Calculation of Cech homology of Hawk-Eye data

Abstract

Many tennis players attempt to participate on the highest level. Almost as many players do not make it to the top. In this thesis Hawk-Eye data is investigated to determine the actual difference in the first serve between top players and players that have a lower ranking. The data is coming from Davis Cup matches, provided by the International Tennis Federation. To find the difference, a barcode for dimension 1 is calculated for both the top players and the lower ranked players using ˇCech homology. It turns out that there is a clear difference in the barcodes for the top players and lower ranked players. The barcodes for the top ranked players indicate the existence of a cycle that is the main feature of the data. For lower ranked players the data is not scattered along one clear cycle. This difference is due to the speed just before the bounce in the x-direction. This is higher for higher ranked players.