## Modeling European Soccer Team Passing Strategy with Game Theory and Networks

The article referenced makes interesting conclusions given a large accumulation of data through the use of relational nodes to model interactions as subsets of a graph in the form of traversal paths. It uses this to make assumptions about the successes of various play styles without having to model passing as a formal game, which would be difficult to condense and make generalizations about due to the many external variables and choices that form the probabilities of success or failure in soccer. This model can be used to set up a formal game between two opposing teams and given more data could make conclusions about how patterns are best employed in response to others in order to maximize chance of winning the game or maximizing possession. The article posits information that allow such a theoretic game to be modeled, but unfortunately does not have additional data that relates the success of a play style with the play style used by the opposing team, nor how well it did overall. It was simply stated that the one outlier that predominantly used a certain style had, “the most success of its age.”

In order to understand how conclusions can be made about a formal game dealing with passing, we must understand how the data from hundreds of soccer games was modeled and analyzed. Laszlo Gyarmati of the Qatar Computing Research Institute and two of his colleagues used principal component analysis in order to model the data in relation to common or successful patterns. They modeled passes as 3 pass sequences where the player could either pass it to someone new (A), pass it to another player on his side (B), or pass it to either of the two players involved in the sequence (C,D). A sequence of 4 passes would be considered two separate 3 pass sequences. They noticed that there were patterns that stood out from the majority for teams that consistently did better. This sets up a theoretic game with 3 choices on the part of the player. This differs from the traditional perfect game with two players and delves more into a single-player game because we are ignoring the choices of an opposing force and choosing to look at the chance of the successes based on solely the choice of the first player. We can observe that while on the individual level there are 3 choices, we know that there are a finite number of combinations of passes that are used by each team. They are as follows: {ABAC,ABCB,ABAB,ABCA,ABCD}. This means that we can set up the problem as a game with two players and give them 5 choices for strategy. Unfortunately, this study does not show how well a strategy did in relation to another strategy, rather how often a strategy was used overall. This means that any payoffs would be the same regardless of what the other player chooses. We can see a map of the game below:

A\B | ABAC | ABCB | ABAB | ABCA | ABCD |
---|---|---|---|---|---|

ABAC | A1,B1 | A1,B2 | A1,B3 | A1,B4 | A1.B5 |

ABCB | A2,B1 | A2,B2 | A2,B3 | A2,B4 | A2,B5 |

ABAB | A3,B1 | A3,B2 | A3,B3 | A3,B4 | A3,B5 |

ABCA | A4,B1 | A4,B2 | A4,B3 | A4B4 | A4,B5 |

ABCD | A5,B1 | A5,B2 | A5,B3 | A5,B4 | A5,B5 |

This model could prove to be beneficial in planning play styles for teams especially in match-ups against teams that predominantly choose a certain style. It would be very interesting to see what sort of conclusions could be extrapolated given a large volume of data that relates the styles and their success.

Source: http://www.economist.com/blogs/gametheory/2014/09/analysing-football-styles