The Oracle (6)
Quick update, now that the group stage is finished. We needed a few tweaks to the simulation process (described in some more details here), which we spent some time debating and implementing.
First off, the data on the last World Cups show that during the knock out stage, there are substantially fewer goals scored. This makes sense: from tomorrow it’s make or break. This wasn’t too difficult to deal with, though $-$ we just needed to modify the distribution for the zero component of the number of goals ($\pi$, as described here). In this case, we’ve used a distribution centered on around 12% with most of the mass concentrated between 8% and 15%.
These are the predictions for the 8 games. Brazil, Germany, France and (only marginally) Argentina have a probability of winning exceeding 50%. The other games look closer.
Technically, there is a second issue, which is of course that in the knock out stage draws can’t really happen $-$ eventually game ends either after extra time, or at penalties. For now, we’ll just use this prediction, but I’m trying to think of a reasonable way to include the extra complication in the model; the main difficulty is that in extra time the propensity to score drops even further $-$ about 30% of the games that go to extra time end up at penalties. I’ll try and update this (if not for the this round, possibly for the next one).