Who is the best player ever? A complex network analysis of the history of professional tennis

Abstract

We considered all matches played by professional tennis players between 1968 and 2010, and, on the basis of this data set, constructed a directed and weighted network of contacts. The resulting graph showed complex features, typical of many real networked systems studied in literature. We developed a diffusion algorithm and applied it to the tennis contact network in order to rank professional players. Jimmy Connors was identified as the best player in the history of tennis according to our ranking procedure. We performed a complete analysis by determining the best players on specific playing surfaces as well as the best ones in each of the years covered by the data set. The results of our technique were compared to those of two other well established methods. In general, we observed that our ranking method performed better: it had a higher predictive power and did not require the arbitrary introduction of external criteria for the correct assessment of the quality of players. The present work provides novel evidence of the utility of tools and methods of network theory in real applications.

Figure 1. Properties of the data set.

In panel a, we report the total number of tournaments (top panel) and players (bottom panel) as a function of time. In panel b, we plot the fraction of players having played (black circles), won (red squares) and lost (blue diamonds) a certain number of matches. The black dashed line corresponds to the best power-law fit with exponent consistent with the value .

Figure 2. Top player network and scheme for a single tournament.

In panel a, we draw the subgraph of the contact network restricted only to those players who have been number one in the ATP ranking. Intensities and widths are proportional to the logarithm of the weight carried by each directed edge. In panel b, we report a schematic view of the matches played during a single tournament, while in panel c we draw the network derived from it.

Figure 3. Prestige score in a single tournament.

Prestige score as a function of the number of victories in a tournament with rounds (Grand Slam). Black circles are obtained from Eqs. (7) and valid for . All other values of have been calculated from Eqs. (6): red squares stand for , blue diamonds for , violet up-triangles for and green down-triangles for .

Figure 4. Relation between prestige rank and other ranking techniques.

In panel a, we present a scatter plot of the prestige rank versus the rank based on the number of victories (i.e., in-strength). Only players ranked in the top 30 positions in one of the two lists are reported. Rank positions are calculated on the network corresponding to all matches played between 1968 and 2010. In panel b, a similar scatter plot is presented, but now only matches of year 2009 are considered for the construction of the network. Prestige rank positions are compared with those assigned by ATP.