I would estimate the number of layer-years improved in expectation in year Y from “expected population of layers in year Y”*(“expected population of layers in cages in year Y without the intervention as a fraction of all of them in year Y”—“expected population of layers in cages in year Y with the intervention as a fraction of all of them in year Y”) = P(Y)*(f_control(Y) - f_intervention(Y)), which is correct by definition.
Cost-effectiveness analyses (CEAs) of interventions accelerating animal welfare reforms usually estimate the increase in the welfare of the target animals (for example, hens in cages) based on the acceleration in years of the full implementation of the reform. This makes sense if each level of implementation of the reform is accelerated as much as its full implementation.
However, there are many cases where the acceleration of the full implementation of the reform is not enough to determine the number of animals helped, or animal-years improved. I discuss some below.
Here is a post illustrating this.