Tokenization is a critical component of the language modeling pipeline, but it is poorly understood. Tokenizers can drastically impact downstream performance, but currently there is mixed evidence about which intrinsic tokenizer evaluations are able to predict which tokenizers will result in a better language model before training the model. In this paper, we analyze approximately 200 language models trained on nine different languages. We evaluate both models and their tokenizers and test whether there is a relationship between any proposed intrinsic tokenizer evaluations and model performance, as measured by a wide variety of benchmarks. Despite the quantity and variety of proposed intrinsic tokenizer metrics, none consistently predicts downstream performance across model families, tasks, and languages. This motivates the need for novel tokenizer evaluation metrics and approaches. Our analysis of a novel linguistically grounded metric introduced in this work shows that new metrics can capture aspects of tokenizer quality that existing metrics miss, though their predictive power is likely to vary across model families and languages.