World Cup Prognostication
June 29, 2010
On Saturday morning, inspired by Andrew Moylan’s article on Wolfram’s Blog, I sat down to work out a simulation of the knockout stage of the World Cup competition. I used the bracket shown at right, and found elo ratings of the sixteen teams, as of that morning, at Wikipedia:
1 BRA Brazil 2082
2 ESP Spain 2061
3 NED Netherlands 2045
4 ARG Argentina 1966
5 ENG England 1945
6 GER Germany 1930
7 URU Uruguay 1890
8 CHI Chile 1883
9 POR Portugal 1874
10 MEX Mexico 1873
15 USA United States 1785
19 PAR Paraguay 1771
25 KOR Korea 1746
26 JPN Japan 1744
32 GHA Ghana 1711
45 SVK Slovakia 1654
The table shows that there are forty-four national teams with ratings higher than Slovakia’s rating of 1654; they are lucky to be in the tournament.
The likelihood that a team will win its match can be computed from the elo rankings of the team and its opponent according to the formula 
Every time a match is played, the elo rating of a team changes. The amount of the change is based on the actual result as compared to the expected result. If a team wins when they have a high expectation of winning, their elo rating goes up by a small amount, since they were expected to win. However, if a team wins when they have a low expectation of winning, their elo rating goes up by a large amount. The formula is 
Your task is to use the data and formulas described above to simulate the knockout stage of the World Cup a million times and report the number of times each nation wins. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.
Programming Praxis 