Hippocampal activity represents many behaviorally important variables, including context, an animal's location within a given environmental context, time, and reward. Here we used longitudinal calcium imaging in mice, multiple large virtual environments, and differing reward contingencies to derive a unified probabilistic model of hippocampal CA1 representations centered on a single feature -the field propensity. Each cell's propensity governs how many place fields it has per unit space, predicts its reward-related activity, and is preserved across distinct environments and over months. The propensity is broadly distributed-with many low, and some very high, propensity cells -and thus strongly shapes hippocampal representations. The result is a range of spatial codes, from sparse to dense. Propensity varied ~10-fold between adjacent cells in a salt-and-pepper fashion, indicating substantial functional differences within a presumed cell type. The stability of each cell's propensity across conditions suggests this fundamental property has anatomical, transcriptional, and/or developmental origins.