近年來，QS 世界大學排名已成為衡量高等教育機構國際競爭力的重要指標。2024 年 QS 正式由六指標制度擴展為九指標制度，新增國際研究網絡、就業成果及永續發展三項指標，並調整既有指標權重。然而，制度改革對大學排名之影響，以及師生比指標之評分機制仍缺乏系統性研究。此外，QS 師生比指標之實際評分函數尚未公開，使大學難以評估改善師生比所能帶來之實際效益。因此，本研究旨在分析 QS 排名制度改革對全球大學排名之影響，並建立師生比指標之數學模型，以提供大學資源配置與策略規劃之參考。本研究蒐集 2022 年至 2026 年 QS 世界大學排名、教師與學生人數及各項指標資料。第一部分重新建構六指標與九指標排名，比較制度改革前後之排名變化，並分析在制度改革下的受益學校，採用分群標準化、Welch’s t 檢定、邏輯思迴歸（Logistic Regression）等方法，分析影響受益之關鍵指標。第二部分則以 4，227 筆有效樣本，利用基於遺傳編程（Genetic Programming）之符號回歸（Symbolic Regression） 建立師生比與 QS 師生比指標分數之函數模型，並透過邊際效益分析評估教師資源投入效益，並以台灣四所大學作為實際案例分析。研究結果顯示，約 58.43% 的學校於九指標制度下排名提升，其中永續發展、就業成果及國際研究網絡為受益之主要正向因素， 而師生比則呈顯著負向關聯。此外，本研究成功建立具良好預測能力之師生比非線性函數模型，有效描述師生比與指標分數之關係，並發現教師資源投入存在最大邊際效益區間，其後分數增益將逐漸遞減，案例研究進一步表明，所提出的模型能夠有效量化教師資源投入的效益，提供大學政策規劃之參考。整體而言，本研究不僅揭示 QS 制度改革對全球大學排名之影響與主要驅動因素，亦建立可量化評估師資投入效益之數學模型，可作為高等教育機構進行排名策略、資源配置及校務發展決策之參考。;The QS World University Rankings have become an important indicator for evaluating the international competitiveness of higher education institutions. In 2024， QS expanded its evaluation framework from a six-indicator system to a nine-indicator system by in- troducing International Research Network， Employment Outcomes， and Sustainability. However， the impacts of this reform and the scoring mechanism of the Faculty–Student indicator remain insufficiently understood. Therefore， this study investigates the effects of the QS ranking reform and develops a mathematical model for the Faculty–Student indicator to support university resource allocation and strategic planning. This study col- lected QS World University Rankings data， faculty and student data， and indicator scores from 2022 to 2026. The first part reconstructed the six-indicator and nine-indicator rank- ings to analyze ranking changes and identify universities that benefited from the reform using statistical analysis and logistic regression. The second part employed Symbolic Regression based on Genetic Programming to establish a mathematical model relating the Faculty–Student Ratio to the QS Faculty–Student indicator score using 4，227 valid samples. Marginal effect analysis and case studies of four Taiwanese universities were further conducted. The results show that approximately 58.43% of universities improved their rankings under the nine-indicator system. Sustainability， Employment Outcomes， and International Research Network were identified as the major positive factors associ- ated with beneficiary status， whereas the Faculty–Student indicator showed a significant negative association. The proposed symbolic regression model successfully captured the relationship between the Faculty–Student Ratio and indicator score， and marginal ef- fect analysis revealed a maximum-benefit region followed by diminishing returns. Case studies further demonstrated that the model can effectively quantify the benefits of fac- ulty resource investment， providing practical support for university policy and resource planning.
