A multidimensional momentum chain model for tennis matches based on difference equations

by Jingya Wang, Sihang Guo, Yuanyun Zhou

In the process of pushing the limits of human performance, competitive sports are dedicated to the pursuit of excellence. In this context, the concept of "momentum" has gained significant attention, as it is widely acknowledged to influence the outcomes of competitions. The question of whether momentum affects sports psychology and the mechanisms underlying its generation and influence merits thorough investigation. In this paper, taking the 7,284 scoring points in the men’s singles tennis match at Wimbledon 2023 as an example, we expand upon traditional momentum research by integrating diverse algorithms, including statistical analysis and linear weighting, to construct a multidimensional momentum chain model predicated on difference equations, which aims to quantify the momentum dynamics for athletes in a match. To enhance the authenticity of our model, we incorporate a forgetting curve to modulate the momentum fluctuations. The results show that dominant players have significantly shorter running distances and higher success rates in net strokes than disadvantaged players, indicating that positive events markedly enhance players’ psychological and behavioral performance. Furthermore, the likelihood of scoring is substantially greater for players possessing higher momentum, with data suggesting that the serving side has an 84% chance of securing a match victory. When applied to 6,870 tennis matches, our model achieves a prediction accuracy exceeding 80%. Accordingly, we have proposed tennis training suggestions based on the mechanisms of momentum and developed strategies to effectively harness the "hot hand" phenomenon in matches.