The standby is nearly always first, however there is a rule in Equity stating that if a person plays a role for a specfic number of performances, they must be promoted to the role full time. So, if someone is out for an extended amount of time, they'll rotate out the other understudies.
And, in some cases the swing that covers the role will be more likely to go on. To the best of my knowledge Jay A. Johnston has gone on for Gavin Creel more times than Paris Remillard, who is in the ensemble.
Honestly, I think it changes company to company.
All three leads in Aida (Aida, Radames, and Amneris) had standbys. Not all of them.
When it opened, the only standbys were Thursday Farrar (Aida) and Neal Benari (Pharoah/Zoser).
Later, some of the other performers had standbys. I don't think Sherie Rene Scott ever did, and I don't think Idina Menzel did. I'm also fairly sure that Will Chase didn't have a standby.
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