No with 4.2436 you double the effect of the méta on Aegis.
I think, we have misunderstanding problem.
3% is not applicable on the aegis after calculation of its value ( in that case, it would be 4.2436) but applicable on the heal which is used to create Aegis.
For Ever, formula is
PoH critical = PoHch + 2*PoHch*30%*(1 + %mastery)=2*PoH heal * (1+ 3%meta) + 4 * POH heal * 30% * (1 + %mastery)*(1 + 3% meta)
PoH critical = 2*PoH heal * (1+ 3%meta) * [ 100% + 2 * 30% * (1 + %mastery)]
Aegis part coef is 4.12
now , you can stay with your certitude but what we say is exactly the same except that 3%meta is taken in aegis because the heal which is used to calculate Aegis integrates already the 3% meta in its value.
edit : maybe, last chance to convince you
13946*0.3*2*1.3736111=11493,8
Meta gem doesnt work with aegis
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I agree on your calculation but let me show you your error in your conclusion.
You use the formula CriticalAegis = (PoH critical heal with meta)*30%*2*(1+%mastery)
Which is correct because the value of (PoH critical heal with meta) is the heal that you see on screen when you equiped with meta.
Until this point , i hope that we are alright.
The value that you have for (PoH critical heal with meta) is higher than which you would have without meta.
In fact, of course : (PoH critical heal with meta) = (PoH critical heal without meta)*(1 + %meta)
That mean that Aegis formula can be converted to :
Critical Aegis = (PoH critical heal without meta)*(1 + %meta)*30%*2*(1+%mastery)
and if you are not equiped with meta , the formula is only :
Critical Aegis = (PoH critical heal without meta)**30%*2*(1+%mastery)
Conclusion : When you are equiped with meta, the valeur of aegis is higher than when you do not have it.
So Meta is tacken into account in the Aegis.
Even if your calculation are good , your conclusion is wrong because you do not compare with the same value of critical heal (PoH critical heal without meta and Aegis) and (PoH critical heal without meta).
The good conclusion can be also : there is no additionnal effect of the meta on the Aegis.(double counting)