## 4 Discussion  
Using a novel methodological proposal, this study sought to identify which characteristics of serves determine their efficiency in men's professional doubles tennis. The results showed that the characteristics of the serves in which the point ended in two, three or more shots were very similar. However, it was possible to identify different characteristics for the aces, compared to those in which the point lasted more than three shots. Therefore, these results allow us to establish the variables and values which are associated with a higher probability of serving an ace in men's professional doubles tennis. In addition, the methodology used has been shown to be a novel, valid and reliable way that can be replicated for the calculation of the efficiency of actions in different sports disciplines. The results have shown that the service angle is one of the variables that best determines the probability of serving an ace in men's professional doubles tennis. These results are consistent with a previous study of the serve in singles tennis, which indicated that if the serve angle was less than 5.88\({}^{\circ}\), the serve will be returned with a probability of 92.52% [11]. In doubles tennis, according to the data obtained in the present study, an angle of between 5.7\({}^{\circ}\) and 8.7\({}^{\circ}\) theoretically increases the probability of serving an ace from 29.77% to 88.21% on the advantage side and from 33.70% to 88.68% on the deuce side. These results support those obtained by previous studies, where [PERSON] and [PERSON] [11] reported that there is a higher probability of getting an ace when the serve is played wide than to the T zone, with probabilities of 42% on the advantage side and 52% on the deuce side. Wide serves generate a greater angle than those played to the T, so it is logical, according to the data obtained, that they are also more effective. Furthermore, from a technical point of view, and specifically related to the different types of serve spin used, it has been shown that players use the slice serve to generate a greater serve angle on the deuce side, whereas they opt for flat or topspin serves for a greater angle when serving to the T on the advantage side [6; 19; 41]. Another of the variables found to have a greater relevance in determining the probability of serving an ace has been the distance from the bounce of the ball to the sideline \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Variable** & **Side** & **Values (Min–Max)** & **Effectiveness before (\%)** & **Effectiveness after (\%)** \\ \hline \multirow{3}{*}{dL (m)} & DEUCE & & 33.05 & 83.40 \\  & AD & 0–0.28 & 30.64 & 81.26 \\  & BOTH & & 33.49 & 88.48 \\ \hline \multirow{3}{*}{Serve angle (deg)} & DEUCE & & 33.70 & 88.68 \\  & AD & 5.7–8.7 & 29.77 & 88.21 \\  & BOTH & & 33.25 & 89.04 \\ \hline \multirow{3}{*}{Speed (km h\({}^{-1}\))} & DEUCE & & 35.17 & 45.75 \\  & AD & 187–220 & 34.36 & 44.13 \\ \cline{1-1}  & BOTH & & 30.38 & 39.91 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results of the predictions using the trained model. of the service box. This reinforces the idea that one of the main objectives of the server is to gain an advantage over the receiver, trying to get the ball as far away from the receiver as possible [6; 14; 15]. [PERSON] and [PERSON] [11] determined that in 77.53% of cases, if the distance to the line was less than 15.27 cm and, in addition, the serve angle was greater than or equal to 5.88\({}^{\circ}\), the serve would be an ace. In the case of men's professional doubles tennis, in this study, it has been shown that, if the serve distance is between 0 and 28 cm, the probability of a serve being an ace would increase from 30.64% to 81.26% on the advantage side and from 33.05% to 83.40% on the deuce side. The results on the importance of the angle of the serve and the distance of the bounce of the ball to the line also support what has been found in previous studies on the professional doubles game. According to [PERSON] et al.