Party optimisation philosophy

[Eldariel]

Per DMG p. 82, a "Deadly" encounter for a single level 1 character is 100 XP, or one orc. Two orcs would fall between "Hard" and "Deadly" for a 3rd level fighter.

Actually, it's above Deadly because for a party of 2 or less characters you adjust the multiplier one step up and thus it takes 1,5x XP multiplier for 150 XP. So it's Deadly x 1,5. 2 Orcs is Deadly x 4 which is about equivalent to the point where the party is at a 50-50 fight. Standard encounters aren't interesting since any party will plow through any number of such adventuring days. The default guidelines are made so that PCs basically can't die no matter how idiotic things they do and how bad the dice fall (unless they forget basics like "yoyo heal", "focus fire", "rotate party formation", "always stealth", "kill casters", "avoid AOE", etc.) though, so they aren't interesting when stress testing the system and determining optimality. It's pointless to test "everyone wins"-scenarios, which goes for every DMG encounter for the majority of parties (of course, basically all published modules feature fights much more difficult than the cap level introduced in the DMG, acknowledging that it's boring to play like that).

Of course, it depends on the party and indeed, this test of single level 1 characters vs. two orcs is a supersimplified example that showcases the point perfectly: high nova party with resources available has a rather high likelihood of winning while at-will heavy party with little nova has an abysmal shot. Whereas the Wizard has ~86% chance of winning Initiative and then he needs for the Orcs to just not kill him with a single Javelin attack (which does have a relevant likelihood of ~15% or so) for a total of 75% chance of victory in a neutral terrain (most terrain favours him since Sleep ignores cover and concealment while javelins have to deal with all of that; let alone precast protection from Minor Illusion and Mold Earth which can be cast out of combat every round for free). And that's without going into options like fighting in the open, where casting Expeditious Retreat and kiting them at above max range and finishing them off with Light Crossbow Disadvantageous attacks (+5 to hit vs. AC 13 for 42% to hit; it won't even take that long) is pretty trivial (you can do other tricks to negate the disadvantage and thus reduce bolt consumption, but no need to go there in this case).

Meanwhile, without nova Orcs have 15 HP and 13 AC while a Fighter with Defense fighting style has +5 to hit, 1d8+3 damage. The Fighter averages 5,1 damage a turn so he takes about 3 rounds to drop an Orc on average (huge variance of course; not gonna do the exact math since it would take too long) while Orcs at +5 to hit vs. AC 19 (Defense Fighting Style, Shield, Chain Mail) and effective 1d12 damage (-3 from Heavy Armor Master) average 2,6 damage each (5,2 damage per turn) vs. Fighter's 13 HP and Second Wind (+6,5 HP) or a total of 19 HP. Orcs thus deal as much damage as the Fighter each round on average but have over twice the HP pool. The Fighter will have a decent shot at dropping a single Orc but he'll be so beat up by that point that the second Orc will most likely effortlessly finish him off (of course, this assumes both Orcs don't hit on the same round; if they do, it's fully possible they drop the Fighter before he gets to use Second Wind so full benefit cannot be assumed and in such a case, the Fighter is not favourite to drop even a single Orc).

The reason at-will attacks are important is that they let you efficiently turn defense into offense, which in turn matters because 5E makes defense much cheaper to acquire than offense. E.g. there is no spell which can triple your DPR against an orc, but there are spells that can triple your longevity against an orc (e.g. Blur if you're already in heavy armor).

This is of course also reason why the efficiency of your At-Will matters. It's again easy to showcase with the level 1 single character party. A Dex 16 Wizard should buy a Light Crossbow on level 1 100% of the time, because +5 to attack for 1d8+3 damage is much more reliable than +5 to attack for 1d10 or 1d12 damage (and of course averages more damage too). Not to mention the option of acting at higher ranges. When you're going nova, this doesn't matter, but you don't want to have to "go nova" (i.e. use resources) against a single Goblin, since that would leave you with far lesser resources for a more serious fight. Light Crossbow increases kill reliability from having to first hit 50% hit and 5% crit rate and then having to roll a 7+ (40%) on the d10 damage roll or 7+ (85%) on the crit roll to same hit rate and then a roll of 4 (so 62,5%) sufficing on the d8 or 95,3% on crit roll. So the overall chance of a kill with e.g. Fire Bolt vs. Goblin would be 24,25% per attack while the chance to kill with Light Crossbow would be 36%. So L. Crossbow brings about approximately a 50% improvement in the likelihood of killing a Goblin with each given attack and thus an equivalent decrease in the likelihood of the Goblin having a chance to potentially burn through your defensive resources (in this case, Shield and HP - of course, crit is immediately quite likely to be fatal so there's extra pressure to minimise enemy actions but burning one of your level 1 slots is probably still a bit too much and probably the favourable tactic would be using your utility cantrips to craft a more favourable environment and thus skew the numbers in your favour).

The power of the party's at-will directly influences how often you need to use your nova and also how likely you are to have to burn defensive resources (i.e. take hits) when using at-wills against lesser encoutners and thus, how many lesser encounters the party can go through. In essence, at-will power is a defense multiplier for weaker encounters and nova power is a defense multiplier for strong encounters. Where the line between the weak encounter and the strong encounter (or unfavourable and favourable circumstances; sometimes a nominally weak encounter can turn out dangerous when e.g. half the party rolls poorly on their saves vs. Intellect Devourers or Banshees and you suddenly need all the nova in the world to survive) is of course one of the problems that's hard to quantify without a more robust challenge rating system.


All of this ties directly to...

That does raise an interesting question though: does a party which is optimizing to have a decent chance at beating extremely tough foes (a series of uber-Deadly 20th level encounters and 3x 20th level DMG adventuring days at party level 13) get built differently from a party which is optimizing to have a 100% chance at beating moderate foes very quickly (13th level DMG adventuring days at party level 13, but all the fights end in 1-2 rounds), or is one a superset of the other?

I think there's definitely at least corner cases where the party that can deal with more moderate encounters per day is not necessarily the same party that can deal with the highest difficulty encounters each day. I think this definitely warrants further study and this is in fact where the whole concept of "at-will party" and "long rest party" outlined in the might be useful. I think this has to be testable. Build extreme parties for both examples (I think the size of the party shouldn't matter overtly much so a party of 3 would be optimal for ease of computation) and then see how they perform against an extreme number of medium-easy encounters (it has to be run to the point of failure, I think, to truly test the long rest party's resources and on the other hand to see the sufficiency of the short rest party's encounter deletion power - in which case we're probably talking about ~50ish encounters at least; I'm thinking higher up long rest party using all-day slots will probably plow through them without burning any resources though so multiple level ranges have to be considered).

I feel like the only feasible way of running this would be a simplified computer test with flowchart behaviour for each character and monster. It'll lose a lot of complexity inherent to D&D but it should answer the main point itself since both parties are principally able to make use of environmental factors and creativity to probably extend their day a bit more to much the same extent, I'd assume, so it should cancel itself out if omitted (well, casters of course have more tools to be creative with so they'd be more hurt by the restriction but if some general uses like "Silent Image to block enemy LoS while maintaining party LoS" are coded in, the lost complexity should default to edge cases).