"Fast kickin', low scorin',...and ties--you bet!"
I just returned home to the good ol' USA after a week overseas. Evidently, there is some sort of sporting tournament underway in some other country somewhere. It's confusing because sometimes they call this sport "football," except that it's the same sport my daughter played when she was five. Too funny! Still, it is considered a real sport by some, and so it's my job to suck the fun out of it by creating a Win Probability (WP) model, making you realize there's no chance your favorite team can come back to win.
The model I used is a simple Poisson model, which is the same technique I used for NHL hockey. It looks at how often teams tend to score and how much time is left in the game to calculate the likelihoods of possible outcomes. It adds up the chances for all the possible final scores where the trailing team comes back to win, and that's the WP. The parameters of the model are based on the most recent World Cup tournament in 2006.
The model is relatively rough because it does not consider strategy effects. In other words, if a team is ahead, it may alter its strategy to preserve its lead at the expense of scoring more goals, thus maximizing their chances of winning. And if a team is trailing, it may alter its strategy to bias toward scoring at the expense of possibly giving up a larger lead to its opponent. However significant these effects, they would likely cancel out to a large degree, leaving the ultimate win probabilities close to the idealized estimates in the Poisson model.
Additionally, the model is generic. A great team that happens to be down by a goal probably has a better chance of winning than a lousy team down by a goal. Nevertheless, the WP numbers are good guideposts, particularly in the elimination round when team strength is relatively equal.
WP for soccer is slightly more complicated than most other sports because of the ties. In the group round, where teams play a round robin schedule within a 4-team group, ties are allowed (and common). The top eight teams from group play begin a single-elimination tournament, which does not allow ties. There is also the matter of stoppage. Play continues past the 90-minute mark to account for the time taken for stoppages in play. Only the officials know exactly how much time is really left in the game.
For group round play, here is the WP of the trailing team for winning outright (no tie). For example, at the 30-minute mark (with 60 minutes left to play), a team trailing by one goal would have about a 11% chance of winning outright.
And here is the probability of a tie as the final result. In this case, a team down by one goal would have a 21% chance of forcing a tie on top of its 11% chance of winning outright. That would leave about a 69% chance of winning outright for the team currently ahead by a goal.
For the elimination round, things are a little simpler because there can be no ties. In this case, I assume a 50/50 chance for each team in a penalty kick shootout. Here is the WP for the trailing team:
In this case, a team down by a goal at the 30-minute mark has a 22% chance of winning, either outright or via shootout. (This is simply the teams 11% chance of winning outright, plus half the chance of a tie.)
I'll leave you with one of the greatest moments in soccer history, the 1994 Mexico-Portugal classic:
Extra credit to anyone who knows where the term "soccer football" comes from. No cheating using Wikipedia.