How useful are time of use rates and critical peak pricing schemes? To answer this question, this paper analyzes data from all seven competitive wholesale power markets in the US between 2000 and 2020. To maximize efficiency, retail rates need to align with marginal generation costs, which we proxy with wholesale prices. In practice, we find that feasible time of use and critical peak pricing schemes are poorly correlated with wholesale prices. Well-designed schemes can potentially save hundreds of millions of dollars in avoided dead-weight loss per year over flat tariffs, but this is typically under 10% of what might be regained through real-time pricing. Increasingly complex schemes can better match wholesale price variation only when the are (unrealistically) calibrated to wholesale prices ex post. When rates must be set ahead of time given imperfect information, complex schemes perform poorly and are often worse than flat rates. Rather than adding complexity, our results emphasize the importance of schemes that update more often to better incorporate new information.