This is a deep problem with 3.0/3.5 edition D&D that needs to be solved!
Clearly, I see that it was a bad idea to use troglodytes as an example. This bad example caused people to get sidetracked by the revision to that particular creature in 3.5 as well as the phenomenology of bad smells.
Nail was the one who got the point of the question quite precisely. The statistics of making a new Save for each individual creature encountered weigh heavily against a party of PCs when faced by more than a dozen opponents, no matter how easy the save is to make! (BTW, thanks for providing a tabular breakdown of cumulative save likelihoods, Nail.)
Plus, it seems to me that in many cases, once I've made a few saves against a specific effect, it should be less likely that I would succumb to that specific effect when faced with it for the upteenth time in just a few rounds. For instance, suppose I'm fighting Shadow Mastiffs who have a Fear effect caused by their baying (Will DC 13). Suppose I'm a fighter who has saved 10 times against this Fear effect and am happily hacking-and-slashing my way through these opponents. Then I turn a corner and see another one and hear its bay. Should the likelihood that I succumb to Fear on this Save be exactly the same as the likelihood on all the previous Saves? Shouldn't I be getting used to hearing this awful sound at some point? (Sure, you can rationalize the RAW if you really want to, but before you succumb to this knee-jerk reaction, ask yourself if you really want to.)
I'm honestly not sure what the solution to this problem is. Should a single save be made at a higher DC to represent multiple targets? That would be effective when you face a bunch of opponents all at once, but what about the scenario that I just described where you turn a corner and suddenly encounter more of the same creature. If you only make one save at a higher DC, should that DC include the creatures (like the one around the corner) that you haven't encountered yet, or just the ones you see/hear? If you take the former option, it doesn't quite seem fair to the PCs that their Save is getting harder for creatures they haven't faced yet (and may never face). If you take the latter option, then you arrive at the same statistical problem all over again simply by spreading out the foes.
BTW, this problem isn't limited to just Saves. It also applies to competitive rolls. A staple of the fantasy fiction genre is the infiltration mission: a small band of brave adventurers sneaks into the heavily guarded fortress of the evil overlord. Well, if I've got 4 PCs all making Move Silently checks past 25 low-level guards, the chances that my lowest Move Silently roll will beat the highest Listen check are virtually nil. Hence, we see the same statistical problem rearing its ugly head again. This core game mechanic that requires multiple rolls for multiple adversaries is getting in the way of the what should be possible for PCs to do in a fantasy genre role-playing game.
It would surprise me greatly if no one has attempted to overcome this serious problem since it seems to be one that lies at the very heart of the d20 system. If anyone knows of a satisfactory solution, please share it.
P.S. If anyone who reads this is working on 4E for Wizards of the Coast, please make fixing this problem in a workable way one of your top priorities! Thanks.
Clearly, I see that it was a bad idea to use troglodytes as an example. This bad example caused people to get sidetracked by the revision to that particular creature in 3.5 as well as the phenomenology of bad smells.
Nail was the one who got the point of the question quite precisely. The statistics of making a new Save for each individual creature encountered weigh heavily against a party of PCs when faced by more than a dozen opponents, no matter how easy the save is to make! (BTW, thanks for providing a tabular breakdown of cumulative save likelihoods, Nail.)
Plus, it seems to me that in many cases, once I've made a few saves against a specific effect, it should be less likely that I would succumb to that specific effect when faced with it for the upteenth time in just a few rounds. For instance, suppose I'm fighting Shadow Mastiffs who have a Fear effect caused by their baying (Will DC 13). Suppose I'm a fighter who has saved 10 times against this Fear effect and am happily hacking-and-slashing my way through these opponents. Then I turn a corner and see another one and hear its bay. Should the likelihood that I succumb to Fear on this Save be exactly the same as the likelihood on all the previous Saves? Shouldn't I be getting used to hearing this awful sound at some point? (Sure, you can rationalize the RAW if you really want to, but before you succumb to this knee-jerk reaction, ask yourself if you really want to.)
I'm honestly not sure what the solution to this problem is. Should a single save be made at a higher DC to represent multiple targets? That would be effective when you face a bunch of opponents all at once, but what about the scenario that I just described where you turn a corner and suddenly encounter more of the same creature. If you only make one save at a higher DC, should that DC include the creatures (like the one around the corner) that you haven't encountered yet, or just the ones you see/hear? If you take the former option, it doesn't quite seem fair to the PCs that their Save is getting harder for creatures they haven't faced yet (and may never face). If you take the latter option, then you arrive at the same statistical problem all over again simply by spreading out the foes.
BTW, this problem isn't limited to just Saves. It also applies to competitive rolls. A staple of the fantasy fiction genre is the infiltration mission: a small band of brave adventurers sneaks into the heavily guarded fortress of the evil overlord. Well, if I've got 4 PCs all making Move Silently checks past 25 low-level guards, the chances that my lowest Move Silently roll will beat the highest Listen check are virtually nil. Hence, we see the same statistical problem rearing its ugly head again. This core game mechanic that requires multiple rolls for multiple adversaries is getting in the way of the what should be possible for PCs to do in a fantasy genre role-playing game.
It would surprise me greatly if no one has attempted to overcome this serious problem since it seems to be one that lies at the very heart of the d20 system. If anyone knows of a satisfactory solution, please share it.
P.S. If anyone who reads this is working on 4E for Wizards of the Coast, please make fixing this problem in a workable way one of your top priorities! Thanks.