The one-shot I am working on has the party primarily rolling against basic NPC's, however I have difficulty figuring out how tough a 3d4 amount of lvl 1 warriors would be for four lvl 3 PC's.
Can someone give me some pointers?
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Level 1 human warriors that possess ability scores of 13, 12, 11, 10, 9, and 8 arranged as the DM sees fit are CR ½. In fact, any creature of a Level Adjustment +0 race that possesses no racial Hit Dice (like, for example, most elves, humans, and orcs) and that possesses that default nonelite ability score array and that takes levels in an NPC class has a Challenge Rating of its levels in that NPC class −1 (which is why a human warrior 1 has a Challenge Rating less than 1).
The Encounter Level of a group of human warrior 1s will depend on that group's size:
Number of Encounter Warriors Level 3............2 4.......2 or 3 5 to 6.......3 or 4 7 to 9.......4 or 5 10 to 12...5, 6, or 7
(Adapted from Table 3–1: Encounter Numbers on Dungeon Master's Guide 49.) While Challenge Rating tells the DM how individually tough in the abstract a certain foe may be in relation to a party of 4 PCs, Encounter Level tells the DM about how tough an encounter typically is with one or more foes in relation to a party of 4 PCs. (Challenge Rating and Encounter Level are typically about equal is it's just one foe.) The Dungeon Master's Guide on What's Challenging? says
An encounter with an Encounter Level (EL) equal to the PCs’ level is one that should expend about 20% of their resources—hit points, spells, magic item uses, and so on. This means, on average, that after about four encounters of the party’s level the PCs need to rest, heal, and regain spells. A fifth encounter would probably wipe them out. (ibid.)
So anywhere from 4 to 6 human warrior 1 NPCs versus 4 level 3 PCs is a challenging encounter (see Table 3–2: Encounter Difficulty (ibid.)).
The chart provides wiggle room for the DM based on the PCs and the foes. For example, if the PCs are all fighters, the Encounter Level is probably closer to the higher end—4 Ftr3 PCs versus 6 human warrior 1 NPCs is probably an Encounter Level 4 encounter—, yet if the PCs are all wizards, the encounter level is probably nearer the low end—4 Wiz3 PCs versus 12 human warrior 1 NPCs is probably an Encounter Level 5 encounter.
However, this also goes the other way. For example, if the 6 human warrior 1 NPCs have carefully picked their feats—either Shape Soulmeld (dissolving spittle (Magic of Incarnum 64-5)) (MoI 40) and another feat that gives them 1 essentia or Animal Devotion (Complete Champion 54-5) and Law Devotion (CC 61), for instance—then wisely spent their 900 gp on good armor, trained attack dogs, and fantasy beer hats loaded with cheap, effective potions, then the DM has substantially increased how dangerous these foes are compared to the typical dudes with armor, shield, sword, crossbow, bolts, and sacks of leftover loot.
In other words, the DM must determine how difficult he's made the encounter with this group of 3d4 warriors. The game helps by providing guidelines, but these are only guidelines, and the best judge of how difficult an encounter actually will be is the DM because the DM knows the PCs. Challenge Rating and Encounter Level are starting points for the DM to develop his own feel for how difficult encounters should be for his group.
Note: Some creatures' Challenge Ratings are wildly inaccurate. It's a good idea when considering using a monster to imagine—or even playtest if that kind of time's available—an encounter before using a particular monster. Some creatures are notoriously weak and others surprisingly strong… and, either way, the monster's actual printed Challenge Rating entry is useless. Read a monster's Challenge Rating, but don't accept it as gospel.
1) don't have 3d4 warriors, unless they're drawn from a overall budget of warriors. It's best to have a set number of enemies in the module, especially in case the players ask questions about their opponents before they wind up in battle.
The problem with a variable number of enemies is not so much a concern for the encounter budget, as a concern for verisimilitude. What do you tell your players when they attempt to track the group? What do you say when they get their hands on their opponents' financial records? What about talking to the survivors of previous combats? How many bad guys there are is likely to impact the game well before the bad guys are actually encountered. It's weird, and in my experience leads to Fun With Superposition shenanigans, when players get told "the band of orcs you are tracking seems to consist of 2d6 warriors and 1d4 fighters" or "The blueprints seem to indicate 1d3-1 identical passageways leading from the foyer into the dining room" or "The disguised bandit quartermaster purchased only exactly enough goods for troupe, and seems to have pocketed the change. The troupe consists of between 10 and 60 bandits, himself, and the Bandit Lord. Each person required 10 gp of goods, and the quartermaster pocketed the difference between the total sum and 70 gold, returning 30 gp of the hundred he was loaned to the Bandit Lord as change. The Bandit Lord tolerates a certain level of embezzlement, but anything more than 30% will anger him sufficiently to have the quartermaster killed, should the PCs point out that he's been duped".
People aren't generally used to people existing in indeterminate amounts, and you're going to have to come down on a number eventually anyways, so you may as well figure it out beforehand.
That's not to say that a variable number of opponent's is never a good idea-- if those people are coming from or going to somewhere than a changing number of persons makes sense. Perhaps there's 17 bandits total, but only 2d4 guard the kitchen at any one time. If the players fight 5 bandits in the kitchen then there're 12 left in the base. Or perhaps reinforcements from somewhere with an arbitrarily large population arrive each day, so that the PCs face a demon army with 15 demons plus 2d6 for each day it takes them to make it to the site of the magic portal. These kinds of situations are fine. We're just trying to avoid situations like "Barracks: 4 beds, 2d100 cp in each below-bed lock box, 1d6 orcs sleep here", where you don't in fact intend to imply 1/3 of the time that the orcs are so poor they are forced to share bunks.
2) The appropriate CR for a humanoid NPC depends heavily on class. The Monster Manual will tell you it's 1:1 CR:level for PC classes and 1:2 CR:level for NPC classes, but that rule does not actually work at all, especially at higher levels (where e.g. 15 levels in monk is nearly meaningless, but 15 levels in wizard is a huge deal).
3) Warrior is a pretty weak NPC class, and a CR 1/2 for a level 1 warrior would not be amiss. A group of 7 typical level 1 warriors should probably be around EL 2, at least in the sense that it's an easy fight for a level 2 party but will probably consume significant resources (e.g. spell slots and hp). Terrain and such could significantly affect this.