At what point did firearms become more effective than bows in one on one combat?

by dubious_79

I understand that muskets and early firearms replaced bows in mass formations early on for logistical reasons. For many nations they were easier to train and supply. But at what point in firearms development did the gun become mightier than the bow in one on one combat with no concern for logisitics? I ask because I was just watching The Revenant.

Searocksandtrees

Not to discourage further discussion here, but fyi, you'll find a couple of posts on this subject in the FAQ