# Who will be World Champion 2014?

## by Matthias Ludwig and Iwan Gurjanow

The Germany national football team has been drawn in a really difficult Group G. But what does it really mean? Are Portugal and Ghana really that strong? What is the situation with the US? The troupe of Löw has lost the last game against this team. On this website we try to bring some clearness to the situation with the help of stochastic models and simulations developed by the MATIS working group.

# Prediction and Simulation

Prediction model and simulation are provided on this website. The impacting factors in the prediction model are historical results and goal difference between the teams, as well as currently achieved FIFA-points. The user can change the weighting of these factors. One problem that still remains unresolved is how to convert FIFA-points into expected values for goal differences. It can be determined, that FIFA-points correlate pretty well with the value of a team. The value of a team can be very interesting in the short term , but it’s not clear, how the difference in the value can be depicted in the goal difference. During the simulation a user can play a really individual world championship game. The result of the simulation will be shown after each click, thus it is likely to occur, that Honduras will be the world champion. But just in one out of 1000 cases. During the simulation the tournament will be played till the end, the results of the games in the K.O.-phase will also be shown. Individual outcomes of the games will be calculated through the respective goal difference and actual Fifa-rang. Currently you don' have any configuration options here.

# Probabilities of Win, Draw or Loss

Calculations are based on a simple Bernoulliexperiment.
So one can understand the basic principles of calculations at school.

If we assume, that the results of the football games are chance events with a
certain kind of probability, then we are allowed to do so. What is the basis of our
assumption? We give a certain number of shots to each team. The average goal rate per
shot amounts 1/6. Each team shoots on average 9 times. But one team scores more often than
the others from past experience. It has a higher probability to score at every shot.
So we can estimate the probability of winning for individual matches.

# Prediction

How will these values be calculated in the table? The table with percentages is based on the probability of winning among participating teams. This probability of winning will be partially calculated from the results of the historical matches (the number of wins, draws, losses and goal difference). The present number of FIFA-points of the team have also influence, as for instance some teams have never played against each other, or the information is very poor. First, group games will be calculated. Here each team plays against all the others. Each team plays 3 times. The maximum scores to achieve amounts to 9 points. To become the head of the group a team should reach at least 7 points (2xwin, 1xdraw), in some cases 6 points are also enough. 5 points from the group games are in any case enough to reach the quarter-final, sometimes 4 points and in rare cases even 3 points. You will therefore receive a certain probability of reaching the K.O.-phase for each team. Now all the possible matches in the K.O.-phase will be calculated. For each team will be considered the possibility, if this team will struggle as the head of the group (Path 1) or the best second place (Path 2) in the K.O.-phase. At the very end respective probabilities of winning of the individual stages of the K.O.-phase will be added and you come to the probability, that a certain stage (quarter final, half final or final) of the K.O.-phase will be reached. As a lot of additions, multiplications and memory inquiries are necessary, you should wait for some seconds for the re-calculating of the table. When the World Championship begins, every new result of the game will be uploaded, so the probability of winning for the individual teams will change during the World Championship.