Ok, so where is the cut-off between reasonable and unreasonable?
For Sherlock Holmes or the D&D equivalent? 18 int. Anything lower and the difference between him and the best is too noticeable. Also, once you hit 16, the number of 16 int NPCs in the world vs. the number of 18+ int PCs is extreme
First, I agree with Elfcrusher about the argument structure. That's why, upthread, I pointed out that the 5 INT version of Sherlock Holmes isn't crucial, and that the real issue is just about falling short of maximum INT.
Second, I already posted an example upthread where the toughest dwarf around starts play with 16 STR and CON, and at 30th level has "only" 26 STR and 20 CON whereas the maximum stat at 30th level is 30, and the maximum STR/CON pair is 30/28. There is no in principle reason why, in my game, it couldn't have been a 16 INT detective rather than a 16 STR/CON tough guy.
Third, I reject the NPC claim. In my game, there are not NPC dwarves out there who are tougher, other than perhaps Moradin; and other than divine beings its been clear since 15th level that there are no tougher dwarves, and indeed that has probably been true since 11th level. (Even though, at 11th level, the character had "only" 19 STR and (I think) 17 CON.)
What has made it the case that this character is the toughest dwarf? He is the one who led a group of (NPC) dwarf scouts to safety, when an angel from Moradin appeared to them and told them that a warrior priest was at hand to rescue them after they had been beaten nearly to death by hobgoblins. (This was at 11th level.) Then, when he led them to a friendly town he was
recognised by the baron of that town as "Lord Derrik of the Dwarfholm of the east", and by the local dwarven community as their natural leader. Not long after that, he and his companions finally destroyed the hobgoblin armies threatening the town, with Derrik facing down
multiple phalanxes of hobgoblin in the course of this (as well as other monsters, like a chimera and a three-headed dragon). And then, when Derrik's dwarven thrower artefact was being reforged into a great two-handed maul, he was able to
shove his hands into the forge to hold it down, despite the immense heat and arcane energies, so that the dwarven artificers could take control of it with their tongs.
Since then, he has performed such feats as being
the main wrecker of Torog's Soul Abattoir,
leaping onto the back of an ancient white dragon and pinning its wings, so that it crashed to the ground, and
single-handedly taking on and defeating a dojo of the best githzerai monks after falling through the Elemental Chaos to land on their practice field. These all reinforce, in play and in the shared fiction that play generates, that there is no dwarf about tougher than this character.
It's simply not relevant that a D&D player in the real world
could, if s/he wanted to, build a dwarven character whose stats and capabilities made him even tougher than this PC. Because no such character has actually been build and played in the campaign. Similarly, the fact that the mechanics of the game would permit there to be some tougher NPC is not relevant; no actual such NPC has figured in the game, nor performed feats of toughness comparable to those which this PC has performed.
All of what I have just described could, in principle, be true of a detective PC. When it comes to actually playing a game of D&D, being the best detective around is not about holding up your character sheet and pointing to some numbers: it's about how the play of the game reveals your PC to be the best detective around. Of course those numbers (and other resources) written on the sheet are important as
inputs to play; but they are not the outputs. The outputs are events in the shared fiction.
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Perhaps, for those who play in very detailed campaign settings (eg FR), where it is taken for granted that there are a whole host of NPCs who importance and deeds rivals those of the PCs, the above characterisation of D&D play does not resonate. Maybe, in such a game, it is obvious that even if - in play - the character with the 16 INT is the one who performs all the deductions, unravels all the dastardly plots, etc, there is nevertheless some NPC detective off screen who, if s/he had been on screen, would have done the same with even greater facility.
If that is how you play D&D, you nevertheless need to recognise that not everyone plays in that fashion, and that for some of us the shared fiction is primarily the result of playing the game, rather than something whose content is given independently of and prior to play. Even if, in your style of D&D, the 16 INT PC could never be Holmes because there is some cleverer 18 or 20 INT detective off-screen solving even more mysteries more quickly and more thoroughly, for those of us who play in the way I have described, it is quite feasible for the actual play of the game to reveal the 16 INT PC to be the greatest detective around (just as, in my campaign, has occurred with the considerably-less-than-max-statted-but-nevertheless-toughest-dwarf-around).