As someone who is both a fan of the World Cup and statistical modeling, it was with great interest that I read “The World Cup and Economics 2014,” a report issued by Goldman Sachs. They have outlined their predictions in a 67 page report. Goldman Sachs estiamtes that Brazil, the host nation, has a 48.5% chance to win the tournament, while Argentina, Germany, and Spain are the follow-up favorites (14.1%, 11.4%, and 9.8% to win the World Cup 2014, respectively).
The Goldman Sachs methodology is rather straightforward:
The explanatory variables in the regression analysis are as
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.
From there, it’s up to Monte Carlo simulation to make the predictions:
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.
Unfortunately, the model has some limitations:
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.
You can read the entire report here: Goldman Sachs – World Cup 2014 Economic Report
For further reading, compare the Goldman Sachs predictions to the Five Thirty Eight World Cup Model (both models have pegged the probabilities of Brazil, Argentina, Germany, and Spain to win World Cup 2014 to within a couple of percentages, and in the same rank order of winning the tournament):