| Theoretical relationship between maximum agonist response, system maximal response, and the operational efficacy of a drug (Black et al. 2010) |  (1) |
| or |
| (2) |
| Anticipated experimental maximum response of reference agonist () | Since in high-amplification systems, eq. 1 becomes (3a) | Since in low-amplification systems, eq. 1 becomes (3b) |
| Anticipated experimental maximum response of a test agonist () | Since , eq. 1 can be rewritten as | Since , eq. 1 becomes |
| (4a) | (4b) |
| Experimental implementation of operational model to determine operational efficacy | Implementation of the operational model assumes eq. 2 to be true for experimentally measured values; in other words, |
|
| Since operational model also assumes hyperbolicity, that is, that the reference agonist can evoke system maximal response, . |
|
| Experimental determination of operational efficacy, , of a test agonist | Substituting eqs. 3a and 4a | Substituting eqs. 3b and 4b |
| |
| | |
| (5a) | | (5b) |
(1)
(2)
)
in high-amplification systems, eq. 1 becomes 
(3a)
in low-amplification systems, eq. 1 becomes 
(3b)
)
, eq. 1 can be rewritten as
, eq. 1 becomes
(4a)
(4b)
.
, of a test agonist
(5a)
(5b)