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Written by Dr. Willy Gerber

Sunday, 15 February 2009 15:06

Soccer game

Based on a simple probabilistic model for retaining, advancing and catching the ball we simulate soccer games of different strong teams. The simulation is repeated to get a probability of a particular goal result and the wining chance of each team. The following Applet allows you to change the factors for each team and model a possible game:

(if you miss the popup, please reload the page and wait 5-20 sec depending on the speed of your internet)

Explanation of the Simulator

The simulator is based three different events:

The field confrontation

Each time a player controlling the ball is confronted, there is a probability that the player keeps or loses the ball. In addition the confrontation itself will reduce the game-time.

You may change the probability of keeping the ball by the local and by the visiting team on the upper fields of the simulator. You also can modify the time that the confrontation will last (yellow fields):

The shoot

For simplicity the shoot has been modeled with a constant speed. We also assume a probability distribution for achieving a distance and kicking in an angle relative to the direction of the opponent goal.

The probability distribution of the distance shoot is modeled by a Gaussian distribution with a mean distance and a standard deviation:

The probability distribution of the angle depends on the position of the player on the field. What in the distance probability distribution is the mean value is in this case defined by the location of the opponent’s goal. This means that for a Gaussian distribution we only have to define the kick cone standard deviation. In addition we must limit the direction in a way that the ball has only a reduced chance to leave the field:

You can modify the mean distance and standard deviation of the distance and angle in (yellow fields):

Caching the ball

The last element of the model is the probability the goal keeper can catch the ball:

You can modify the probability for each team in (yellow fields):

Running the Simulator

Before you start the simulator you should defined the number of times the game will be played. Because it’s a probabilistic simulation you will get in each run a different result. Averaging over a number of games you will recognize a tendency. If you don’t know how many runs you should chose, run it with different numbers finding the number for which the results is stable. The number can be changed on the top right corner of the panel:

To start the simulator press the left bottom button

Press the same bottom again for pausing and for continuing the calculation. With the second button you can reset the simulation and start again without changing the fields you modify:

Press the third bottom to reset the simulation with the default values:

If you activate the field "Animation":

the system will show the game on a separated frame :

This display will slow down strongly the calculation process. The number of games played can be read on the field on the right side of the animation checkbox.

The Results

You have three different results. First the detail statistics of the results indicating by probability of specific goal results:

On the bottom of the goal table is the probability of winning of the local and visiting team and the chances of an even result:

You also get the distribution of the position of the ball alog the field:

For a real application we have to study the performance of a team measuring the parameters that are only estimated in this simulator. After testing the program on a large amount of real games, it should be possible to get simulator that allow us to optimize strategies testing them before the real game happens.

Last Updated ( Wednesday, 14 July 2010 12:33 )

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