Category: Math & Statistics

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.

	Team	FT	ET	PK
20%	Paraguay
80%	France
32%	Canada
68%	Morocco
41%	Portugal
59%	Spain
47%	United States
53%	Belgium
68%	Brazil
32%	Norway
44%	Mexico
56%	England
77%	Argentina
23%	Egypt
45%	Switzerland
55%	Colombia

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.

	Team	FT	ET	PK
67%	Germany	1	0	3
33%	Paraguay	1	0	4
82%	France	3
18%	Sweden	0
38%	South Africa	0
62%	Canada	1
49%	Netherlands	1	0	2
51%	Morocco	1	0	3
55%	Portugal	2
45%	Croatia	1
74%	Spain	3
26%	Austria	0
76%	United States	2
24%	Bosnia and Herzegovina	0
57%	Belgium	3
43%	Senegal	2
62%	Brazil	2
38%	Japan	1
48%	Ivory Coast	1
52%	Norway	2
65%	Mexico	2
35%	Ecuador	0
78%	England	2
22%	DR Congo	1
88%	Argentina	1	2
12%	Cape Verde	1	1
49%	Australia	1	0	2
51%	Egypt	1	0	4
59%	Switzerland	2
41%	Algeria	0
79%	Colombia	1
21%	Ghana	0

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.

	Home			Away
25%	Scotland	0	3	Brazil	75%
87%	Morocco	4	2	Haiti	13%
54%	Switzerland	2	1	Canada	46%
45%	Bosnia and Herzegovina	3	1	Qatar	55%
26%	Czechia	0	3	Mexico	74%
34%	South Africa	1	0	Korea	66%
27%	Curaçao	0	2	Côte d’Ivoire	73%
33%	Ecuador	2	1	Germany	67%
65%	Japan	1	1	Sweden	35%
23%	Tunisia	1	3	Netherlands	77%
32%	Türkiye	3	2	USA	68%
46%	Paraguay	0	0	Australia	54%
24%	Norway	1	4	France	76%
70%	Senegal	5	0	Iraq	30%
48%	Egypt	1	1	IR Iran	52%
15%	New Zealand	1	5	Belgium	85%
47%	Cabo Verde	0	0	Saudi Arabia	53%
32%	Uruguay	0	1	Spain	68%
22%	Panama	0	2	England	78%
76%	Croatia	2	1	Ghana	24%
48%	Algeria	3	3	Austria	52%
10%	Jordan	1	3	Argentina	90%
47%	Colombia	0	0	Portugal	53%
54%	Congo DR	3	1	Uzbekistan	46%

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.

	Home			Away
56%	Czechia	1	1	South Africa	44%
72%	Switzerland	4	1	Bosnia and Herzegovina	28%
63%	Canada	6	0	Qatar	37%
61%	Mexico	1	0	Korea	39%
86%	Brazil	3	0	Haiti	14%
28%	Scotland	0	1	Morocco	72%
62%	USA	2	0	Australia	38%
57%	Türkiye	0	1	Paraguay	43%
65%	Germany	2	1	Côte d’Ivoire	35%
76%	Ecuador	0	0	Curaçao	24%
69%	Netherlands	5	1	Sweden	31%
31%	Tunisia	0	4	Japan	69%
75%	Uruguay	2	2	Cabo Verde	25%
83%	Spain	4	0	Saudi Arabia	17%
62%	Belgium	0	0	IR Iran	38%
25%	New Zealand	0	3	Egypt	75%
41%	Norway	3	2	Senegal	59%
86%	France	3	0	Iraq	14%
76%	Argentina	2	0	Austria	24%
33%	Jordan	1	2	Algeria	67%
85%	England	0	0	Ghana	15%
34%	Panama	0	1	Croatia	66%
77%	Portugal	5	0	Uzbekistan	23%
71%	Colombia	1	0	Congo DR	29%

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

	Home			Away
75%	Mexico	2	0	South Africa	25%
59%	Korea	2	1	Czechia	41%
69%	Canada	1	1	Bosnia and Herzegovina	31%
68%	USA	4	1	Paraguay	32%
31%	Qatar	1	1	Switzerland	69%
52%	Brazil	1	1	Morocco	48%
33%	Haiti	0	1	Scotland	67%
47%	Australia	2	0	Türkiye	53%
84%	Germany	7	1	Curaçao	16%
59%	Netherlands	2	2	Japan	41%
44%	Côte d’Ivoire	1	0	Ecuador	56%
52%	Sweden	5	1	Tunisia	48%
87%	Spain	0	0	Cabo Verde	13%
66%	Belgium	1	1	Egypt	34%
27%	Saudi Arabia	1	1	Uruguay	73%
79%	IR Iran	2	2	New Zealand	21%
67%	France	3	1	Senegal	33%
40%	Iraq	1	4	Norway	60%
78%	Argentina	3	0	Algeria	22%
69%	Austria	3	1	Jordan	31%
75%	Portugal	1	1	Congo DR	25%
61%	England	4	2	Croatia	39%
32%	Ghana	1	0	Panama	68%
27%	Uzbekistan	1	3	Colombia	73%