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 highamplification systems, eq. 1 becomes (3a)  Since in lowamplification 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) 