Tokenization is a fundamental component of modern language models: before a model sees data, its tokenizer has already determined how the data appears. We identify and challenge three myths in the tokenization research literature. Myth #1: Bits-Per-Byte (BPB) is agnostic to the tokenizer and/or the vocabulary size: BPB is tokens per byte times bits per token, and the two factors do not cancel; using untrained models, we show that BPB prefers some tokenizers over others: the model has learned nothing, but the tokenizer--model pair has. Myth #2: lower BPB means a better model: On untrained models, BPB strongly prefers some vocabulary sizes, even though accuracy remains at chance, and on real models trained on the same data, BPB correlates weakly with downstream performance. Myth #3: different "tokenizer-agnostic" metrics yield consistent results: The "unigram-normalized loss" is not tokenizer-agnostic; its reported correlation of 0.989 with BPB comes from a confounder and falls to 0.057 once fixed; from the same data the two metrics select different vocabularies at each model size. We present a tokenizer trilemma: no metric can score only the true distribution best, give the same predictions the same score, and tie all untrained models, so choosing a metric is choosing a research question. We conclude with a caution for reading the tokenization literature and a conjecture for future work.

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