# A Study on the Optimisation of Tennis Players' Match Strategies from the Perspective of Momentum
## 4 Construction of a Momentum-Based Player Match Strategy Optimisation Model
### Evaluation of Player Match Performance
#### 4.1.2 Calculation of Player Performance Scores  
In accordance with the preceding analysis, the weights of each indicator were determined by means of the entropy weight method, where the weight of the \(j\)-th indicator is denoted as \(w_{j}\). Subsequently, the TOPSIS method was employed to calculate the differences between the evaluation object and the optimal and worst vectors, thereby assessing the relative performance of the evaluation object.  
Utilising the normalised data for each indicator, the optimal solution is denoted as \(\bigl{(}Z_{1}^{+},Z_{2}^{+},\ldots,Z_{m}^{+}\bigr{)}\), and the worst solution is denoted as \(\bigl{(}Z_{1}^{-},Z_{2}^{-},\ldots,Z_{m}^{-}\bigr{)}\). The distances between each evaluation indicator and the optimal and worst vectors were calculated using the expression shown in Equation (9).  
\[D_{i}^{+}=\sqrt{\sum_{j=1}^{m}w_{j}\bigl{(}Z_{j}^{+}-z_{ij}\bigr{)}^{2}},D_{i} ^{-}=\sqrt{\sum_{j=1}^{m}w_{j}}\bigl{(}Z_{j}^{-}-z_{ij}\bigr{)}^{2}, \tag{9}\]  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multirow{2}{*}{**Index Item**} & \multicolumn{3}{c}{**P1**} & \multicolumn{3}{c}{**P2**} \\ \cline{3-8}  & & **Entropy Value e** & **Utility Value d** & **Weight (\%)** & **Entropy Value e** & **Utility Value d** & **Weight (\%)** \\ \hline
1 & Momentum & 0.986 & 0.014 & 1.475 & 0.987 & 0.013 & 0.990 \\
2 & Ace & 0.384 & 0.616 & 65.461 & 0.148 & 0.852 & 65.697 \\
3 & Winner & 0.722 & 0.278 & 29.597 & 0.598 & 0.402 & 30.993 \\
4 & Double\_fault & 0.996 & 0.004 & 0.387 & 0.998 & 0.002 & 0.120 \\
5 & Unf\_err & 0.975 & 0.025 & 2.645 & 0.978 & 0.022 & 1.691 \\
6 & Rally\_count & 0.997 & 0.003 & 0.306 & 0.997 & 0.003 & 0.222 \\
7 & Dtop & 0.999 & 0.001 & 0.129 & 0.996 & 0.004 & 0.287 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Entropy weight calculation results for P1 and P2.  
The proximity of the evaluation object to the optimal solution is determined using Equation (10), which is based on the calculated distances.  
\[C_{i}=\frac{D_{i}^{-}}{D_{i}^{+}+D_{i}^{-}}, \tag{10}\]  
It can be demonstrated that an elevated value of \(C_{i}\) is indicative of the evaluation object being in closer proximity to the optimal solution. The performance scores were obtained through the substitution of the normalised data and entropy weights, as illustrated in Figure 3, utilising the match data from 1701 as a case study.  
As demonstrated in Figure 3, there is a clear correlation between the fluctuations in performance scores and actual match events. For instance, the maximum scores achieved by Player P1 correspond to the completion of a break point and an ace at the 15 th and 96 th points, respectively, while the minimum score attained by Player P2 is concomitant with an error at the 147 th point. These observations are consistent with the technical actions and outcomes during the match. This demonstrates that the entropy weight-TOPSIS evaluation model can objectively reflect players' real-time performance levels. The fluctuations in scores not only reveal changes in player states but can also be integrated with match trends prediction models to provide more precise insights into in-match strategy optimisation.