避免輸家得利之賽程分析與最佳化

Abstract

中華職棒由於其賽程、賽制的設計，將一整年的比賽分為上、下半季進行，於 2017 年時出現了有隊伍能夠藉由輸掉比賽得到晉級機會的情形，雖然中華職棒在 2022 年採用了新賽制，但是時至今日，已採用新賽制的中華職棒，這個現象仍然有可能發生。 我們的論文提出了以樹的結構方式分析中華職棒的賽程，並提出方法找出可能有輸家得利發生的時機點。我們設計了一些實驗來測試加速分析方式的有效性。我們也成功用 2017 年的賽程驗證了程式結果，並且以此方法於中華職棒 2017~2023 年的賽程來比較新賽制與舊賽制何者較容易導致輸家得利，也成功找出了新賽制在 2023 年其實有可能比舊賽制差的情形。 我們提出一些計算賽程損失的方式，以可能發生輸家得利的程度來比較賽程的好壞，並設計了一些實驗比較這些損失函數的好壞。並且透過了模擬退火法來搭配我們的分析方法及賽程的損失，試圖重新調整中華職棒因雨延賽後的賽程，減少中華職棒發生輸家得利的可能性。

The Chinese Professional Baseball League (CPBL) divides its annual games into two halves, adopting a unique schedule and format. In 2017, a situation occurred where a team could advance to the playoffs by intentionally losing a game. Although the CPBL introduced a new format in 2022, this phenomenon remains possible even under the current system. This thesis proposes a tree-structured approach to analyze the CPBL schedule and identifies scenarios where losing may lead to an advantage. We designed experiments to test the effectiveness of accelerated analysis approaches. Our approach successfully verified the results using the 2017 schedule. Additionally, we applied this method to schedules from 2017 to 2023, comparing the likelihood of “tanking for playoff” under the new and old formats. Interestingly, we identified cases where the new format could potentially perform worse than the old format in 2023. We also proposed several approaches for calculating schedule loss to evaluate the quality of a schedule based on the occurrence of “tanking for playoff.” Experiments were conducted to compare these loss indices. By integrating our analytical approaches with simulated annealing, we attempted to reschedule CPBL games affected by rain, aiming to reduce the occurrence of "tanking for playoff."