Euros prediction (3)
OK: I’ve now re-run the model using the updated data including all the games after the group stage. Firstly, a few comments/caveates:
I think the model predictions for the round of 16 make kind of sense and I’m reasonably happy with them.
BUT: there’s lots that the model doesn’t really know… For example, I’ve made no real adjustment for the fact that this batch of games is at the knockout stage, which means that, probably, we may see fewer goals as some teams may have a different attitude and would rather not lose the game at the 90th minute, in search of penalty glory. As far as the model is concerned, these are just another set of games, which may well end in draws — and more importantly, the model doesn’t really account for tactics (overly-defensive teams etc). It wouldn’t be too hard, I think, to modify the model and, for instance, add a layer of complexity — maybe an interaction between the type of tournament and the stage (group vs knockout).
Interestingly, most (if not all) of the predictions are pretty much aligned with the latest odds (more on this below).
So: here’re the prediictions. 
When I saw that, I thought that perhaps the model was being a bit too generous with Denmark (and, to some extent, I still think it’s very much possible that Wales go through), but then again, this is very aligned with the bookies odds, which give Denmark at \(\frac{11}{12}\) — that is \[\frac{\Pr(\sf{\text{Denmark lose}})}{\Pr(\sf{\text{Denmark win}})} = \frac{11}{12}\] which implies \[\Pr(\sf{\text{Denmark win}})\approx 0.53.\] My model is a bit overly-enthusiastic about the Danes, I think — but also, note that the bookies’ odds do not sum to 1 (in fact, their sum is greater than 1 so that they don’t lose too much money, no matter what…).
If you rescale all the odds to probabilities and then ensure that they sum to 1, you get the following table.
| Game | Home | Draw | Away |
|---|---|---|---|
| Wales - Denmark | 0.1906 | 0.3050 | 0.5043 |
| Italy - Austria | 0.6354 | 0.2411 | 0.1235 |
| Netherlands - Czech Republic | 0.5764 | 0.2489 | 0.1747 |
| Belgium - Portugal | 0.3882 | 0.2939 | 0.3179 |
| Croatia - Spain | 0.1426 | 0.2560 | 0.6014 |
| France - Switzerland | 0.6359 | 0.2466 | 0.1176 |
| England - Germany | 0.3762 | 0.2946 | 0.3292 |
| Sweden - Ukraine | 0.4034 | 0.3074 | 0.2892 |
For all the games, the model seems to suggest the same favourite as the bookies — though I think there could be a couple of upsets (Croatia and Ukraine?).
Anyway — let’s see what happens!