Deriving global rankings from noisy and incomplete pairwise comparisons is a fundamental problem with applications in sports analytics, preference aggregation, and evaluation. Many recent approaches rely on learning-based models, but in practice ranking systems are often required to operate under strict constraints on training cost, runtime, and reproducibility. We study a scalable, training-free alternative that constructs rankings directly from weighted directed comparison graphs. Our approach represents pairwise comparisons as a weighted digraph and leverages the connection between ranking inconsistency and feedback-arc-set removal to build an acyclic comparison backbone. The proposed pipeline is time-bounded and consists of three stages: a local-ratio-style cycle-breaking heuristic, a stable weight-prioritized add-back procedure with up to three passes while preserving acyclicity, and an optional bounded score-refinement stage under upset-based objectives used in recent ranking benchmarks. The resulting method outputs a real-valued score vector whose induced order is consistent with the recovered acyclic structure. Across the benchmark suite used in recent ranking-from-comparisons work, the proposed method is competitive with strong classical baselines and delivers substantial runtime advantages over training-based GNNRank configurations under fixed wall-clock budgets. These results position the method as a practical, deterministic, and scalable alternative for ranking on large pairwise-comparison graphs when training cost and deployment efficiency are important.