A Subgraph-Based Ranking System for Professional Tennis Players

Abstract

This paper introduces a novel ranking system for competitive sports based around the notion of subgraphs. Although the system is targeted specifically to professional tennis it could be applied to any dominance network due to its generality. The results of about 140,000 tennis matches played between Top-100 players are used to create a colored directed network where colors represent different surfaces and edge direction depends on head-to-read results between players. The main contribution of this work is a ranking system which relies on the occurrences of 4-node directed subgraphs and the positions (or orbits) where the players appear on them. Since the concept of orbit is intrinsically connected with node dominance, appearing frequently in dominant orbits indicates that the player himself is dominant. Even in a very sparse network and without any background knowledge on the tournaments or stages of the matches, our proposal is able to extract meaningful rankings which capture the intricate competitive relationships between players from different eras.

GoT-WAVE: Temporal network alignment using graphlet-orbit transitions

“…For this particular dataset, also optimizing edge conservation (i.e., α = 1 2 ) decreases performance of both methods, even though it was previously argued that α = 1 2 is the best-case scenario [45,43]. Actually, we also verify that α = 1 2 is indeed the best-case scenario on our considered real networks (Section 3.2). It is just that on our considered synthetic networks, α = 0 happens to be both the fair and best-case scenario for both methods, and under this scenario, GoT-WAVE is superior to DynaWAVE.…”

“…On synthetic networks, we also find that extracting GoT features is overall 64% faster than extracting DGDV features (Table 1 (b)). Because both methods use their features in the same alignment strategy (WAVE), their alignment times Table 1: Results on synthetic networks when only node conservation is optimized (α = 0) or when node and edge conservation are optimized (α = 1 2 ). In parentheses, we show relative improvement (positive gain) or degradation (negative gain) in performance of GoT-WAVE compared to DynaWAVE.…”

Complex Network Analysis of Men Single ATP Tennis Matches

“…Dingle et al in [23] applied the previous work to ATP and WTA (Women's Tennis Association) matches and they also provided a simple comparison on the basis of predictive power. In [15] the authors proposed yet another ranking method applying PageRank to the subgraph of the Top-100 players. In [16] many ranking methods, both through network and Markov chains analysis, have been proposed and verified by means of prediction power.…”

“…In case of multiple links the weights are just summed. Similar representations were adopted in [14] considering data up to 2010, in [13] considering data between 90s and 00s of male and female matches of Grand Slams only with different weights function, and in [15] with data of top-100 players only and different weights function. The obtained graph is not symmetric, not even if the respective unweighted version is considered.…”

“…Then an important contribution was brought by [14], where a different network modeling is proposed and the 1 The datasets used in this paper are made publicly available at: https://drive.google.com/open?id=1mCxZfkkpIC9o-nxZ1yW3GBBdvBOPW6mQ [1] PageRank algorithm is applied identifying Jimmy Connors as the most important single tennis player between 1968 and 2010. More recent tennis-related complex network studies regard new ranking methods proposal and evaluations (see as reference [15], [16] and [17]), or are related to doubles matches [18] or to the gender and handedness effects in top ranking positions [19].…”