Since the inception of the FIRST Robotics Competition (FRC) and its special playoff system, robotics teams have longed to appropriately quantify the strengths of their designed robots. The FRC includes a playground draft-like phase (alliance selection), arguably the most game-changing part of the competition, in which the top-8 robotics teams in a tournament based on the FRC’s ranking system assess potential alliance members for the opportunity of partnering in a playoff stage. In such a three-versus-three competition, several measures and models have been used to characterize actual or relative robot strengths. However, existing models are found to have poor predictive performance due to their imprecise estimates of robot strengths caused by a small ratio of the number of observations to the number of robots. A more general regression model with latent clusters of robot strengths is, thus, proposed to enhance their predictive capacities. Two effective estimation procedures are further developed to simultaneously estimate the number of clusters, clusters of robots, and robot strengths. Meanwhile, some measures are used to assess the predictive ability of competing models, the agreement between published FRC measures of strength and model-based robot strengths of all, playoff, and FRC top-8 robots, and the agreement between FRC top-8 robots and model-based top robots. Moreover, the stability of estimated robot strengths and accuracies is investigated to determine whether the scheduled matches are excessive or insufficient. In the analysis of qualification data from the 2018 FRC Houston and Detroit championships, the predictive ability of our model is also shown to be significantly better than those of existing models. Teams who adopt the new model can now appropriately rank their preferences for playoff alliance partners with greater predictive capability than before.

自从FIRST机器人竞赛（FRC）及其特殊的季后赛系统启动以来，机器人团队就渴望适当地量化其设计的机器人的实力。FRC包括一个类似于操场的选秀阶段（联盟选择），可以说是比赛中最具变化的部分，其中基于FRC排名系统的锦标赛前8名机器人团队将评估潜在联盟成员的机会。在季后赛阶段合作。在这样的三对三比赛中，已经使用了几种度量和模型来表征实际或相对的机器人强度。但是，发现现有模型的预测性能很差，这是因为观测值与机器人数量的比例很小导致对机器人强度的不精确估算。因此，提出了一个具有潜在的机器人强度簇的更通用的回归模型，以增强其预测能力。进一步开发了两个有效的估算程序来同时估算群集的数量，机器人的群集和机器人的强度。同时，一些措施用于评估竞争模型的预测能力，已发布的FRC强度度量与基于模型的所有人，季后赛和FRC top-8机器人的力量之间的协议，以及FRC top-8机器人之间的协议和基于模型的顶级机器人。此外，调查估计的机器人力量和准确性的稳定性，以确定预定的比赛是否过多或不足。在分析2018 FRC休斯敦和底特律锦标赛的资格数据时，我们的模型的预测能力也显示出明显优于现有模型的预测能力。现在，采用新模型的团队可以以比以往更高的预测能力适当地选择他们对季后赛联盟伙伴的偏好。