So, we are down to the 3rd place match and the final. My model likes Germany to win the 3rd place match and Spain the final. I personally want to see Germany and the Netherlands win. We’ll see.

The model continues to perform within expectations.

Matches for the quarterfinals have been determined. Here is how the knockout round is going so far. The matches for the semifinals, third place match, and final (all in italics) are theoretical and based on the probabilities up to the quarterfinals.

As to the model accuracy to this point — it is still doing well.

Let’s start with the advancements to the Round of 16. The probabilities in the model were calculated using FIFA rankings at the beginning of the tournament. I did not adjust the probabilities after each match like I do for the match predictions. It’s possible to do so, but more work than I wanted to do this year. Still, the model faired well, though performing slightly better than expected.

The model continues to do well with the match to match probabilities.

So, for the knockout round so far and the probabilities for upcoming matches which have been determined:

Eight teams have advanced. How well did my model predict those teams? Within expectations. Here is the analysis.

As for the match to match probabilities: 

And here is the results table with the probabilites for upcoming fixtures, including Round of 16 matchups that have already been determined.

After the first twelve matches completed, I revised my methodology for probabilites. The old method was: 

1. Start with the FIFA ranking points
2. Add my modifier based on injuries, regional adder (+50 points for African teams), and my personal assessment of momentum
3. Calculate a probability factor as 10^(points/400)

The tendancy of this method was to overrate the good teams. I modified step 3 to be closer to what I used in the 2006 World Cup:

1. Start with the FIFA ranking points
2. Add my modifier based on injuries, regional adder (+50 points for African teams), and my personal assessment of momentum
3. Use the points as the initial probability factor

Since this World Cup I am also recalculating the probabilities after each match, I needed to modify how to get the probability factor for each subsequent match. I use Elo ranking to do this. (See Wikipedia for a good article on Elo ranking.) Following the notation in the Wiki article, I use the FIFA points as the team’s initial Q. I back-calculate R. From there I recalculate R after each match then forward-calculate the new Q. Simple, right?

Well, here is how the new method looks diagnostically:

And now the prediction table, with current results added.

With each team having completed their first match, it is a good time to check in on the accuracy of my modelled predictions. As you can see below, the model underperformed. This was driven largely by upsets against the biggest favorites.

This chart shows in blue the distribution of possible outcomes assuming the model is correct. The red bar represents the actual model performance. Notice that it is just barely in distribution. Basically, at predicting a winner, so far the model is just a little better than flipping a coin.

As this model fit shows, the model underperformed primarily at the high end, meaning the biggest favorites ended up being the biggest upsets. Greece, Camaroon, and Spain all lost and Mexico, Italy, Slovakia, and Portugal all tied. It’s like my brother, Daniel, says: “Anything is possible at the World Cup.”

Here are updated predictions for the remainder of group play, with the results so far.