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Message: <blockquote data-quote="NotAYakk" data-source="post: 9686323" data-attributes="member: 72555">So one thing I've noticed in simulation+attrition based games (of whatever kind - HP, fate points) is that (K times as many foes) generates as much attrition as (one foe that is K times tougher, but does (K+1)/2 times as much threat per turn).In D&D, toughness is (for the most part) HP, and threat is DPR (each modulated by accuracy).This means that replacing 5 foes with 1, the combination monster should have roughly 5x the HP and 3x the damage output to maintain roughly the same pace of conflict.  (The length of a conflict is determined by the toughness of the foes, the threat of the conflict is the accumulated damage they do, roughly).Now, if we want to be able to use "higher difficulty" foes as "bosses" at lower difficulty levels, and the same bosses to later be a normal difficulty foe, we need the bosses to grow in toughness faster than they do in threat output.  This isn't always a need, but I think it is a nice feature?Next, we want the pace of conflict to not get out of hand as the game difficulty level increases; if a conflict takes 3 rounds at low difficulty levels, we probably want it to take roughly 3 rounds at higher difficulty levels, barring some external reason.  (If the game's conflicts are most fun at a certain pace, why not have the fun pace be always instead of sometimes?)This means that player threat - the number of rounds to defeat a foe of a given toughness - should be relatively uniform compared to even-difficulty foes toughness, and vice versa.So when player power goes up (however fast you choose it to happen), player threat should go up faster than player toughness.  And similarly, the foe's durability should go up faster than their threat.We can measure the scale of power by saying that if you could defeat 2 of some opponent roughly as easily as you could have defeated 1 before, your power has "doubled".  And for foes, if 1 of the foe could replace 2, that 1 foe has "double" the power of the 2.  We hope that this is going to be reasonably consistent with higher multiples as well.Now, the rate at which doubling happens can determine how flat the progression is.  A game could have a starting character and an "endgame" character have a power ratio of 2.  In 5e a level 20 PC has roughly 40x the power of a level 1 PC (using the formula HP ratio * DPR ratio * 2^((ATK+DEF delta)/10))^0.6.(Note that 5e doesn't have PC damage output growing significantly faster than HP over 20 levels, despite my derivation above.  This is one of the reasons why boss monsters don't work well in 5e; they don't have enough HP and they hit too hard, so they either TPK instantly or die instantly.)But I think the lessons from 5e (and 4e etc) are worth applying to other games.  I find that far too many games don't pay nearly enough attention to the violent conflict game loop and its pacing; they throw numbers at it and pretend what shows up as what is intended.---For 5e, this says I should set up so that player damage output does increase exponentially faster than durability.Some rather silly math follows.  No hard conclusion.[spoiler]Now, I don't want to mess with 5e's PC HP curve.  So let's make that a baseline; a d8 HD character with 14 con.Also, level 1 being "greatsword with 3 strength" as baselineSampling every 4 levels, PCs get:L1: 10 HP, 10 DPRL5: 38 HPL9: 66 HPL13: 94 HPL17: 122 HPL21: 150 HPNow, we want 3 round combat.  Assuming 50% monster accuracy, over 3 rounds we want to seriously hurt the PCs - say down to 1/4 HP.  So PC_HP * 3/4 = 3 * .5 * M_DPR, or PC_HP = 2 * M_HP.  Similarly, we want PCs to kill the monsters in 3 rounds.  With 2/3 accuracy baseline, this means DPR * 2/3 * 3 = MHP, or MHP = DPR*2L1: 10 HP, DPR=10: MDPR=5, MHP=20L5: 38 HP: MDPR=19L9: 66 HP: MDPR=33L13: 94 HP: MDPR=47L17: 122 HP: MDPR=61L21: 150 HP: MDPR=75Now to fill in the DPR and MHP at higher levels than level 1.If monster DPR doubles when HP goes up by 3, we want log_2(MDPR) = log_3(MHP)*K for some k.  We can solve for K at level 1.log_2(5) = log_3(20)*KK = log_2(5)/log_3(20)K =~ 2.727 / 2.322 =~ 0.85We need MHP as a function of MDPRln(MDPR)/ln(2) = ln(MHP)/ln(3) * 0.85ln(MDPR) * ln(3) / (ln(2)/0.85) = ln(MHP)e^{ ln(MDPR) * ln(3) / (ln(2)*0.85) } = MHPe^{ ln(MDPR) * 1.865 } = MHPMDPR^1.85 ~= MHPL1: 10 HP, DPR=10: MDPR=5, MHP=20L5: 38 HP: MDPR=19, MHP=225L9: 66 HP: MDPR=33, MHP=650L13: 94 HP: MDPR=47, MHP=1250L17: 122 HP: MDPR=61, MHP=2000L21: 150 HP: MDPR=75, MHP=3000Then, PC DPR = MHP/2L1: 10 HP, DPR=10: MDPR=5, MHP=20L5: 38 HP, DPR=112: MDPR=19, MHP=225L9: 66 HP, DPR=325: MDPR=33, MHP=650L13: 94 HP, DPR=625: MDPR=47, MHP=1250L17: 122 HP, DPR=1000: MDPR=61, MHP=2000L21: 150 HP, DPR=1500: MDPR=75, MHP=3000This fails the "omg those numbers are way too big" test.We can fix this somewhat.  We used HP instead of Toughness.  In reality we'll have a relative accuracy effect.If PC ATK and monster AC+Saves goes up faster than PC AC+Saves and monster ATK, we can massively flatten the PC DPR and monster HP curves while maintaining the right toughness ratio.Ie, suppose PC DEF and monster ATK goes up 5 points, while PC ATK and monster DEF goes up 10 over these 20 levels.  As we calculated MHP based on the ratio of HP when we really wanted Toughness:We really want log_2(Threat) = log_3(Toughness)*KEvery +1 to hit on a foe hitting ~50% of the time increases threat by 10%, or roughly:Threat ~= DPR * 2^(ATK/7)Similarly, against foes hitting ~1/2 of the time, each +1 in DEF (AC and Saves) increases toughness by 10%, soToughness = HP * 2^(DEF/7)If ATK = 3+L/2 and DEF=3+L, log_2(DPR * 2^(3/7+L/14)) = log_3(HP * 2^(3/7+L/7))*Klog_2(DPR) + log_2(2^(3/7+L/14)) = log_3(HP) * K + log_3(2^(3/7+L/7))*Klog_2(DPR) + 3/7+L/14 = log_3(HP) * K + (3/7+L/7)*K/log_3(2)log_2(DPR)  = log_3(HP) * K + 0.68K + L*K*0.226 - 3/7 - L/14solving for level 1 to get K;log_2(5)  = log_3(20) * K + 0.68K + 1*K*0.226 - 3/7 - 1/142.32 = 2.73 * K + 0.68K + K*0.226 - 3/7 - 1/142.82 = 3.64 KK = 0.77simplifying:log_2(DPR)  = log_3(HP) * 0.77 + 0.68*0.77 + L*0.77*0.226 - 3/7 - L/14log_2(DPR)  = log_2(HP)/2 + 1/14 + L/10as DPR=(7L+3)/2log_2(7L+3) - 1  = log_2(HP)/2 + 1/14 + L/102 log_2(7L+3) - 2  = log_2(HP) + 1/7 + L/52 log_2(7L+3) - 13/7 - L/5 = log_2(HP)HP = 2^{  2 log_2(7L+3) - 13/7 - L/5 }HP =~ 2^{  2 log_2(7L+3) } / 2^ {13/7 + L/5 }HP(L) =~ (7L+3)^2 / [ 4.3 * 2^(L/5) ]HP(1) = 10^2 / [4.3 * 2^.2] =~ 20HP(5) = 1444 / [4.3 * 2^1] =~ 168HP(9) = 4356 / [4.3 * 3.5] = 290HP(13) = 8836 / [4.3 * 6.1 = 339HP(17) = 14884 / [4.3 * 10.6] = 328HP(21) = 22500 / [4.3 * 18.4] = 285which in turn tells me we need faster AC/DEF growth at low levels and slower AC/DEF growth at higher levels, as the exponential advantages of AC/DEF dominate over polynomial impact of HP inflation and Toughness:Threat ratio changes.If I move the AC/DEF increases on monsters to lower levels and flatten it at higher levels we can smooth out the monster HP.  The issues is, I guess that PC HP-based toughness increases by large percentages at low levels, but at higher levels barely moves.In theory, improved scaling on abilities like Lay On Hands, Second Wind, Healing Spells, and Beastmaster Companions, monk Dodge/Deflect/Heal and Rogue defensive roll, plus spellcaster defensive options, could make true PC toughness grow faster than HP growth.But on the easier to analyze of these I don't see it; LoH in 2014 and 2024 is a flat 5 HP/paladin level.  There is no "mass LOH" or "When you LOH a creature, you also heal" or "When you LOH, they gain temporary HP equal to the amount healed until the end of your next turn".  Those kind of abilities would make LOH scale faster than linearly and result in a steeper toughness curve for PCs.Oh well, I'll keep on scratching away at this.  I feel I'm getting closer.  If I pull this off, we'd get:1. Monster "levels" that let you have one-monster at the same level per PC be a reasonably tough challenge.2. XP values that let you swap in one "higher level" monster for two lower level monsters of half XP, and get an equally tough challenge.3. Encounter pacing and difficulty that stays roughly the same under such swaps.4. Optionally "Tank" and "Glass Cannon" type monsters that mess with pacing and encourage tactical choices (PCs will want to take Glass Cannons out before Tanks), done explicitly (ie, as a DM you can tell which monsters are which and what it should do to pacing).  (Sort of like 4e monster roles; a fight with 4 tanks and 1 glass cannons feels very different than 1 tank and 4 glass cannons)[/spoiler]</blockquote>

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