  Subword tokenization is a key part of many NLP pipelines. However, little is
known about why some tokenizer and hyperparameter combinations lead to better
downstream model performance than others. We propose that good tokenizers lead
to \emph{efficient} channel usage, where the channel is the means by which some
input is conveyed to the model and efficiency can be quantified in
information-theoretic terms as the ratio of the Shannon entropy to the maximum
possible entropy of the token distribution. Yet, an optimal encoding according
to Shannon entropy assigns extremely long codes to low-frequency tokens and
very short codes to high-frequency tokens. Defining efficiency in terms of
R\'enyi entropy, on the other hand, penalizes distributions with either very
high or very low-frequency tokens. In machine translation, we find that across
multiple tokenizers, the R\'enyi entropy with $\alpha = 2.5$ has a very strong
correlation with \textsc{Bleu}: $0.78$ in comparison to just $-0.32$ for
compressed length.
