成功的驱动因素：用于分解一级方程式赛车中潜在车手与车队能力的贝叶斯状态空间模型
Drivers of Success: A Bayesian State-Space Model to Disentangling Latent Driver and Constructor Abilities in Formula One
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中文总结 AI 辅助
本研究针对一级方程式车手与车队能力随时间不可观测且变化的问题，提出贝叶斯状态空间模型，利用排位赛圈速和比赛排名分解二者动态能力，发现车队能力对成绩的贡献常强于车手能力。
中文摘要 AI 辅助
一级方程式（Formula One）的比赛结果反映了车手与车队的共同贡献，但这些贡献不可观测且会随时间变化。我们提出一种贝叶斯状态空间模型，利用两个可观测结果（最快排位赛圈速和比赛排名）分解动态的车手与车队潜在能力。两个结果均共同依赖于大奖赛层面演化的潜在车手与车队状态，而比赛排名方程还额外考虑了发车顺位。该分解通过将车手与车队能力中心化至零的约束，以及车手与车队组合随时间变化的情况来支撑。贝叶斯推断采用无回退采样器（No-U-Turn sampler），并使用对车手与车队能力对称处理的弱信息先验。将模型应用于2014至2021年的一级方程式混合动力时代，我们发现车手与车队能力均存在显著异质性：车手能力通常随时间更稳定，而车队能力表现出更大的变化，且在许多车手-车队组合中，车队能力对观测到的比赛成绩贡献更强。
英文摘要
Formula One outcomes reflect the joint contributions of drivers and constructors, but these contributions are unobserved and vary over time. We propose a Bayesian state-space model that disentangles dynamic driver and constructor abilities using two observed outcomes: fastest qualifying lap times and race rankings. Both outcomes depend jointly on latent driver and constructor states that evolve at the Grand Prix level, while the race equation additionally accounts for starting-grid position. The decomposition is supported by constraints that center the driver and constructor abilities at zero, together with variation in driver-constructor assignments over time. Bayesian inference is performed using the No-U-Turn sampler under weakly informative priors that treat driver and constructor abilities symmetrically. Applying the model to the Formula One hybrid era from 2014 to 2021, we find substantial heterogeneity in both driver and constructor abilities. Driver abilities are generally more stable over time, whereas constructor abilities exhibit greater variation and, for many driver--constructor combinations, contribute more strongly to observed performance.
