## 4 Discussion  
### Impact of Scoring the First Goal and Temporal Patterns of Goal Scoring  
The present analysis confirmed the significant influence of scoring the first goal on match outcomes in the FIFA Club World Cup, with teams that scored first winning 62.5% of matches and losing only 10.4%. This finding aligns with an established body of literature demonstrating the competitive advantage conferred by gaining an early lead [3; 4; 5; 6; 7; 8; 9]. Prior studies reported comparable or higher win rates following the first goal in domestic and international contexts. For example, in the Chinese Super League, [PERSON] et al. [3] found a 66.3% win rate and an 87.01% unbeaten rate for teams scoring first, while in European women's leagues, [PERSON] et al. [4] observed that 75.9% of match winners had \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline
**Predictor** & **AUC** & **95\% CI** & \(p\) & **Cutoff** & **Sensitivity** & **Specificity** & **Accuracy** & **PPV** & **NPV** \\  & & & & **(\%)** & **(\%)** & **(\%)** & **(\%)** & **(\%)** & **(\%)** \\ \hline Attempts at Goal & 0.74 & 0.65–0.84 & 0.001 * & \(\geq\)3.5 & 80.0 & 60.7 & 67.7 & 53.9 & 84.1 \\  & & & & & & & & \\  & & & & & & & & \\  & & & & & & & & \\  & & & & & & & & \\ \hline Total Passes & 0.76 & 0.66–0.87 & 0.001 * & \(\geq\)478.5 & 62.9 & 83.6 & 76.0 & 68.7 & 79.7 \\  & & & & & & & & \\  & & & & & & & & \\ \hline  & & & & & & & & \\  & & & & & & & & \\ \end{tabular}
\end{table} 
Table 2: Diagnostic performance of individual key predictors for match outcome based on ROC curve analysis. Figure 10: Receiver Operating Characteristic (ROC) curves for individual predictors in logistic regression model of match outcome. scored first. Similar trends were documented in the K-League [6], UEFA Champions League [5], and across major European men's leagues [10]. On the international stage, [PERSON] and [PERSON] [7] found that in FIFA World Cup and UEFA Euro knockout phases, teams scoring first won 78.46% of the time, although this advantage diminished in extra time (62.5%) and during penalty shootouts (57.14%). In the UEFA Champions League, a more stratified tournament, [PERSON] et al. [5] reported that teams scoring first had a 92% win rate when facing weaker opponents, 71% against balanced teams, and 59% against stronger ones. The UEFA Euro 2024 analysis revealed a significant association (\(\chi^{2}\) = 8.167, \(p\) = 0.017) between scoring first and positive outcomes, with only four of thirty-six teams losing after scoring first [8]. Similarly, [PERSON] et al. [10] observed that home teams scoring first in Europe's top leagues secured 84.85% of available points, while away teams scoring first still won 76.25% of matches. These findings collectively confirmed that scoring first offered a substantial competitive advantage across contexts. However, the current study contributed uniquely by situating this advantage within the specific framework of the FIFA Club World Cup. Unlike domestic leagues or continental tournaments, the Club World Cup comprised champions from six confederations with disparate tactical systems, seasonal calendars, and resource levels. The tournament's short, knockout-based format, often played at a neutral venue, reduced contextual familiarity and diminished traditional advantages such as home support and environmental adaptation. As a result, although the win rate after scoring first (62.5%) remained considerable, it was notably lower than in more structurally stable settings (e.g., 78-92% in [4; 5; 6; 7]). This moderation likely reflected the inherent unpredictability of intercontinental encounters, where dominant ball possession or tactical superiority could not always be converted into control after an early goal. Thus, this study revealed that while scoring first was an important predictor, its influence may have been less deterministic in global competitions where contextual asymmetries and limited preparatory time reduced the capacity to consolidate psychological and tactical momentum.