
McDaygo |

I’ve been playing around with an NPC generator to try to save time in building encounters and I noticed when I had a NPC multi-class the CR was different for example:
-HalfElf Bard 11 is a CR 10
-HalfElf Bard 5/Ranger 5/ Arcane Archer 3 is a CR 9.5
Clearly the Multi-class lowers the CR as the three extra levels apparently make it a lesser challenge (barely). What is the math I am missing here?

InvisiblePink |

When you add class levels to a monster, the game advises you to add 1/2 CR for each class level that doesn't synergize with the monster's role. The generator is likely considering "a Half-Elf Bard 5" to be a monster, concluding that "Ranger" is not a class that synergizes with that monster, and counting its level as 5+2.5+3 rather than 5+5+3.
I'm not sure what the exact definition of "monster" is, but I'm 90% sure that that's a silly interpretation, and the multiclassed Bard should in fact be CR 11.
EDIT: Here is an official Paizo multiclassed NPC: Cleric 5/Wizard 5/Mystic Theurge 10, with CR 19. You can find others like that if you go digging.

McDaygo |

Mostly for appropriate Experience and to make sure the threat is in the range cause my table as a player that likes to complain when the CR doesn’t meet the +3 hard limit. It’s annoying but my players otherwise mow through everything so I have to get creative with custom stuff or bend the CR rule so its not too easy.

Mathmuse |
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The usual guidance is in the Gamemastering chapter of the Core Rulebook,
Adding NPCs: Creatures whose Hit Dice are solely a factor of their class levels and not a feature of their race, such as all of the PC races detailed in Races, are factored into combats a little differently than normal monsters or monsters with class levels. A creature that possesses class levels, but does not have any racial Hit Dice, is factored in as a creature with a CR equal to its class levels –1. A creature that only possesses non-player class levels (such as a warrior or adept) is factored in as a creature with a CR equal to its class levels –2. If this reduction would reduce a creature's CR to below 1, its CR drops one step on the following progression for each step below 1 this reduction would make: 1/2, 1/3, 1/4, 1/6, 1/8.
However, a Bard 5/Ranger 5/Arcane Archer 3 is less threat than a Bard 13. Whether CR 9.5 is correct, i.e. less threat than a Bard 11, is a matter of opinion. My opinion is that that number is low.
When you add class levels to a monster, the game advises you to add 1/2 CR for each class level that doesn't synergize with the monster's role. The generator is likely considering "a Half-Elf Bard 5" to be a monster, concluding that "Ranger" is not a class that synergizes with that monster, and counting its level as 5+2.5+3 rather than 5+5+3.
I'm not sure what the exact definition of "monster" is, but I'm 90% sure that that's a silly interpretation, and the multiclassed Bard should in fact be CR 12.
EDIT: Here is an official Paizo multiclassed NPC: Cleric 5/Wizard 5/Mystic Theurge 10, with CR 19. You can find others like that if you go digging.
InvisiblePink has put his or her finger on the source of the NPC generator's result. Class abilities don't necessarily mix. For example, monk has a lot of abilities to fight without sword and armor, and multiclassing it with a class that uses sword and armor will result in a level of abilities being wasted. In contrast, a prestige class, such as arcane archer, is designed to mix well with several classes that meet its prerequisites. Thus, the generator counted 5 levels of a base class at full value, 5 levels of another base class at half value, and 3 levels of prestige class at full value to give 5 + 5/2 + 3 = 10.5. Then apply CR = level - 1 to get CR 9.5.
In practice, bard and ranger are not a bad mix. The animal companion from ranger will be uselessly fragile, and the spells from the bard will be designed for encounters against easier targets, so it loses a level or two in challenge rating, but not a full 2.5 levels. Some feats, such as Boon Companion, can correct parts of the mismatch. A well-designed Bard 5/Ranger 5/Arcane Archer 3 with NPC gear would be CR 11.

McDaygo |

He would have the boon companion instead of animal companion. Basically the full encounter is meant to be 3 NPCs
-Deep Walker Ranger goblin 11(ranged spec)
-Feral Knasher Oversized Goblin Half Orc (custom race) 11
-Said half Elf bard ranger Arcane Archer. I needed him to be around a CR 10 by himself for a total of 3 CR 10s.
Tactics would be both rangers would share the boon of favorite enemies (entire party is same race) the Bard would as swift actions do bardic performances to buff party

InvisiblePink |

If your players think CR is a good yardstick, try throwing a few Siege Owlbears at them for giggles.

Mathmuse |

Mostly for appropriate Experience and to make sure the threat is in the range cause my table as a player that likes to complain when the CR doesn’t meet the +3 hard limit. It’s annoying but my players otherwise mow through everything so I have to get creative with custom stuff or bend the CR rule so its not too easy.
I bend the CR rule.
My players have mastered teamwork, alliances, scouting, and preparation. They operate as effectively as a party one level higher than their actual level. Thus, I design my encounters one CR higher. The party would be an effective two levels higher, except that they don't care for looting and therefore are underequipped in level-appropriate gear.
Giving my party more XP because I raised the CR of the challenges does not make them level up faster, because taking advantage of scouting and preparation often means skipping unnecessary encounters. That reduces the XP earned--unless avoiding the encounter was a challenge in itself, such as Diplomacy with hostiles.
He would have the boon companion instead of animal companion. Basically the full encounter is meant to be 3 NPCs
-Deep Walker Ranger goblin 11(ranged spec)
-Feral Knasher Oversized Goblin Half Orc (custom race) 11
-Said half Elf bard ranger Arcane Archer. I needed him to be around a CR 10 by himself for a total of 3 CR 10s.Tactics would be both rangers would share the boon of favorite enemies (entire party is same race) the Bard would as swift actions do bardic performances to buff party
The Boon Companion feat (link) enhances an animal companion, so it is not used instead of the Hunter's Bond that gives a ranger an animal companion. A bard/ranger archer would usually be better off giving up his animal companion in exchange for another class feature, but a mount for mounted archery or a bird for scouting at a distance could still work for an archer.
If both rangers have the companion bond version of Hunter's Bond, the effects won't stack.
Deliberately designing the encounter around the weaknesses of the party bends the CR rules, too, because the real challenge from the encounter does not match the CR and the XP. It is okay to have a ranger's favored enemy match a race in the party, if that race is common in the area. Nevertheless, the party having only one race counts as a weakness in the party, just like a lacking a healer in a party would count as a weakness. (I remember one time the party in my game attacked an evil ranger who had favored enemy humans and human-bane arrows. The party did not know this, because the module gave little warning except that he was cruel and sadistic. Nevertheless, the first wave to reach him was a dwarf and a strix, who had used their climbing and flying abilities for mobility. The ranger's specialty worked against himself.)