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(By Achim Zeileis)
Three weeks we had published a Predictive Bookmaker Consensus Model for the UEFA Euro 2016 that provided probabilistic forecasts for all teams in the UEFA European Championship 2016. By combining bookmaker odds with simulation techniques and paired comparison models we obtained not only a winning probability for each team but also estimates of the abilities (or strengths) of each team. Now after the group stage of the tournament is completed it is time to take a first look back and update our expectations about the knock-out phase of the tournament.
Overall we have seen many close and exciting matches with many expected and some unexpected outcomes. However, there were no huge surprises and all tournament favorites advanced to the next stage. Compare that to the last FIFA World Cup where Spain was eliminated in the group stage and Costa Rica won the “group of death” and eliminated both Italy and England. Nevertheless, the expectations about the winning probabilities changed rather clearly! The reason for this is not so much a change in the (now revealed) abilities of the teams but the “sloppiness” of England and Spain in not winning their groups which resulted in a rather unbalanced knockout stage.
To quantify these observations that were also observed in many other media, we re-ran our entire predictive bookmaker consensus model. Thus, we obtained the current (as of 2016-06-23) winning odds from the same bookmakers as a month ago, removed their overrounds and averaged them (on the logit scale) to winning probabilities. This shows some fairly large changes: France and Germany are still the top favorites but their absolute winning probabilities decreased while there are large increases, especially for Belgium and Croatia.
Simulating the possible courses of the remaining tournament (100,000 times) to infer which possible match results can lead to the probabilities above, we obtained again estimates of the abilities of each team. These are then adjusted for the rather imbalanced tournament draw with top teams France, Germany, Spain, England, and Italy in the same leg of the tournament (i.e., only one of these teams can proceed to the final). Somewhat surprisingly the estimated team abilities of most teams are almost unchanged compared to our results from before the start of the tournament. There are moderate decreases for France and Germany who were not quite as strong as expected by the bookmakers and a moderate increase for Spain whose performance was more convincing. The biggest change is observed for Croatia who won group D against Spain. But not that the ability of Belgium is almost unchanged while their winning probability (see above) increased by almost 5 percentage points. (The clear decreases of the abilities of Iceland and Northern Ireland have to be taken with a grain of salt as the exact abilities of the weakest teams are hard to estimate precisely.)
These moderate changes in the abilities are also reflected in the relatively small changes in the predicted pairwise probabilities for the matches in the round of 16. The table below shows all eight matches with the corresponding winning probability (in %) for the team listed first. Our corresponding predicted pairwise probabilities from before the start of the tournament are given in parentheses for comparison.
In summary, the tournament draw with the complicated determination of the 16 teams that advance to the knockout stage has lead to a somewhat surprising situation with rather different winning probabilities for the championship. However, only a small part of this can be attributed to changes in the now revealed team strengths.