We construct a stochastic model that generates a distribution of outcomes for each of the 64 matches of the 2014 World Cup, from the opener between Brazil and Croatia on June 12 in São Paulo through the final on July 13 in Rio de Janeiro.

 The predictions for each match are based on a regression analysis that uses the entire history of mandatory international football matches—i.e., no friendlies—since 1960
 This gives us about 14,000 observations to estimate the coefficients of our model. The dependent variable in the regression analysis is the number of goals scored by each side in each match. Following the literature on modelling football matches, we assume that the number of goals scored by a particular side in a particular match follows a Poisson distribution
 
 The explanatory variables in the regression analysis are as follows:
1. The difference in the Elo rankings between the two teams. The Elo ranking is a composite measure of national football team success that is based on the entire historical track record. Unlike the somewhat better known FIFA/Coca-Cola rating, the Elo rating is available for the entire history of international football matches. Statistically, we find that the difference in Elo rankings is the most powerful variable in the model.
2. The average number of goals scored by the team over the last ten mandatory international games.
3. The average number of goals received by the opposing team over the last five mandatory international games.
4. A country-specific dummy variable indicating whether the game in question took place at a World Cup. This variable is meant to capture whether a team has a tendency to systematically outperform or underperform at a World Cup.
We only include this variable for countries that have participated in a sufficient number of post-1960 World Cup games (including Brazil, Germany, Argentina, Spain, Netherlands, England, Italy and France).
5. A dummy variable indicating whether the team played in its home country.
6. A dummy variable indicating whether the team played on its home continent, with coefficients that are allowed to vary by country.

 We generate a probability distribution for the outcome of each game using a Monte Carlo simulation with 100,000 draws, using the parameters estimated in the regression analysis described above. We use the results of this simulation analysis to generate the probabilities of teams reaching particular stages of the tournament, up to winning the championship. We use the rounded prediction of the goals scored to determine the outcomes of each game during the group stage and the unrounded forecast to pick the winner in the knockout stage.

 To be clear, our model does not use any information on the quality of teams or individual players that is not reflected in a team’s track record. For example, if a key player who was responsible for a team’s recent successes is injured, this will have no bearing on our predictions. There is also no role for human judgment as the approach is purely statistical.

A Brazil 4 Croatia 1
A Cameroon 1 Mexico 1
B Netherlands 1 Spain 1
B Australia 1 Chile 1
C Colombia 1 Greece 1
D Costa Rica 1 Uruguay 1
D England 1 Italy 1
C Ivory Coast 1 Japan 1
E Ecuador 1 Sw itzerland 1
E France 2 Honduras 1
F Argentina 2 Bosnia 1
G Germany 2 Portugal 1
F Iran 1 Nigeria 1
G Ghana 1 Usa 1
H Algeria 1 Belgium 1
A Brazil 4 Mexico 1
H Korea 1 Russia 1
B Australia 1 Netherlands 2
B Chile 1 Spain 2
A Cameroon 1 Croatia 1
C Colombia 1 Ivory Coast 1
D England 1 Uruguay 1
C Greece 1 Japan 1
D Costa Rica 1 Italy 2
E France 1 Sw itzerland 1
E Ecuador 1 Honduras 1
F Argentina 2 Iran 1
G Germany 2 Ghana 1
F Bosnia 1 Nigeria 1
H Belgium 1 Russia 1
H Algeria 1 Korea 1
G Portugal 1 Usa 1
B Australia 1 Spain 2
B Chile 1 Netherlands 2
A Brazil 5 Cameroon 0
A Croatia 1 Mexico 1
D Costa Rica 1 England 1
D Italy 1 Uruguay 1
C Colombia 1 Japan 1
C Greece 1 Ivory Coast 1
F Argentina 3 Nigeria 1
F Bosnia 1 Iran 1
E Honduras 1 Sw itzerland 1
E Ecuador 1 France 1
G Germany 2 Usa 1
G Ghana 1 Portugal 1
H Algeria 1 Russia 1
H Belgium 1 Korea 1