Movement Model

What are movement models in general?

And what can our movement model do for you?

Movement models are mathematical models that can be used to calculate the position and speed a player might adopt in the future. This does not refer to the movements of the player’s body parts and limbs. Rather, ‘position’ refers to the centre of gravity of the player’s body on the pitch, expressed by the coordinates (x, y) on this plane.

A movement model is therefore an excellent way of describing WHAT players actually do on the pitch. Sports scientists refer to this as the game-action (Spielhandlung). If, for example, a pass is played, this game-action can be fully described using the variables of position and speed of all participants: Where are the ball and the players at specific points in time, before, during and after the pass? And what are the speeds of the ball and the players at these different points in time?

Movement models, on the other hand, do not go into detail about HOW the game-action is carried out at the level of competitive behaviour, for example, which part of the body is used to play the pass. How well or poorly a player can generally execute a game-action is reflected in their technical abilities. Sports scientists refer to this as playing ability (Spielfähigkeit). Movement models only consider the result of a technical execution, regardless of how it looks.

A movement model is therefore a concept that helps to identify key aspects for understanding the game. Using this method, football can not only be consumed through visual observation, but the game events consisting of movements can also be analysed at a computational level. Potential game actions can be calculated and highlighted. A video recording, on the other hand, can only show past events. A video recording cannot provide any insight into a possible game future, whereas our movement model can.

A comprehensive movement model must incorporate the following concepts in order to avoid producing unrealistic results:

• The player’s ability to accelerate as a means of changing their speed and position (path)
• The player’s ability to react
• Event management and control (actions as triggers for reactions)
• The player’s body as a means of shaping the game (shielding the ball when in possession)
• Ability to anticipate: the player’s ability to foresee the future movement of the ball, opponents and teammates

The positional data collected by tracking systems during matches plays a key role here. It forms the starting point on which movement models are based. At specific points in time, questions about the match can then be asked by linking the movement model with the movement data:

• Could this or that pass have been completed?
• How much pressure was the player under?
• How many passing options did the player have?
• Generally speaking: What if?

Our movement model we have implemented is entirely deterministic. This enables us to provide unambiguous answers to all ‘what if’-questions and to clearly identify cause and effect at all times. This is a major advantage over analysis methods based on AI or stochastic. Pure pattern recognition – as will become increasingly clear – is not sufficient to successfully and accurately explain the dynamic and highly interactive processes in football.

The difficulties artificial intelligence faces with causality are discussed in the Max Planck Research article: Not without reason

Another major advantage of our purely physical-mathematical model is that it is certain the model cannot generate ‘impossible’ movement sequences, because the model of the player – just like the real player – must obey the laws of physics. The player model is just as unable to break free from this physical framework as a real player on the pitch.

Football Simulation

What is Simulation in general?

Wikipedia on this: ‘Simulation refers to the reproduction of real-world scenarios for the purposes of training, entertainment or the analysis of systems’.

... in simulation, experiments or training exercises are carried out on a model in order to gain insights into the real system.

A model (movement model) on its own is of no use unless the process is controlled, parameterised and the results cannot be displayed. The model is therefore dependent on interaction with humans. Therefore:

Movement-Model + Control and Visualisation = Football-Simulation

Simulations are always used where gathering information for training or analysis in real-world systems is too expensive or too dangerous.

In the real-world system of football with ‘real’ players, it is not possible to carry out exhaustive experiments, e.g. to find out what the optimal solution for a play looks like. This is not feasible because the various options can be very numerous, and real players would quickly become exhausted and reach their physiological limits very quickly.

In summary, it can be said that simulation models can be modified much more easily and cost-effectively than the real system.

The analogy with aircraft simulation becomes clear. In an aircraft simulation, kerosene, landing rights and maintenance staff are saved. Risks are reduced when practising engine failure and emergency landing scenarios. The football simulation saves recovery time as well as the time taken to carry out the exercise. Risks are reduced by preventing injuries and unnecessary strain.

What makes our football simulation so sexy?

As well as training and analysis, the football simulation also offers plenty of entertainment. It’s simply great fun to uncover all the secrets behind the players’ actions and discuss them using brand-new insights.