We postulate that a simple, three-state synaptic switch governs changes in synaptic strength at individual synapses. Under this switch rule, we show that a variety of experimental results on timing-dependent plasticity can emerge from temporal and spatial averaging over multiple synapses and multiple spike pairings. In particular, we show that a critical window for the interaction of pre- and postsynaptic spikes emerges as an ensemble property of the collective system, with individual synapses exhibiting only a minimal form of spike coincidence detection. In addition, we show that a Bienenstock-Cooper-Munro—like, rate-based plasticity rule emerges directly from such a model. This demonstrates that two apparently separate forms of neuronal plasticity can emerge from a much simpler rule governing the plasticity of individual synapses.