World Cup Qualification Prediction - How it works
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How it Works?
A Probabilistic Expert System based on a Bayesian Belief Network
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Bayesian Belief Networks are made of Two Distinct parts
Structure
Directed Acyclic Graph
Nodes represent the variables of the studied domain (e.g.: URU-FRA to model the Match Uruguay versus France)
Each node has exclusive states (e.g.: FRA, Draw, URU)
Arcs represent the direct probabilistic influences between the variables (possibly causal), e.g.: the results of the matches implying France have a direct impact on the final number of points of France
Parameters
Probability distributions are associated to each node, usually by using tables
MARGINAL PROBABILITY DISTRIBUTION
We here consider that Uruguay has a 15% chance to win the match against France, 60% that it will
be a draw, and 25% that France will win it
CONDITIONAL PROBABILITY DISTRIBUTION
The result of the first match has an impact on the team’s spirit and then on the probability
distribution of the second match
Here, for a France’s defeat against Uruguay, we set a 45%
chance that France wins the second match vs Mexico, 40%
for a draw, and 15% for a defeat.
On the other hand, if France wins, we set a 85% chance for a win in the second match, 10% for a draw, and 5% for a defeat
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Bayesian Belief Networks are Powerful Inference Engines
We exploit all the information available on a subset of variables for updating, in a rigorous way, the probability distribution of the other variables
All kinds of inference are allowed:
Simulation: from “causes” toward “effects”
“What are the consequences on the Qualification probability for Stage 2 when the team loses its first match?”
Diagnosis: from “effects” toward “causes”
“When a team is qualified for Stage 2, what is the probability that this team has lost its first match?”
All the combinations of those two kinds of inference:
“When a team is qualified for Stage 2, with a draw during its first match, what is the probability that this team has won its second match?”
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The Bayesian Network used for the Application
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The structure: 3 layers
The 6 matches of Group A
The points for each team
The qualification for each team
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Marginal probability distribution defined as Equiprobable.The user will define his/her own distribution by using the
web application’s sliders, for describing his/her own knowledge/belief
Deterministic relation between the 3
matches and the total number of points for
Stage 1
A probabilistic equation describes the different
qualification scenarios
The Parameters
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Initially, without modifying the equiprobable distribution on the
matches’ results, the Qualification probability is 50%
Probabilistic Computation: Simulation
“What are the consequences on the Qualification probability for Stage 2 when the team loses its first match?”
If Uruguay loses the first match, the Qualification probability falls from
50% to 23.59% (without any information on the other matches’
results)
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Probabilistic Computation: Diagnosis
“When a team is qualified for Stage 2, what is the probability that this team has lost its first match?”
Given that France is qualified for Stage 2 .....
... there is a 15.73% chance that France has lost the first match
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Probabilistic Computation
“When a team is qualified for Stage 2, with a draw during its first match, what is the probability that this team has won its second match?”
... and France is qualified for Stage 2 .....
Given that France made a draw during the first match ....
... there is then a 58.49% chance that France won the second
match
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Probabilistic Computation
“Is it possible to be qualified for Stage 2 with 2 points only?”
Given that South Africa gets 2 points only ....
... there is still a 1.23% chance that South Africa is qualified
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We wish you pleasant simulations ...
and a great World Cuphttp://worldcup.bayesialab.com
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Contact
6 rue Léonard de Vinci BP011953001 LAVAL CedexFRANCE
Dr. Lionel JOUFFEPresident / CEO
Tel.: +33(0)243 49 75 58Skype: +33(0)970 46 42 68Mobile: +33(0)607 25 70 05Fax: +33(0)243 49 75 83