Probability in Football

The World Cup is undergoing and many football fans like guessing the results of the games. Before a game finishes, no one can be certain about the result of the game unless if there is a fraud. Then guessing game results is a game of probability.

If a strong team is defeated by a relatively weak team, some fans may think that other strong teams could also be defeated by relatively weak teams. If a positive correlation between these strong teams can be found, then this conclusion is reasonable; however, I do not see any existence of such correlation, then such conclusion might not be reliable.

Of course, football fans tend to exam teams’ future performances based on their history. This could be reasonable. As we can see this from a time series model, a team’s performance could be a model consisting a variable containing its previous period’s performance and a time factor. If the team is improving over time, then this time series model has a fixed effect (at least an always positive effect) from the time; if the team is worsening over time, then the time effect is opposite. Some teams’ performances volatile a lot, this might signal these teams’ performance models follow random walk.

If we can actually create such models, it might help to improve our predictions about football games; however, because there are too many factors and relatively very small samples, it is hardly for ordinary people to create models to make predictions; of course, it would very time consuming to build such models even if people could have sufficient information.