# Notational Analysis of Men's Singles Pickleball: Game Patterns and Competitive Strategies
## 3 Results  
### Descriptive Analysis  
Table 3 presents a descriptive analysis of the study, including the \(\chi^{2}\) goodness-of-fit test. Significant statistical differences were found in the \(\chi^{2}\) test for each of the criteria analyzed. In general terms, the start of the point predominantly occurred without a service fault (nearly 98%) and was followed by a medium-length rally (44%), although short rallies were also common (43%). It was more common for the tetramer to win the point (53%). Points mostly ended due to an unforced error (58%), with the server making the error more frequently (32.9%). In more than half of the points played (51%), the final shot was executed from striking zone 2. More than half of the final shots were hit out or into the net (58%). Winners were typically directed to finishing zone 4 (11%) or finishing zone 6 (9%). The most common final shot was a forehand (34%), followed by a backhand (22%), although numerous volleys were also observed (18% forehand and 21% backhand). \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Criteria** & \begin{tabular}{l} **Intra-Kappa** \\ **Obs1-Obs1** \\ \end{tabular} & \
\begin{tabular}{l} **Intra-Kappa** \\ **Obs2-Obs2** \\ \end{tabular} &
\begin{tabular}{l} **Inter-Kappa** \\ **Obs1-Obs2** \\ \end{tabular} \\ \hline Service & 1 & 1 & 1 \\ Rally length & 0.98 & 0.99 & 0.98 \\ Strike zone & 0.96 & 0.97 & 0.96 \\ Finish zone & 0.97 & 0.99 & 0.98 \\ Winner & 0.99 & 0.99 & 0.97 \\ Point ending & 0.97 & 0.97 & 0.96 \\ Final stroke & 0.96 & 0.99 & 0.96 \\ \hline Mean reliability & 0.98 & 0.99 & 0.97 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Degree of reliability of the study. On the other hand, significant differences (\(\chi^{2}=38.200\); \(p=0.000\)) were observed when comparing the data concerning rally length based on the point winner (whether the server or the receiver wins the point). The effect size test indicated that the relationship was weak (\(V=0.183\)). As shown in Figure 2a, the analysis of adjusted residuals reveals distinct patterns in point winning across different rally lengths. In short rallies (SH), servers won significantly more points than expected, with an adjusted residual of 6.2, indicating that this type of rally favors the server. Conversely, in medium rallies (MD), receivers gained more points than expected, reflected by an adjusted residual of 4.9, highlighting a significant advantage for them. In long rallies (LN), although receivers also won more points than anticipated, with an adjusted residual of 1.9, these differences did not reach statistical significance. When crossing the variable point ending with rally length (Figure 2b), statistically significant differences are again observed (\(\chi^{2}=106.774\); \(p=0.000\)). The effect size test indicated that the relationship was moderate (\(V=0.216\)). In short rallies (SH), it was observed that servers predominantly won due to unforced errors by the opponent (SWUE), with an adjusted residual of 8.8. Overall, unforced errors (SWUE and RWUE) were more common than winners (SWW and RWW). In medium rallies (MD), the receiver won a greater number of points, primarily due to unforced errors (RWUE, with an adjusted residual of 0.8), but especially through winners (RWW), which had an adjusted residual of 5.6, showing a notable increase compared to short rallies. It is noteworthy that the server's unforced error (SWUE), which was the most recorded value in short rallies, became the least frequent in medium rallies, while the receiver's winners (RWW) increased. In long rallies (LN), a trend similar to that of medium rallies was maintained, though with a decrease in the number of recorded points. When analyzing the data between winner/point ending and striking zones (Figure 2c,d), statistically significant differences were observed (\(\chi^{2}=31.696\); \(p=0.000\) and \(\chi^{2}=437.636\); \(p=0.000\), respectively).