But we have no idea how much or little or even if branding was used.
The idea of branding for certain crimes stemmed not so much from punishment as the need to identify potential recidivists. In a period where there was no way to identify an individual scientifically (like fingerprints, photos, etc.) branding would serve to identify a criminal. The reason a crime like counterfeiting was a crime that was punishable by branding was that it was believed (possibly with good reason) that counterfeiters were likely to commit their crimes again after release from incarceration, unlike like a murder (which might be a crime of passion).