Estimating Robot Strengths with Application to Selection of Alliance Members in FIRST Robotics Competitions

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.