Evaluating the in-context learning classification performance of language models poses challenges due to small dataset sizes, extensive prompt-selection using the validation set, and intentionally difficult tasks that lead to near-random performance. The standard random baseline -- the expected accuracy of guessing labels uniformly at random -- is stable when the evaluation set is used only once or when the dataset is large. We account for the common practice of validation set reuse and existing small datasets with a stronger random baseline: the expected maximum accuracy across multiple random classifiers. When choosing the best prompt demonstrations across six quantized language models applied to 16 BIG-bench Lite tasks, more than 20\% of the few-shot results that exceed the standard baseline do not exceed this stronger random baseline. When held-out test sets are available, this stronger baseline is also a better predictor of held-out performance than the standard baseline, avoiding unnecessary test set evaluations. This maximum random baseline provides an easily calculated drop-in replacement for the standard baseline.

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