The Common Out-Neighbor (or CON) score quantifies shared influence through outgoing links in competitive contexts. A dynamic analysis of competition networks reveals the CON score as a powerful predictor of node rankings. Defined in first-order and second-order forms, the CON score captures both direct and indirect competitive interactions, offering a comprehensive metric for evaluating node influence. Using datasets from Survivor, Chess.com, and Dota~2 online gaming competitions, directed competition networks are constructed, and the dynamic CON score is integrated into supervised machine learning models. Empirical results show that the CON score consistently outperforms traditional centrality measures such as PageRank, closeness, and betweenness centrality in classification tasks. By integrating dynamic centrality measures with machine learning, our proposed methodology accurately predicts outcomes in competition networks. The findings underline the CON score's robustness as a feature in node classification, offering a significant advancement in understanding and analyzing competitive interactions.