Simulating the World Cup Knockout Stage(blog.wolfram.com)
blog.wolfram.com
Simulating the World Cup Knockout Stage
http://blog.wolfram.com/2010/06/24/simulating-the-world-cup-knockout-stage/
6 comments
The folks over at fivethirtyeight.com (usually a political-statistics blog) have a somewhat more complex simulation model that adds information about teams' average goal-scoring / goal-conceding, an estimate of home-field or home-region advantage, etc. It also uses ESPN's continually updated rankings instead of FIFA's stale ones. Still subject to a lot of the same problems, especially the small-sample-sizes issue, but it's at least an improvement. See the sidebar at: http://www.fivethirtyeight.com/
And unlike chess Elo rankings, where a 2006 Kramnik is mostly the same player (except for experience) as a 2010 Kramnik, football teams are continuously restaffed.
There are just too many variables to predict properly a single world cup match. Things you might not think of right away can completely change the outcome: weather, bad referees (even good referees doing just a bad call), combined strategies, bad player changes, to name just a few.
It's part of the taste of watching football, you can't be too sure about what's going to happen and very often even recent history data doesn't match outcome.
Perhaps this teaches how modeling highly unpredictable events shouldn't be taken lightly.
It's part of the taste of watching football, you can't be too sure about what's going to happen and very often even recent history data doesn't match outcome.
Perhaps this teaches how modeling highly unpredictable events shouldn't be taken lightly.
Of course, there was a paper that came out about a year ago that basically said that of all the major sports, football was statistically the least predictable. Basically this means that you need to change the formula used by the ELO rankings so that it is much flatter than the equation that Wolfram has chosen here. Once that has been done, the error bars on he predictions just sky-rocket.
To give a concrete example from this World Cup; Germany thrashed Australia in their first match, 4-0. Germany then went on to be beaten by Serbia in a closely fought match 1-0, and then Serbia was dominated by Australia in the last round of group matches, 2-1. Other groups have had the world champions - Italy, and runner-ups, France, knocked out of the competition in the group stages, yet none of the current models predicted that either. Makes their value quite dubious, in my opinion.
To give a concrete example from this World Cup; Germany thrashed Australia in their first match, 4-0. Germany then went on to be beaten by Serbia in a closely fought match 1-0, and then Serbia was dominated by Australia in the last round of group matches, 2-1. Other groups have had the world champions - Italy, and runner-ups, France, knocked out of the competition in the group stages, yet none of the current models predicted that either. Makes their value quite dubious, in my opinion.
It's interesting that football doesn't use series of games to try to cancel out some of the randomness. It works pretty well for other sports. If two teams go to seven games, you know they are pretty well matched.
It also seems like the group stage doesn't do a good enough job of canceling out random chance. Too many ties mean that too many of the groups came down to who won the final games of the group.
It also seems like the group stage doesn't do a good enough job of canceling out random chance. Too many ties mean that too many of the groups came down to who won the final games of the group.
Keep in mind, ties are sometimes strategic. Many games this world cup have seen teams playing very conservative/defensive because they were intentionally hoping for a tie.
Side-note, the Champions League and Europa League (where the top teams from each European Country's pro league compete against each other) uses a two-game system, one home and one away. The winner is decided by the cumulative score of the two games.
Side-note, the Champions League and Europa League (where the top teams from each European Country's pro league compete against each other) uses a two-game system, one home and one away. The winner is decided by the cumulative score of the two games.
The graphics are either misleading or wrong, the tie-ups for the winners are incorrect... the winner of the USA v Ghana game plays the winner of the South Korea v Uruguay game, but this simulation has Ghana playing Argentina in the next round???
Yes, certainly wrong.
probability porn comes to mind
World Cup is very difficult, if impossible to predict. For example, I was watching Slovakia-Italy yesterday, and in around 95 minute, Italia had a good chance to equalize to 3:3, it was a matter if the player will hit the ball correctly - I don't know how something like that could be predicted.
Moreover, no one expected that Slovakia will play better than in their previous matches, and Italy will play worse than in their previous matches. One possible factor (for Slovakia) could be that the coach and players were angry at Slovak media, which all blamed them mercilessly for a poor performance in the previous two matches - and that I think had more influence on the outcome than any previous math statistics about those two teams. They wanted to show that the media were incorrect and that added an extra motivation.
Where I think this math approach can work is in the leagues, where the same teams play against each other regularly.
Moreover, no one expected that Slovakia will play better than in their previous matches, and Italy will play worse than in their previous matches. One possible factor (for Slovakia) could be that the coach and players were angry at Slovak media, which all blamed them mercilessly for a poor performance in the previous two matches - and that I think had more influence on the outcome than any previous math statistics about those two teams. They wanted to show that the media were incorrect and that added an extra motivation.
Where I think this math approach can work is in the leagues, where the same teams play against each other regularly.
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One problem I would suggest is that ranking are primarily derived from past performance. I'm not sure about the Elo ranking, but the official FIFA one is based on results from the last four years (eight years before 2006!) -- in highest-level football that is way too long.
Perhaps another problem is that there are simply too few games in the tournament for this to work reliably. Given 50 games, a team's win-draw-lose count might be estimated pretty reliably, because a string of three bad games can be offset by a string of three above-expectations games. With only 3 games in the group round, funny things happen to probability.
See: Paraguay with Elo ranking 22, Slovakia with Elo ranking 48, New Zealand with Elo ranking 60, Italy with Elo ranking 7, France with Elo ranking 12.