- 期刊
On Adopting Elo Rating and Forecasting Game Outcomes in UBA
大專籃球聯賽Elo積分運用與賽事預測
摘要
The purposes of this study were threefold: 1. to investigate the proper setting of the K-factor for adopting the Elo rating system in the University Basketball Association (UBA); 2. to evaluate the Elo's out-of-sample forecasting performance by benchmarking with five other methods (Colley rating, Massey rating, Bradley-Terry model, random guess with a constant probability .5, and winning percentage indicator); 3. to provide a use-case of applying the Elo rating for assisting potential coaching and marketing activities in the future. For data analysis, the samples and variables were extracted from the Men's Division-I tournament of the 2017 ~ 2018 UBA season. There was a total of 152 matches and 304 win-loss records. UBA stages split the collected data into two portions: training dataset (Round of 16 and Round of 8) and testing dataset (Final); the former is for parameter/rating estimation, and the latter is for evaluating the performance of out-of-sample forecast. The results indicated that the K-factor of the Elo method is related to the dispersion of team performance in the UBA tournament. In the Round of 16, the variability of team performance is large; the large K-factor is preferred (e.g., 70). In the Round of 8, teams' abilities are stronger and more stable; therefore, the small K-factor is better (e.g., 35). In addition, the forecasting performance of the Elo method is superior to the other five methods in terms of lower mean square error, lower log-loss, and higher Accuracy (~ 75%). In conclusion, the proper setting of Elo K-factor can underpin a reliable rating estimation for teams in the Men's Division-I tournament of 2017 ~ 2018 UBA season. The self-adjusting feature of the Elo method helps to provide better probabilistic forecasting of future games with lower prediction error. Moreover, the use-cases of Elo can assist coaches in understanding the performance trend for managing training plans, and the rating and prediction information can also underpin the potential marketing activities of UBA in the future.
並列摘要
本研究目的是：一、調查當運用Elo積分系統於大專籃球聯賽時，其合適的參數K值應如何設定；二、比較Elo積分與其他5種方法（Colley積分、Massey積分、Bradley-Terry模型、50/50隨機猜測和勝率指標）在預測賽事之表現；三、提供Elo積分系統之應用案例，以利日後協助賽事訓練與行銷活動。樣本資料來自於106學年度大專籃球聯賽公開男一級賽事，計有152場比賽，304筆勝負球隊之攻守紀錄。樣本資料依賽程階段分為兩部分：訓練資料集（預賽16強階段和複賽8強階段）以及測試資料集（決賽階段），前者為提供參數／積分估算之用，後者作為未來賽事之預測評估。研究結果顯示：在大專籃球聯賽中運用Elo積分系統時，Elo參數K值的設定應與球隊效能指標的變異程度有關。在預賽16強階段，球隊效能指標變異程度大，適合大參數K值（例如：70），在複賽8強階段，球隊能力變強，穩定性高，小參數K值為佳（例如：35）。再者，Elo積分系統對未來賽事之預測能力比其他5種方法好，因為其有較低的均方誤差，較低的對數損失，和較高的正確率（～75%）。本研究結論認為當運用Elo積分系統於106學年度大專籃球聯賽公開男一級賽事時，設定合適的Elo參數K值能提供可靠的球隊效能評估，且其自我校準機制有助於對未來賽事提供誤差較小的機率預測效能。此外在實務應用上，Elo積分系統可協助教練瞭解球隊效能趨勢以利其賽事訓練安排，且其積分與預測資訊也可輔助日後可能的賽事行銷活動。
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