I wish to challenge the Pathfinder forums community to come up with an algorithm/process/system for balancing the adventure paths so that they are the right difficulty for any party. Generally speaking, adventure paths are reasonably well balanced to begin with as according to my understanding, they are designed for play for 4 characters with a 15 point build.
The problem I have when I GM various adventure paths is that I cannot always guarantee how many players I will have at a session, let alone a full adventure path. The number of players I GM can vary from 3 to 6. There must be some way to quickly calibrate encounters to take into account the number of characters you have. I always GM online using D20Pro and Skype and I let my players use 20 point builds with 2 traits and standard wealth.
Please keep in mind that the equation is definitely not just slightly harder or slightly easier when you go down to 3 or up to 5 or 6 players from the standard 4. I think people underestimate the huge impact action economy has on an encounter when suddenly you have an extra player each round doing stuff to overcome any particular challenge.
So I put it out to the community to tell me what methods they use to adjust encounters according to the number of players they have to deal with.
Seems like the best formula is to just make sure there's at least one enemy on the field per party member, even if one of them's a boss (unless the boss is a known Party Wiper).
I handle it with these guidelines.
1)For every player above 4 be sure to add 25% more treasure. Consequently, for every party member less than four subtract -25% of the placed treasure. This is important as it maintains W.B.L.
2)With 5 players it seems best to increase the number of minions in any encounter by 25% per additional player. With 6 or more players continue adding minions plus adjust any BBEG's CR +1 by adding the advanced template or by advancing the monster. With 8 or more players continue adding another point of CR, and do not forget to keep increasing minions by 25% per additional player over 6.
3)Personally, when the number of players dips below four I do not reduce the number of monsters at all, because my players enjoy the challenge.
Best of Luck,
Weslocke of Phazdaliom
Add two minions or one lieutenant type to every encounter when you add your fifth player. Maximize all the baddies hit points when you add the sixth and see if that works for you.
I'm going to say not possible. So much of it depends on the makeup of the players and of the party. A party of four veteran gamers will be more effective than a party of four new gamers. A party of four bards will probably be weaker than a party with a meatshield, healer, skill character and arcane spellcaster.
You can have guidelines, but, well ... those guidelines are already freely available on the boards and in places like the GMG.
For your personal use, I'd say right off that your baseline NPCs and monsters should gain some bonus for the PCs' higher stat bonuses, even when there aren't greater or fewer players than normal.
I know a lot of GMs that cave in to giving their players higher ability generations than the APs / modules assume, but veteran players honestly don't need the help, and new players can be smarter than you think -- I have a player that went from PF newbie to seasoned across a single AP.
When dealing with additional players, the greatest tool in your arsenal is to disrupt the plans of your players. Even if you increase the raw HP and damage of your opponents as much as the players' own statistics have been increased, you'll find them falling behind in combats because a lot of a fight's difficulty is from not having it under control: A domino-effect starting from the very first turn.
The fact that you can have two whole initiative rolls that might take act before the enemies changes the game. That might be the difference between the players eating a mounted charge while they're flat-footed, receiving triple damage and requiring the party cleric to abandon his offensive action to heal instead ... or the new party Bard winning first initiative, casting Grease and ruining the enemy's ability to Charge, forcing him to simply move up and maybe attack for regular damage before being mauled by a whole turn of the remaining five party members.