NOTATION OF SOCCER GAMES IN THE AUSTRIAN NATIONAL LEAGUE IN STATISTICS AND PROBABILITY CALCULUSThis diploma thesis gives an insight into the frequency of goals of Austrian league-soccer games by well-known distribution function of probability calculus, in particular the Poisson distribution and Negative Binomial distribution. In the introductory chapter, features of these distribution functions will be prepared and their characteristics will be studied. The constitution of various derivations of the Poisson distribution, for example the properties to Binomial distribution and the relationship to Skellam distribution with reference to the modified Bessel functions will be described. An important aspect is the description of coherences from the Negative Binomial distribution with the attribute of the Hypergeometric function. Hereafter, an introduction of familiar methods of inductive statistics for the analysis of soccer goals in the Austrian Fußball-Bundesliga will be given.The main part of this paper focuses on the analysis and notation of scores in the last seasons 2010/11 and 2011/12 by the abovementioned distributions. At this point, a computation of parameter from the Negative Binomial distribution by Maximum Likelihood-Estimation including the Expectation-Maximization-Algorithm and the modified Newton method are described. It will focus on mathematical modeling of soccer games and state an outlook for next spring season which will be based on last winter season?s results.The closing chapter deals with extreme value theory. An alternative description of goal frequency is the General extreme value distribution. A testing of the outlook will be compared with the collected data, then evaluated and recorded. This diploma thesis shows an application of probability distributions in the field of soccer games.