On the use of simulation methods to compute probabilities: application to the first division Spanish soccer league
We consider the problem of using the points a given team has in the First Division Spanish Soccer League to estimate its probabilities of achieving a specific objective, such as, for example, staying in the first division or playing the European Champions League. We started thinking about this speci...
| Autores: | , |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 2010 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2099/11242 |
| Acceso en línea: | https://hdl.handle.net/2099/11242 |
| Access Level: | acceso abierto |
| Palabra clave: | Mathematical statistics Monte Carlo simulations Multinomial distribution Prediction Soccer league Estadística matemàtica Estadística matemàtica -- Aplicacions Classificació AMS::62 Statistics::62F Parametric inference Classificació AMS::62 Statistics::62P Applications Àrees temàtiques de la UPC::Matemàtiques i estadística::Estadística matemàtica |
| Sumario: | We consider the problem of using the points a given team has in the First Division Spanish Soccer League to estimate its probabilities of achieving a specific objective, such as, for example, staying in the first division or playing the European Champions League. We started thinking about this specific problem and how to approach it after reading that some soccer coaches indicate that a team in the first division guarantees its staying in that division if it has a total of 42 points at the end of the regular season. This problem differs from the typical probability estimation problem because we only know the actual cumulative score a given team has at some point during the regular season. Under this setting a series of different assumptions can be made to predict the probability of interest at the end of the season. We describe the specific theoretical probability model using the multinomial distribution and, then, introduce two approximations to compute the probability of interest, as well as the exact method. The different proposed methods are then evaluated and also applied to the example that motivated them. One interesting result is that the predicted probabilities can then be dynamically evaluated by using data from the current soccer competition. |
|---|