@MASTERSTHESIS\{IMM2011-06142,
author = "M. Krajowski-Kukiel",
title = "Modelling And Visualization Of A Bridge Player's Performance",
year = "2011",
school = "Technical University of Denmark, {DTU} Informatics, {E-}mail: reception@imm.dtu.dk",
address = "Asmussens Alle, Building 305, {DK-}2800 Kgs. Lyngby, Denmark",
type = "",
note = "Supervised by Associate Professor Michael Kai Petersen, mkp@imm.dtu.dk, and Sune Lehmann, {DTU} Informatics",
url = "http://www.imm.dtu.dk/English.aspx",
abstract = "The thesis consists of two main parts. The first one is building a model of a bridge player's performance. The solution used is based on a popular rating system known as Elo. The idea is to express a skill level as a random variable following a Logistic Distribution. Since the rules and scoring in bridge are considerably complicated, an extensive amount of work has been put into improving the basic formulas and to reflect some real life dependencies in the model. The second part is a visualization of how the model works by applying it to real bridge players' statistics. In the final process 22; 000; 000 games were considered for more than 200; 000 players. Two metrics have been used to verify the model's correctness and usefulness - Root Mean Square Error and Binomial Deviance. The latter one can be directly transformed into accuracy. The final rate of correct prediction is 50,0158\%, which is a little better than the null model, with an accuracy of 50\% (a model of 50/50 random outcome). Even though it is not an impressive score, it is considered a success. Comparing to chess, which is a two-player game and includes only one additional parameter - the person who started the game is more likely to win - it is much harder to predict the winner of a bridge game. The main reasons of this are that bridge is a game of chance, in one game many independent partnerships are involved, which results are compared to each other. Several visualization techniques have been used to investigate what features of the obtained model behave correctly and which appear erroneous. It also helped in defining the problems, which are most likely to result in low accuracy. The analysis is summarized by creating a list of future tasks. The obtained system in its current form is not optimal, however it gives some reasonable results and a proper base that can be extended in the future."
}