Lunar Motion Posts

The World Cup 2026 is over. Below is the basic analysis of model accuracy through the end of the tournament. The blue bars represent the distribution of expected results, the red bar represents the actual model performance and the darker blue bars represent roughly the middle 90 percent of expected results.

The model consistently over-predicted the match results up until the semifinals. The cumulative over-prediction was statistically significant with the 90-percent confidence interval between 62.3 and 77.8. This means that through the tournament, the FIFA rankings and my adjustments underestimated the chances the favored team had of winning the match. This effect was driven largely by the second round of the group stage, and the knockout rounds through the Quarterfinals. Indeed, the three rounds of knockout play only saw three upsets (Paraguay and Switzerland on penalty kicks and Norway in regular play) where we would have expected about 10 or 11 upsets. There were no upsets in the Quarterfinals. However, the Semifinals, the Third Place match, and the Final saw three upsets out of four matches. See the chart below where the blue line and dots with error bars represent the actual performance with 90% confidence intervals and the gray dash represents the expected model performance.

Throughout the tournament we saw an effect where when the game mattered more, the favored team performed better than the model. This held true until the final four matches where we saw three upsets. In summary, the data suggests that the FIFA rankings are good predictors for the outcome probabilities of matches for friendlies, qualifying matches, and group stage matches where a loss or tie is not a tournament-breaker.

Below is the basic analysis of model accuracy through the end of the Quarterfinals. The blue bars represent the distribution of expected results, the red bar represents the actual model performance and the darker blue bars represent roughly the middle 90 percent of expected results.

The model continues to over-predict the match results. The cumulative over-prediction is statistically significant with the 90-percent confidence interval between 60.3 and 75.5. This means that through the Quarterfinals, the FIFA rankings and my adjustments underestimate the chances the favored team has of winning the match. This effect is driven largely by the second round of the group stage, and all of the knockout rounds. Indeed, the three rounds of knockout play only saw three upsets (Paraguay and Switzerland on penalty kicks and Norway in regular play) where we would have expected about 10 or 11 upsets. There were no upsets in the Quarterfinals. See the chart below where the blue line and dots with error bars represent the actual performance with 90% confidence intervals and the gray dash represents the expected model performance.

Here are the Semifinal probabilities based on rankings updated from the Quarterfinal results. Scores will be updated periodically throughout the round.

Below is the basic analysis of model accuracy through the end of the Round of 16. The blue bars represent the distribution of expected results and the red bar represents the actual model performance.

The model continues to over-predict the match results. The cumulative over-prediction is statistically significant with the 90-percent confidence interval between 58 and 73. This means that through the Round of 16, the FIFA rankings and my adjustments underestimate the chances the favored team has of winning the match. This effect is driven largely by the second round of the group stage, the Round of 32 and the Round of 16. Indeed, the two rounds of knockout play only saw three upsets (Paraguay and Switzerland on penalty kicks and Norway in regular play) where we would have expected about eight upsets. See the chart below where the blue line and dots with error bars represent the actual performance with 90% confidence intervals and the gray dash represents the expected model performance.

Here are the Quarterfinal probabilities based on rankings updated from the Round of 16 results. Scores will be updated periodically throughout the round.

Below is the basic analysis of model accuracy through the end of the Round of 32. The blue bars represent the distribution of expected results and the red bar represents the actual model performance.

The model continues to over-predict the match results. The cumulative over-prediction is statistically significant with the 90-percent confidence interval between 53 and 67. This means that through the Round of 32, the FIFA rankings and my adjustments underestimate the chances a team has of winning the match. This effect is driven largely by the second round of the group stage and the Round of 32. Indeed, the Group of 32 only saw one upset (Germany on penalty kicks) where we would have expected five or six upsets. See the chart below where the blue line and dots with error bars represent the actual performance with 90% confidence intervals and the gray dash represents the expected model performance.

Here are the Round of 16 probabilities based on rankings updated from the Round of 32 results. Scores will be updated periodically throughout the round.

Below is the basic analysis of model accuracy through the end of the group stage. The blue bars represent the distribution of expected results and the red bar represents the actual model performance.

The model continues to slightly over-predict the match results, though the cumulative over-prediction is not statistically significant. This means that through the third round and the completion of the group stage, the FIFA rankings and my adjustments are good indicators of the chances a team has of winning the match. It is interesting to note that the second round over-prediction by itself was a statistical anomaly with the expected model performance falling below the lower 90% confidence interval of the actual performance. See the chart below where the blue line and dots with error bars represent the actual performance with 90% confidence intervals and the gray dash represents the expected model performance.

Here are the round of 32 probabilities based on rankings updated from the third round results. Scores will be updated periodically throughout the round.

With the conclusion of the second round, below is the basic analysis of model accuracy. The blue bars represent the distribution of expected results and the red bar represents the actual model performance.

The model now seems to slightly over-predict the match results, though the over-prediction is not statistically significant. This means that through the second round, the FIFA rankings and my adjustments are good indicators of the chances a team has of winning the match.

It is interesting to note that favored teams did perform slightly better in the second round as seen in this trend chart. The dots represent the match result; 0 means the favored team lost, 0.5 means the match was a tie, and 1 means the favored team won. The heavy red line is the four-game moving average. The light gray dashed line is the expected model mean. The red dashed line is the actual model mean. The vertical lines separate the different tournament stages.

From this, we can see the favored team performance improving in the second round. Perhaps this is to be expected.

With that, here are the third round probabilities based on rankings updated from the second round results. Scores will be updated periodically throughout the round.

My model for World Cup match win probabilities is based on the FIFA rankings which are based on an Elo ranking system. I made adjustments to each team’s ranking score based on the geography. It is well established that teams from the continent of play perform better than those who have to travel farther. I do give consideration to where team players are based for club play. Below is the basic analysis of model accuracy. The blue bars represent the distribution of expected results and the red bars represent the actual model performance.

The model is right on target. This means that the FIFA rankings and my adjustments are good indicators of the chances a team has of winning the match.

With that, here are the second round probabilities based on rankings updated from the first round results. Scores will be updated periodically throughout the round.

The World Cup started today. Here are my probabilities of all the first round matches. Scores updated at the end of the first round.