none, but actual investigations tend to have actual persons doing a specific thing in a specific way and either the investigators discover this, or they fail.
In the absence of an actual murder to investigate the equivalent would be for the GM to set up a predetermined mystery / crime for the players to solve.
<snip>
The difference is that the DM did not set up a predetermined mystery that the players either discover or fail at discovering, the way an investigation of a real life crime would
The epistemic situation of an investigator isn't changed by the fact that there is an "external" truth. They have no access to that truth
other than by uncovering clues, finding patterns, forming conjectures, and doing their best to make sense of it all. Whereas the position of players in the sort of game you describe is that the players can
ask the author if they got the answer that the author intended; that's why I compared it to a crossword puzzle (or any other clue-based puzzle where the author has written the puzzle with an intended solution). This capacity to get authorial confirmation; or to be critiqued by the author for failing to solve the puzzle; makes a CoC-type module pretty different from the actual process of solving a mystery.
By focusing on
correctness/
truth, you are focusing on something which is the main point of
difference between solving a mystery and playing a CoC scenario. (This is also why I made the comparison to Agatha Christie.) Whereas Brindlewood Bay, as described by
@Fenris-77 and
@Arilyn, foregrounds the epistemic position of an investigator, in which
correctness is not available in any unmediated "authorial" fashion.
it’s not arbitrary in the sense that any nonsense is equally convincing to the players, even if the die roll were to say it is the correct answer because they collected enough clues at that point. It is arbitrary in that the die roll decides whether it is the solution even if the theory feels pretty unconvincing
"Unconvincing" to whom? As
@Fenris-77 posted, if players are making conjectures that they find implausible, that's not a
system problem.
If you mean "unconvincing to some external audience", well so what? Was every explanation ever of a murder that took place convincing to those people? Sometimes the best theory of how a murder occurred isn't the one that you or I would arrive at left to our own devices.