Analysis of Markov processes in team sports modeling

Petar Vračar (2017) Analysis of Markov processes in team sports modeling. PhD thesis.

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Abstract

The increasing computational power and automated collection of ever richer data about sporting events have enabled the development of complex analytical models that offer decision makers a competitive advantage in the world of sport. In the thesis we address the problem of automatic extraction of regularities in the sequence of events in sports games and construction of statistical models for generating a plausible simulation of a match between two distinct teams. We model the progression of a sports game as a random walk through the state space. We express the transition matrix of our Markov model as a function of the current state description which includes factors relevant for the further development of events in the match. The main idea of our approach is to incorporate a cascade of models that sequentially (and conditioned to each other) predict the individual components of the next state description. We present a method for automatic construction of a feature space which does not require any expert knowledge about the domain. The attributes are defined as the ratio between the number of entries and exits from higher-level concepts that are identified as groups of similar game events. The similarity between the events is determined by the similarity between probability distributions describing the preceding and following events in the observed sequences of game progression. Experimental evaluation of the proposed methods applied in the basketball domain showed that the models fitted in the automatically generated feature space are of comparable quality to models that use features based on expert knowledge. Statistical analysis of the generated simulations showed that the models successfully capture the dynamics of the game of basketball.

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