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Understanding the maths behind 5e
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<blockquote data-quote="NotAYakk" data-source="post: 7902054" data-attributes="member: 72555"><p><strong>Warning Edit</strong>: I did the math in this from memory, not from my spreadsheet. The actual exponent is 2/3 not 3/4, and there are a few other errors (corrected in later posts).</p><p></p><p>---</p><p></p><p>As for encounter building, all of that futzy "double XP" crap can be gotten rid of by just raising XP values and budgets to the ^(3/4). This changes the 25%/50%/75%/100% easy/medium/hard/deadly to 40%/60%/80%/100%.</p><p></p><p>The basic idea is, how hard is a monster with 2x the HP and Damage? Is it 2x (I mean, you doubled both), or 4x (2x * 2x = 4x)? If you just double a monster's damage, it is twice as hard, right?</p><p></p><p>So how about 2 monsters? Well, they are more vulnerable to AOE effects, and it tends to be harder to focus fire with 2 monsters, and if you deal 1 monsters worth of HP their damage output halves. How do 2 monsters compare to one with 2x HP?</p><p></p><p>That (3/4) factor is 5e D&Ds answer to that question.</p><p></p><p>Suppose we have X monsters on the left and one monster with Y times the HP and Damage on the right.</p><p></p><p>(HP*Damage)^(3/4) (adjusted for defences and accuracy) answers "how many X monsters does it take to be just as hard as a Y".</p><p></p><p>X * (HP*Damage)^(3/4) = (Y*HP*Y*Damage)^(3/4)</p><p></p><p>X * (HP*Damage)^(3/4) = (Y^2)^(3/4) * (HP*Damage)^(3/4)</p><p></p><p>X = (Y^2)^(3/4)</p><p>X = Y^1.5</p><p></p><p>So if Y is 4, X is 4^1.5 which is about 6.</p><p></p><p>So 6 "small" monsters are just as hard as one "4 times size" monster.</p><p></p><p>How this works in the 5e encounter balancing system is this.</p><p></p><p>Suppose the small monsters are wroth 400 XP each. The big monster will be worth 400*4*4 = 6400 XP or so.</p><p></p><p>400 * 6 is only 2400 XP. But the <strong>encounter size multiplier</strong> then boosts 2400 XP by 2.5-3, making it reach 6000-7200 XP. Roughly the same budget.</p><p></p><p>As far as I can tell, all of those encounter size multipliers can be ignored by first raising XP to the (3/4) power. Now XP is additive.</p><p></p><p>But if we are doing this, we don't have to use the XP values posted. I mean, many people advance by milestones instead anyhow.</p><p></p><p>---</p><p></p><p>Anyhow, you can take the XP values of various CR monsters, raise it to the (3/4) power, then futz around with it and round it. You get something like:</p><p></p><p>CR 1/8: 1</p><p>CR 1/4: 2</p><p>CR 1/2: 4</p><p>CR 1: 6</p><p>CR 2: 9</p><p>CR 3: 12</p><p>CR 4-15ish: +6 per CR</p><p>CR 16-19: +9 per CR</p><p>CR 20: 140ish</p><p>CR 21+: +15 or 20, I forget, per CR</p><p></p><p>I call those "encounter building points". They let you build encounters by just adding up numbers and no multiplication.</p><p></p><p>---</p><p></p><p>On the PC side, you can add up player EBP and divide by 4 to work out what their medium budget should be. Then an easy encounter is 2/3, hard is 4/3, deadly is 5/3 of that, and "crazy" is 2x.</p><p></p><p>If we divide by 3 instead of 4 we get even nicer math. Easy is 1/2, medium is 3/4, hard is that EBP, and deadly is 5/4 (+25%) and crazy is 3/2 (+50% over budget).</p><p></p><p>As the EBP stuff above is already divisible by 3 we get:</p><p>L1: 2 EBP</p><p>L2: 3 EBP</p><p>L3: 4 EBP</p><p>L4-15: +2 EBP per level (or Level*2-2)</p><p>L16-19: +3 EBP per level</p><p>L20: 45 EBP</p><p></p><p>then just add up the party's EBP to give an EBP budget (at "hard" difficulty).</p><p></p><p>(the cutoff at 15-16 might be a level layer, I'm doing this from memory).</p><p></p><p>There is modest differences in the encounters build this way compared to the DMG, but I find it ridiculously easier.</p><p></p><p>Turning this into scene building (budget for time-between-short-rests) and daily budgets isn't hard. Really, 5 times your EBP budget (as calculated above) isn't a bad number to at level 3 and above (at level 1-2, use 4x).</p><p></p><p>So a party of 4 level 5 PCs has an EBP budget of:</p><p>16 easy (don't use anything easier than this)</p><p>24 medium</p><p>32 hard</p><p>40 deadly</p><p>48 crazy</p><p>160 per day</p><p></p><p>If you have 2 short rests per day, that is about 56 EBP per "scene" (period between short rests).</p><p></p><p>Lets build a set of encounters. We are in a village. The baron's daughter is visiting. Mercenaries attack, pinning down the PCs.</p><p></p><p>1. 6 guards (EBP 6) plus PCs against 6 orcs (24 EBP) (18 EBP net, easy fight)</p><p>2. Guards leftover from first 1 (say, 4), plus 5 new guards (so 9 EBP), plus PCs, vs 8 orcs (32 EBP) and a veteran (CR 2, 18 EBP) 41 -- deadly-crazy fight.</p><p></p><p>Short rest. The attackers have kidnapped the baron's daughter! They flee on the water.</p><p></p><p>PCs get on boat and give chase (short rest).</p><p></p><p>3. Neried (36 EBP, hard-deadly) engages PC's boat.</p><p></p><p>PC continue chase (short rest).</p><p></p><p>4. Enemy boat is pulled up on a dock. They left 6 orcs behind to ambush PCs (24 EBP, medium encounter).</p><p></p><p>A boat with 20 guards (EBP 20) and a Guard Captain (EBP 12) arrives after the fight is finished, as they got going slower than the PCs did.</p><p></p><p>5. PCs catch up to fleeing bad guy. They are a mage (CR 6, EBP 30) with a veteran (EBP 18) and 10 orcs (EBP 40) with the daughter (Scout, CR 1/2, EBP 4, but restrained and unarmed). The guards engage the orcs while the PCs+Guard Captain have to fight the mage and veteran. (EBP 36, hard-deadly)</p><p></p><p>(each round 1d6 guards die and 1d3-1 orcs; if the PCs take too long, the orcs fall on them.)</p><p></p><p>6. Clean up leftover orcs. They flee if reduced to 3 or fewer orcs (EBP: 20ish)</p><p></p><p>Total budget: 155-175</p><p></p><p>Now just need to work out what happens if the PCs don't follow the railroad. <img src="https://cdn.jsdelivr.net/joypixels/assets/8.0/png/unicode/64/1f609.png" class="smilie smilie--emoji" loading="lazy" width="64" height="64" alt=";)" title="Wink ;)" data-smilie="2"data-shortname=";)" /></p></blockquote><p></p>
[QUOTE="NotAYakk, post: 7902054, member: 72555"] [b]Warning Edit[/b]: I did the math in this from memory, not from my spreadsheet. The actual exponent is 2/3 not 3/4, and there are a few other errors (corrected in later posts). --- As for encounter building, all of that futzy "double XP" crap can be gotten rid of by just raising XP values and budgets to the ^(3/4). This changes the 25%/50%/75%/100% easy/medium/hard/deadly to 40%/60%/80%/100%. The basic idea is, how hard is a monster with 2x the HP and Damage? Is it 2x (I mean, you doubled both), or 4x (2x * 2x = 4x)? If you just double a monster's damage, it is twice as hard, right? So how about 2 monsters? Well, they are more vulnerable to AOE effects, and it tends to be harder to focus fire with 2 monsters, and if you deal 1 monsters worth of HP their damage output halves. How do 2 monsters compare to one with 2x HP? That (3/4) factor is 5e D&Ds answer to that question. Suppose we have X monsters on the left and one monster with Y times the HP and Damage on the right. (HP*Damage)^(3/4) (adjusted for defences and accuracy) answers "how many X monsters does it take to be just as hard as a Y". X * (HP*Damage)^(3/4) = (Y*HP*Y*Damage)^(3/4) X * (HP*Damage)^(3/4) = (Y^2)^(3/4) * (HP*Damage)^(3/4) X = (Y^2)^(3/4) X = Y^1.5 So if Y is 4, X is 4^1.5 which is about 6. So 6 "small" monsters are just as hard as one "4 times size" monster. How this works in the 5e encounter balancing system is this. Suppose the small monsters are wroth 400 XP each. The big monster will be worth 400*4*4 = 6400 XP or so. 400 * 6 is only 2400 XP. But the [B]encounter size multiplier[/B] then boosts 2400 XP by 2.5-3, making it reach 6000-7200 XP. Roughly the same budget. As far as I can tell, all of those encounter size multipliers can be ignored by first raising XP to the (3/4) power. Now XP is additive. But if we are doing this, we don't have to use the XP values posted. I mean, many people advance by milestones instead anyhow. --- Anyhow, you can take the XP values of various CR monsters, raise it to the (3/4) power, then futz around with it and round it. You get something like: CR 1/8: 1 CR 1/4: 2 CR 1/2: 4 CR 1: 6 CR 2: 9 CR 3: 12 CR 4-15ish: +6 per CR CR 16-19: +9 per CR CR 20: 140ish CR 21+: +15 or 20, I forget, per CR I call those "encounter building points". They let you build encounters by just adding up numbers and no multiplication. --- On the PC side, you can add up player EBP and divide by 4 to work out what their medium budget should be. Then an easy encounter is 2/3, hard is 4/3, deadly is 5/3 of that, and "crazy" is 2x. If we divide by 3 instead of 4 we get even nicer math. Easy is 1/2, medium is 3/4, hard is that EBP, and deadly is 5/4 (+25%) and crazy is 3/2 (+50% over budget). As the EBP stuff above is already divisible by 3 we get: L1: 2 EBP L2: 3 EBP L3: 4 EBP L4-15: +2 EBP per level (or Level*2-2) L16-19: +3 EBP per level L20: 45 EBP then just add up the party's EBP to give an EBP budget (at "hard" difficulty). (the cutoff at 15-16 might be a level layer, I'm doing this from memory). There is modest differences in the encounters build this way compared to the DMG, but I find it ridiculously easier. Turning this into scene building (budget for time-between-short-rests) and daily budgets isn't hard. Really, 5 times your EBP budget (as calculated above) isn't a bad number to at level 3 and above (at level 1-2, use 4x). So a party of 4 level 5 PCs has an EBP budget of: 16 easy (don't use anything easier than this) 24 medium 32 hard 40 deadly 48 crazy 160 per day If you have 2 short rests per day, that is about 56 EBP per "scene" (period between short rests). Lets build a set of encounters. We are in a village. The baron's daughter is visiting. Mercenaries attack, pinning down the PCs. 1. 6 guards (EBP 6) plus PCs against 6 orcs (24 EBP) (18 EBP net, easy fight) 2. Guards leftover from first 1 (say, 4), plus 5 new guards (so 9 EBP), plus PCs, vs 8 orcs (32 EBP) and a veteran (CR 2, 18 EBP) 41 -- deadly-crazy fight. Short rest. The attackers have kidnapped the baron's daughter! They flee on the water. PCs get on boat and give chase (short rest). 3. Neried (36 EBP, hard-deadly) engages PC's boat. PC continue chase (short rest). 4. Enemy boat is pulled up on a dock. They left 6 orcs behind to ambush PCs (24 EBP, medium encounter). A boat with 20 guards (EBP 20) and a Guard Captain (EBP 12) arrives after the fight is finished, as they got going slower than the PCs did. 5. PCs catch up to fleeing bad guy. They are a mage (CR 6, EBP 30) with a veteran (EBP 18) and 10 orcs (EBP 40) with the daughter (Scout, CR 1/2, EBP 4, but restrained and unarmed). The guards engage the orcs while the PCs+Guard Captain have to fight the mage and veteran. (EBP 36, hard-deadly) (each round 1d6 guards die and 1d3-1 orcs; if the PCs take too long, the orcs fall on them.) 6. Clean up leftover orcs. They flee if reduced to 3 or fewer orcs (EBP: 20ish) Total budget: 155-175 Now just need to work out what happens if the PCs don't follow the railroad. ;) [/QUOTE]
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