Almen intensity cannot carry a peening result from one material to another. This paper gives a cavity-based correlation for the depth of compression that can, within a declared domain of materials, media and processes. Johnson’s expanding-cavity model is applied to the shot impact and solved exactly with an energy balance, placing the depth at a fixed multiple of the plastic-zone radius with one fitted depth constant (1.43 on a measured shot-velocity scale), conditional on the constitutive and velocity models; a simpler form, also new, agrees within 8% and is as accurate on every test, so the exact form is preferred for its physics, not its accuracy. On 31 conditions in 15 materials and states, its error on a withheld material is 7.9% (±13% at 90%). Locked, then applied to 30 conditions from seven further laboratories, it predicts depth to 11.4% (9.6% weighting the seven laboratories equally; 22 of the 30 conditions come from one laboratory), against 19.4% for depth proportional to intensity and 12.7% for a four-constant power law in intensity, shot size and strength fitted to the same data. In locked predictions for three more laboratories, steel depths are predicted to 20% weighting laboratories equally, and to 15% for the six profiles measured through the full depth. Nickel alloys need measured velocity. The domain is steel media at 0.125–0.45 mm A and 100–200% coverage in quenched-and-tempered steels and titanium and aluminium alloys; ferrite-dominated mild steels appear to need a higher strain-rate factor. Four propositions explain why intensity fails: among them, under the restricted scaling model a strip record makes shot velocity and size structurally identifiable, with a practical precision that is predicted but not yet demonstrated, and the strip lot only structurally with a dent and metered flow, so shot size must be fixed. Provisional screening factors modelled on B and A basis conventions, not qualified allowables, are 0.74 and 0.61 on the predicted median depth from the strip record alone, rising to about 0.92 with profiles on the part, for use through an AS7045 qualification route once the statistical basis is accepted.