World Cup Follow-Up: Update of Winning Probabilities and Betting Results—Wolfram Blog
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The World Cup is half-way through: the group phase is over, and the knockout phase is beginning. Let’s update the winning probabilities for the remaining teams, and analyze how our classifier performed on the group-phase matches.
Using our classifier, we compute again the winning gt probabilities of each team. To do so, we update the team features gt to include the last matches (that is, we update the Elo ratings and the goal average features), and then we run 100,000 Monte Carlo simulations of the World Cup starting from the round of 16. Here are the probabilities we obtained: gt
Again, Brazil is the favorite, but with a 32% chance gt to win now. After its impressive gt victory gt against Spain, the Netherlands’ odds jumped to 23.5%: it is now the second favorite. Germany (21.6%) and Argentina (8.6%) are following. There is thus, according to our model, an 86% chance that one of these four teams will be champion.
The most probable finals are Brazil vs. Netherlands gt (21.5%) and Germany vs. Netherlands (16.7%). It is however impossible to have a final Brazil vs. Germany, since these teams are on the same side of the tournament tree. Here is the most likely tournament tree:
In the knockout phase, the position in the tournament tree matters: teams being on the same side as Brazil and Germany (such as France and Colombia) will have a hard time reaching the final. On the other hand, the United Sates, gt which is in the weakest side of the tree, has about a 6% chance to reach its first World Cup final.
Finally, let’s see how far in the competition teams can hope to go. The following plots show, for the 9 favorite teams, the probabilities gt to reach (in blue), and to be eliminated at (in orange), a given stage of the competition:
We see that Germany has a 35% chance to be eliminated at the semi-finals stage (probably against Brazil), while France and Colombia will probably be stopped at the quarter-finals stage (probably against Germany and Brazil).
Which is close to the 59% accuracy obtained in the test set of the previous post. The accuracy is an interesting property to measure, but it does not reveal the full power of the classifier (we could have obtained a similar accuracy by always predicting the victory of the highest Elo-ranked team). It is more interesting to look at how reliable the probabilities computed by the classifier are. For example, let’s compute the likelihood of the classifier on past matches (that is, the probability attributed by the classifier to the sequence of actual match outcomes P (outcome 1 ) P (outcome 2 ) P (outcome 48 )):
This value can be compared to the likelihood computed from commonly believed probabilities: bookmakers’ odds. Bookmakers tune their odds in order to always win money: if $3 has been bet on A , $2 on B , and $5 on C , they will set the odds (the amount you get if you bet $1 on the corresponding outcome) for A , B , and C a bit unde
Mathematica Programming Cloud Discovery Platform Data Science Platform Finance Platform SystemModeler Wolfram|Alpha Wolfram|Alpha Pro Personal Analytics for Facebook Problem Generator APIs Business Solutions Mobile Apps Wolfram|Alpha for Mobile Course Assistant Apps Reference Apps Services Corporate Consulting Paid Project Support Training
Wolfram Language Revolutionary knowledge-based programming language. Wolfram Cloud Central infrastructure for Wolfram's cloud products & services. Wolfram Science Technology-enabling science of the computational universe.
Computable Document Format Computation-powered interactive documents. Wolfram Engine Software engine implementing the Wolfram Language. Wolfram Natural Language Understanding System Knowledge-based broadly deployed natural language. gt
Wolfram Data Framework Semantic framework for real-world data. Wolfram Universal Deployment System Instant deployment across cloud, desktop, mobile, and more. Wolfram Knowledgebase Curated computable knowledge powering Wolfram|Alpha.
Engineering, R&D Aerospace & Defense Chemical Engineering Control Systems Electrical Engineering Image Processing Industrial Engineering Mechanical Engineering Operations Research More... Education Higher Education Student Resources Wolfram Education Portal Web & Software Authoring & Publishing Interface Development Software Engineering Web Development Finance, gt Statistics & Business gt Analysis Actuarial Sciences Bioinformatics Data Science Econometrics Financial Risk Management Statistics More... Sciences Astronomy Biology Chemistry More... Trends Internet of Things High-Performance Computing
Find an Answer Documentation Support FAQs Wolfram Community Ask for Help Post a Question Contact Support Guided Learning Videos & Screencasts Training Events Conferences & Seminars Premium Support Premier Service Technical Services
The World Cup is half-way through: the group phase is over, and the knockout phase is beginning. Let’s update the winning probabilities for the remaining teams, and analyze how our classifier performed on the group-phase matches.
Using our classifier, we compute again the winning gt probabilities of each team. To do so, we update the team features gt to include the last matches (that is, we update the Elo ratings and the goal average features), and then we run 100,000 Monte Carlo simulations of the World Cup starting from the round of 16. Here are the probabilities we obtained: gt
Again, Brazil is the favorite, but with a 32% chance gt to win now. After its impressive gt victory gt against Spain, the Netherlands’ odds jumped to 23.5%: it is now the second favorite. Germany (21.6%) and Argentina (8.6%) are following. There is thus, according to our model, an 86% chance that one of these four teams will be champion.
The most probable finals are Brazil vs. Netherlands gt (21.5%) and Germany vs. Netherlands (16.7%). It is however impossible to have a final Brazil vs. Germany, since these teams are on the same side of the tournament tree. Here is the most likely tournament tree:
In the knockout phase, the position in the tournament tree matters: teams being on the same side as Brazil and Germany (such as France and Colombia) will have a hard time reaching the final. On the other hand, the United Sates, gt which is in the weakest side of the tree, has about a 6% chance to reach its first World Cup final.
Finally, let’s see how far in the competition teams can hope to go. The following plots show, for the 9 favorite teams, the probabilities gt to reach (in blue), and to be eliminated at (in orange), a given stage of the competition:
We see that Germany has a 35% chance to be eliminated at the semi-finals stage (probably against Brazil), while France and Colombia will probably be stopped at the quarter-finals stage (probably against Germany and Brazil).
Which is close to the 59% accuracy obtained in the test set of the previous post. The accuracy is an interesting property to measure, but it does not reveal the full power of the classifier (we could have obtained a similar accuracy by always predicting the victory of the highest Elo-ranked team). It is more interesting to look at how reliable the probabilities computed by the classifier are. For example, let’s compute the likelihood of the classifier on past matches (that is, the probability attributed by the classifier to the sequence of actual match outcomes P (outcome 1 ) P (outcome 2 ) P (outcome 48 )):
This value can be compared to the likelihood computed from commonly believed probabilities: bookmakers’ odds. Bookmakers tune their odds in order to always win money: if $3 has been bet on A , $2 on B , and $5 on C , they will set the odds (the amount you get if you bet $1 on the corresponding outcome) for A , B , and C a bit unde
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