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Since the inception of the FIRST Robotics Competition (FRC) and its specialplayoff system, robotics teams have longed to appropriately quantify thestrengths of their designed robots. The FRC includes a playground draft-likephase (alliance selection), arguably the most game-changing part of thecompetition, in which the top-8 robotics teams in a tournament based on theFRC's ranking system assess potential alliance members for the opportunity ofpartnering in a playoff stage. In such a three-versus-three competition,several measures and models have been used to characterize actual or relativerobot strengths. However, existing models are found to have poor predictiveperformance due to their imprecise estimates of robot strengths caused by asmall ratio of the number of observations to the number of robots. A moregeneral regression model with latent clusters of robot strengths is, thus,proposed to enhance their predictive capacities. Two effective estimationprocedures are further developed to simultaneously estimate the number ofclusters, clusters of robots, and robot strengths. Meanwhile, some measures areused to assess the predictive ability of competing models, the agreementbetween published FRC measures of strength and model-based robot strengths ofall, playoff, and FRC top-8 robots, and the agreement between FRC top-8 robotsand model-based top robots. Moreover, the stability of estimated robotstrengths and accuracies is investigated to determine whether the scheduledmatches are excessive or insufficient. In the analysis of qualification datafrom the 2018 FRC Houston and Detroit championships, the predictive ability ofour model is also shown to be significantly better than those of existingmodels. Teams who adopt the new model can now appropriately rank theirpreferences for playoff alliance partners with greater predictive capabilitythan before.

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