## 4 Empirical Results and Discussion
### Match Outcome Prediction  
The predictive performance of PageRank rankings was evaluated using six temporal horizons, ranging from the current season alone to the inclusion of up to five preceding seasons. Table 2 summarizes the results. When relying solely on current-season data, prediction accuracy was low (41.8%). In contrast, incorporating one to five years of prior results significantly improved performance, with accuracy ranging from 76.2% to 83.7%.  
Figure 3 illustrates how accuracy varied by tournament stage. For quarterfinal predictions, using data from the current season and two previous years yielded the best results. Semifinal predictions required a broader historical window of three to five years to achieve optimal accuracy. Moreover, we observed that in high-stakes rounds such as the semifinals and final, predictive accuracy consistently increased with longer historical input.  
The decline in accuracy when using 5-year historical data (76.2%) compared to 4-year data (83.7%) reflects several external influences that affect the tournament's competitive dynamics over time. These include tournament format changes (such as the additional semifinal match in 2013-2014 seasons and the elimination of seeded bracket protections in 2020), the temporal decay of information due to natural program evolution and player turnover cycles typical in high school sports, and COVID-19 impacts on the 2020-2021  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Horizon (Years)** & **Stage** & **Total Games** & **Correct Predictions** & **Accuracy** \\ \hline \multirow{4}{*}{(current season)} & All (Q, S, F) & 79 & 33 & 0.418 \\  & Quarterfinals & 44 & 21 & 0.477 \\  & Semifinals & 24 & 10 & 0.417 \\  & Finals & 11 & 2 & 0.182 \\ \hline \multirow{4}{*}{1} & All (Q, S, F) & 71 & 55 & 0.775 \\  & Quarterfinals & 40 & 34 & 0.85 \\  & Semifinals & 21 & 14 & 0.667 \\  & Finals & 10 & 7 & 0.7 \\ \hline \multirow{4}{*}{2} & All (Q, S, F) & 63 & 50 & 0.794 \\  & Quarterfinals & 36 & 31 & 0.861 \\  & Semifinals & 18 & 13 & 0.722 \\  & Finals & 9 & 6 & 0.667 \\ \hline \multirow{4}{*}{3} & All (Q, S, F) & 56 & 44 & 0.786 \\  & Quarterfinals & 32 & 25 & 0.781 \\  & Semifinals & 16 & 13 & 0.812 \\  & Finals & 8 & 6 & 0.75 \\ \hline \multirow{4}{*}{4} & All (Q, S, F) & 49 & 41 & 0.837 \\  & Quarterfinals & 28 & 22 & 0.786 \\  & Semifinals & 14 & 13 & 0.929 \\  & Finals & 7 & 6 & 0.857 \\ \hline \multirow{4}{*}{5} & All (Q, S, F) & 42 & 32 & 0.762 \\  & Quarterfinals & 24 & 17 & 0.708 \\ \cline{1-1}  & Semifinals & 12 & 10 & 0.833 \\ \cline{1-1}  & Finals & 6 & 5 & 0.833 \\ \hline \end{tabular}
\end{table}
Table 2: Prediction accuracy by historical data horizons and tournament stages.  
tournaments, where key players were unable to participate due to infection or quarantine protocols. Conversely, the exceptionally high Kendall coefficients in 2014 (0.929) and 2018 (0.905) suggest periods of greater competitive stability, where PageRank rankings aligned particularly well with tournament outcomes, possibly indicating more predictable competitive hierarchies during these seasons.  
This analysis suggests that 3-4 years represents the optimal balance between historical depth and temporal relevance for PageRank-based predictions in this context. The deterioration in predictive performance beyond this window indicates that older data may introduce noise rather than signals, particularly when structural changes to the tournament format or external disruptions alter the underlying competitive dynamics. In the later knockout stages, where competition is more selective and match outcomes are harder to infer, multi-year performance data provides more reliable signals of underlying team strength. The inclusion of longitudinal data mitigates the sparsity inherent in single-elimination structures and enhances the model's ability to distinguish relative competitiveness. This underscores the importance of historical depth when applying network-based ranking methods to incomplete or asymmetric competitions.