* - Okay, 14 best teams and 2 host teams. But even the host nations are pretty good: There's no North Korea losing games 7-0.
The group stage just finished, and the tournament is about to get underway. Of the eight teams remaining, who has the best chance of winning it all?
For baseball and basketball games, you can calculate the expected win probability for a single game from the two teams' Pythagorean records using the log5 method. For international soccer, you can use the Elo ratings to determine the expected win probabilities. The formula looks like this:
We = 1 / (10(-dr/400) + 1),
where dr is the difference in Elo rankings between the two teams.
Once you know the probability that a team wins its first game, you can compute the probability that team wins its second game using conditional probabilities. Like this:
P(wins first game)*(P(beats potential opponent A)*P(potential opponent A wins first game)+P(beats potential opponent B)*P(potential opponent B wins first game))
Keep doing that and you eventually get win probabilities for the entire tournament:
And you're never going to believe this, but the teams with the best ratings are the ones with the highest chances to win. You can see that the probabilities depend a bit on matchups: France has only a 17% chance of knocking off Spain in the first round, but a 2.5% chance of winning the championship, whereas the Czech Republic has a 35% chance of beating Portugal but a 1.5% chance of making the finals, since they'd have a lower win probability against the remaining teams if they did advance.
Comparing the odds to the betting markets, it looks like Spain might actually be a good wager: if you believe this method, their odds to win are 2.3-to-1, but the books have them listed at 2.6-to-1. Practically everyone else is overvalued, but laughably so for Portugal (listed at 7.5-to-1), Italy (9-to-1), and France (12).
UPDATE #1: June 21, 4:45 p.m.
Here's what the odds look like after Portugal's win over the Czech Republic:
UPDATE #2: June 22, 4:45 p.m.
Here's what the odds look like after Germany's demolishing of the Greeks:
* - This always looks wrong to me, but everyone else does it. My least favorite thing about soccer.
UPDATE #3: June 25, 9:15 a.m.
Here's what the odds look like after this weekend's games, including the first upset of the knockout stages as the favored England side screwed up some penalty kicks to lose to Italy in a shootout:
This is the last update here, but I'll still post updates on Twitter. Italy's odds are slightly better than Portugal's, just because Germany has a lower rating than Spain's. I do like the fact that every German game from here out (vs. Italy, then vs. Spain/Portugal winner) is another Bailout Bowl, though some of that has to do with the woeful state of the Eurozone.