Analysis of Markov processes in team sports modeling

Naraščujoče računske zmogljivosti in avtomatsko zbiranje čedalje bogatejših podatkov o poteku športnih dogodkov so omogočili razvoj kompleksnih analitičnih modelov, ki nosilcem odločanja ponujajo kompetitivno prednost v svetu športa. V disertaciji naslavljamo problem samodejnega izluščanja zakonitosti o sosledju dogodkov na športnih tekmah in gradnje statističnega modela za generiranje verodostojnih simulacij tekem med specificiranima ekipama. Razvoj športne tekme modeliramo kot slučajni sprehod v prostoru stanj. Matriko prehoda markovskega modela izražamo v funkcijski odvisnosti od opisa trenutnega stanja, ki vključuje faktorje, relevantne za nadaljnji potek dogodkov na tekmi. Osnovna ideja našega pristopa temelji na uporabi kaskade modelov, ki zaporedno (in pogojeno eden na drugega) napovedujejo posamezne dele opisa naslednjega stanja. Predstavljamo postopek za avtomatsko generiranje atributnega prostora, ki ne potrebuje domenskega predznanja. Atribute definiramo v obliki razmerja med številom vstopov in izstopov iz višjenivojskih konceptov, ki jih identificiramo kot množice podobnih dogodkov. Podobnost med dogodki ugotavljamo na podlagi podobnosti porazdelitev, ki opisujejo predhodne oziroma naslednje dogodke v opazovanih sekvencah razvoja športnih tekem. Eksperimentalna evalvacija predlaganih metod na košarkarski domeni je pokazala, da so modeli, dobljeni z učenjem na podlagi avtomatsko generiranih atributov, po kvaliteti napovedovanja naslednjega dogodka in časa med dogodki primerljivi z modeli, naučenimi z ekspertnimi atributi. Statistična analiza dobljenih simulacij je pokazala, da so modeli uspešno zajeli dinamiko razvoja košarkarske tekme.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