The motive in 99% of murder cases will be one of those that I listed.
Sex
Drugs
Money
Secrets
Revenge
The other 1% is going to be the serial killer/madman.
And just because you apply Occam's Razor, doesn't mean a case is easy to solve. You begin at the innermost circle and work your way out. LE may have a suspect and a motive, but unable to arrest for a variety of reasons.
*As in the Kathy Jones case, featured cold case here at WS.
I think an important variable is where a crime takes place too. Inside one's own personal space versus the initial contact being outside of the victim's home.
If the crime in committed where the body is found and the body is found within a short timeframe, the more solvable the crime should be.
Two crimes, I learned lessons from, are Mickey Shunick and Jessica Ridgeway. Both happened outside of the home when the victim was enroute to their destination. Both, it turns out, were murdered by an opportunist stranger. I had always heard that, more likely than not, the perp is someone known to the victim. Both cases had what I call uncanny coincidences associated with them. Mickey's dad had been backing out of his driveway at about 2:00 a.m. to go to a meeting just as Mickey would have been arriving home on her bicycle. I couldn't imagine her father wanting to kill her but I couldn't get that strange info out of my mind. I got stuck thinking it may have been an accident that was intentially hidden. For that, I'm very sorry.
In JR's case the friend she normally walked to school with, who was also related to her in some way, father missed picking her up but took his own kid to school and dropped him off. It turned out this event actually happened the day before or something but it seemed so uncanny to me that I locked onto the idea that the uncle must have encountered Jessica after he dropped the boy off and most likely the perp. I believed, at the time, that the perp usually has some kind of relationship with the victim.
BUT THESE TWO CASES occurred outside the victims' homes. At the time though, even that info had to be taken on faith (LE assessed truth there).
When a crime takes place in one's own home, when there are no signs of struggle, break in or robbery, the perp is normally someone who knows the victim. But it could be a workman, a neighbor or a stalker type rapist - not necessarily a loved one or family member.
Since Paul was a guy, I don't think the last choice fits his case. I feel the perp is someone he knew. Still, he had a lot going on in his world. Like OldSteve asked, what were Paul's secrets?