Incomplete pairwise comparison matrices: ranking top women tennis players

Abstract

The method of pairwise comparisons is frequently used for ranking purposes. The aim of the paper is to apply the method for ranking top women tennis players with the help of their win/lose ratios.  Incomplete pairwise comparison matrices can be constructed from the data obtained from WTA (Women's Tennis Association) homepage. The database contains head-to-head results from the period between 1973 and 2020 for those 27 players who had the position No. 1 in the official rankings of WTA for shorter or longer periods. Their names and the length of their professional tennis carrier can be seen in Figure 1, the W/L ratios are in Table 1. If two players have not met on the court, the element of the matrix is unknown (empty cell). Our goal is to create historical ranking including players even from disjoined time periods as we did with men top tennis players in Bozóki, Csató, Temesi (2016).