Why does standard reduction potential get multiplied by the change in oxidation state and not by the number of electrons transferred?

The whole basis of Frost diagrams is to have a graphical representation of the Gibbs free energy of formation ($\Delta{G}\_{f}$) of different oxidation states of an element using the proportional relation between Gibbs free energy and standard reduction potential:



> 
> $\Delta$$G$ = $-nFE^{o}$
> 
> 
> 


From which we can derive:



> 
> $\frac{{-}\Delta{G}}{F}$ = $nE^{o}$
> 
> 
> 


Thus, if we graph **$nE^{o}$** against the oxidation number (N), we can accurately describe the relationship between oxidation state and ($\Delta{G}\_{f}$).




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I encountered a problem in Shriver's Inorganic Chemistry that asks to draw the Frost diagram of oxygen from its Latimer diagram.



> 
> Construct a Frost diagram for oxygen from the Latimer diagram below.
> 
> 
> 


[![enter image description here](https://i.stack.imgur.com/nk9zT.png)](https://i.stack.imgur.com/nk9zT.png)


I initially though that we would use the standard reduction equations below, which give $nE^{o}$ as $-1.36V$ ($-2$ times $0.68V$) for $\ce{H2O2}$ and $-4.92V$ ($-4$ times $1.23V$) for $\ce{H2O}$.



> 
> $\ce{O2(g) + 2H+ (aq) + 2e- -> H2O2 (aq)}$ $E^{o}$=$+0.68V$
> 
> 
> $\ce{O2(g) + 4H+(aq) + 4e- -> 2H2O(l)}$ $E^{o}$=$+1.23V$
> 
> 
> 


However, the book seems to be using the change in the oxidation number of oxygen to calculate $nE^{o}$ for $\ce{H2O2}$ and $\ce{H2O}$.


[![enter image description here](https://i.stack.imgur.com/oqMI3.png)](https://i.stack.imgur.com/oqMI3.png)


Online images of Frost diagrams corroborate this calculation.


[![enter image description here](https://i.stack.imgur.com/zUpdy.png)](https://i.stack.imgur.com/zUpdy.png)


Why is the change in oxidation state used as the standard to calculate $nE^{o}$ instead of the number of electrons transferred given that $n$ in $nE^{o}$ is the number of electrons transferred?


**References**


Shriver, D. F., Weller, M. T., Overton, T., Rourke, J., & Armstrong, F. A. (2014). *Inorganic chemistry 6th Edition*.


