The coach will switch the starter with the substitute whenever the substitute is more effective compared to the starter.
This is not necessarily true if you're using Strictly Follow the Depth Chart. It is perhaps true that if the starter is tired the coach may decide to sub him out and get the backup to play. However, when it comes to a close game (especially the 4th quarter), it is mostly the starters who play most of the time, not because the coach want them to, but because substitutions is set as SFDC. So in my opinion the effect of the stamina is less evident when using SFDC (but I'm certain there is an effect, just not as much). In this way, in a close game, even if the backup has better skills and everything else compared to the starter (who sucks), it'd most likely be the starter who'll be playing because the substitution is set so.