I think you are right in the broad statistical sense. But... I think there is a third groups of criminals that can "cruise" between criminal activities:Burglar and murderer are 2 completely different types.
I rarely heard of burglars turned murderers.
- Primarily out to burglarize. But is also inherently aggressive against women and known to make impulsive decisions about alot of things. This includes impulsive murders.
House is empty? Then, he is a burglar. House is occupied by a male? Makes a quick "risk reward" analysis. He is willing to risk confrontations with, and willing to kill males- but.... a large reward needs to be obvious. If not, he retreats.
But.... if the house is occupied by a lone female, he does not retreat. Rather, lone females in vulnerable positions awaken his never truly dormant aggression. Little to no risk / reward analysis is needed. He does not retreat.