Man United, Arsenal, Chelsea, Tottenham, Man City
- 6% — Man United, Chelsea, Arsenal, Man City, Tottenham
- 6% — Arsenal, Man United, Chelsea, Tottenham, Man City
After this, we get a slowly decaying tail with many other possible outcomes. In particular, the outcome I chose above — the one that includes the most likely outcome for every match — has a 3.8% chance of occurring. Hence, it may very well be the case that I'd have done better in the contest to choose one of the less likely outcomes that results in the most likely final ordering for the top 5 teams.
The likely winner of the title this season is:
- 54% — Man United
- 39% — Arsenal
- 7% — Chelsea
Finally, the odds of taking a Champions League spot are:
- 100% — Man United
- 100% — Arsenal
- 98% — Chelsea
- 69% — Man City
- 29% — Tottenham
- 5% — Liverpool
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