  We study the following fundamental data-driven pricing problem. How
can/should a decision-maker price its product based on data at a single
historical price? How valuable is such data? We consider a decision-maker who
optimizes over (potentially randomized) pricing policies to maximize the
worst-case ratio of the revenue she can garner compared to an oracle with full
knowledge of the distribution of values, when the latter is only assumed to
belong to a broad non-parametric set. In particular, our framework applies to
the widely used regular and monotone non-decreasing hazard rate (mhr) classes
of distributions. For settings where the seller knows the exact probability of
sale associated with one historical price or only a confidence interval for it,
we fully characterize optimal performance and near-optimal pricing algorithms
that adjust to the information at hand. The framework we develop is general and
allows to characterize optimal performance for deterministic or more general
randomized mechanisms, and leads to fundamental novel insights on the value of
data for pricing. As examples, against mhr distributions, we show that it is
possible to guarantee $85\%$ of oracle performance if one knows that half of
the customers have bought at the historical price, and if only $1\%$ of the
customers bought, it still possible to guarantee $51\%$ of oracle performance.
