Shapelets are discriminative subsequences, originally embedded in shapelet-based decision trees but have since been extended to shapelet-based transformations. We propose Castor, a simple, efficient, and accurate time series classification algorithm that utilizes shapelets to transform time series. The transformation organizes shapelets into groups with varying dilation and allows the shapelets to compete over the time context to construct a diverse feature representation. By organizing the shapelets into groups, we enable the transformation to transition between levels of competition, resulting in methods that more closely resemble distance-based transformations or dictionary-based transformations. We demonstrate, through an extensive empirical investigation, that Castor yields transformations that result in classifiers that are significantly more accurate than several state-of-the-art classifiers. In an extensive ablation study, we examine the effect of choosing hyperparameters and suggest accurate and efficient default values.