10. The necessity for eliminating the little overlooked clues and loose threads
9. The false suspect
8. The cover up
7. The flight
6. The actual killing
5. The first irretrievable step
4. The opportunity
3. The plan
What is the murderer’s ladder without motive? Every detective moves forward on the motive of the criminal, just as they count off their suspicions in that the suspect had the motive, means, and opportunity (fled the scene, resisted arrest, etc.).
This could be said to be the psychotic murderer’s ladder.
As the psychotic murderer has no personal stake in the murder, it must come from another source (a syndicate, or well placed or wealthy individual putting out a contract on the victim; possibly from the victim). It might be argued that the contract price is the motivation for the murderer—but, no. The contract’s price is simple business decision. If a contract murderer did it for free, then there would be a motive for the murderer to deviate from business practices.
There is another perspective that comes from Strangers on a Train, by Patricia Highsmith. There two murders are performed by swapping victims between the two murderers so that motives are lost, means are lost, and opportunities are lost when unassailable, simple alibis are provided.