Oleksandr Sivak (2016) May a weak tennis player win?. EngD thesis.
Abstract
The winner of a competition depends on the choice of actual matches played. We assume that each match is played between two players. Our goal is to examine which players can be made winners of a competition if we know any match result in advance. We only consider competitions in which the winner of a single match progresses to the next round and the loser leaves the competition. We focus on tennis competitions and use real data downloaded from atpworldtour.com. The final winner of a competition depends on the choice of matches in the first round — we call it a bracket. We would like to determine possible competition winners and for every winner π construct an appropriate bracket in which π is the winner. Apart from that we also study how tight are the sufficient conditions for a player to become a winner, as described in the paper Fixing a Tournament (Williams, AAAI 2010). For instance, one of our results is that a player whose relative rank is between 1 and 36 can with high probability be made a winner in a competition of 64 players.
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