(Warning – There will be math. And numbers. They bore me too. Well, not really but I’m trying to empathize. Skip the numbers if you don’t like them – dwell on the poor humor instead.)
In July 2010, Wizards of the Coast released a Dungeons and Dragons (4e) errata update, specifically to the Dungeon Masters Guide, more specifically the monster damage table. Monsters in the upper tiers were proving to be woefully underpowered – they just weren’t hitting hard enough. Now this table (shown very helpfully to the right) is all well and good – useful even. But the footnotes I found vexing.
For brutes, the damage should be 25 percent higher. For limited damage, such as damage from encounter powers or recharge powers, increase the value by 25 to 50 percent.
How do I add 25% to 4d8+18?
It’s not one of those things I picked up in grade school. I must have been sick that day.
I started by investigating – how much damage are we talking about here? 4d8+18 sounds like a lot. On average, 4d8+18 will do 36 points of damage. (Don’t believe me? Wolfram Alpha does dice). Now 36 is a number I can deal with. 25% more is 45. But I don’t think the intent is for monster designers to be doing math on every dice roll. (Other than addition don’t get pedantic on me) I have yet to see a monster block containing the text: “Hit: 2d10+8+25% points of necrotic damage, and DM is dazed (save ends)”. My presumption here is that we need find a dice combination that rolls 25% higher.
Now before I go any further let me explain why I care about any of this: I received Orcus for Christmas. (PSA: You know you’ve been bad, very very bad, when you find a demon in your stocking). I’d also been reading Sly Flourish’s article Pimp my Tarrasque, so I had the brilliant idea of updating Orcy’s statistics and maybe even get an article out of it. I even had thought of the perfect title: Pimp my Orcus. I’m good with titles.
So, to get an average of 45, there’s one very easy way to do that. 4d8+18 already averages 36. Just make it 4d8+27. And that works in a pinch. But I was worried about the extreme end of the damage scale. What about the critical hit?
Now I’d argue to a group of drunken Dungeon Masters and Badger wranglers that the critical hit damage is as important as the average. Especially for brutes and such, and that it deserves the 25% boost too. “Why?!” they’d shout, and I’d answer “Be quiet you sorry lot, drink your Goblin’s Piss Ale, and I’ll tell you.” Monsters do not hit Player Characters on every roll of a d20. Maybe half of the time. For the sake of discussion, let’s suppose a monster misses the PC on any roll 10 or under. 11 or higher, it hits. And on a 20 it gets full damage – a critical hit. This means that 10% of the time (1/10) that the monster hits, it gets full damage. Compare that to rolling a 4d8. The changes of getting full damage (rolling all 8s) is 1 in 512. When rolling multiple dice, it’s hard to deviate from the average roll. You should be familiar with this exercise. Roll an 18 on 3d6. Go ahead. Do it now. Didn’t do it? Really? An 18 appears on 3d6 less than 1% of the time (I don’t want to turn this into a dice and probability lesson, so you’ll have to trust me). A maxed out roll – full damage – gets even more rare the more dice you roll. So having the critical happen 10% of the time is often. And that makes it important to get right.
Returning to the 4d8+18, the critical on that is 50, and 25% on top of that is 62.5. The “works in a pinch solution” of 4d8+27, only produces a critical of 59. I’m not going to claim that is a huge difference, but – is there a way to get the best of both worlds? Is there combination of dice and bonus that produces an average roll of 45, and a critical of at least 62.5? There is: 4d10+23 gives us exactly that. An average of 45, and a critical of 63. So, being an altruistic anal retentive fool (lawful good), I set out to find a dice and bonus combo for every entry on the table. And I set myself some limitations. The new combo couldn’t be fundamentally different from the original – I didn’t want to go from 4d8+18 to 1d20+35, or 13d6+3. I wanted the critical damage to be at least 25% higher than the base roll and the average should be within 1 or 2 points of ideal.
And thus was created my first masterworks armor damage chart. Only it had a fatal flaw. An Achilles heel that those paying attention will have already caught. Orcus is level 33 – the table in the DMG is a few levels too short. But the trend of the table is easy to spot. Average normal damage is level + 8, with a little wiggle room. I extended it downward to level 35, and calculated the brutes damage.
At this point I decided to return to Sly Flourish, to check my work and compare notes. And discovered that Mike Shea is a rat fink time traveler who traveled into my future, read this brilliant classic article, returned to the past and put it on his blog. He even stole my great title – Pimp My Orcus. If you had popped open the hatch on the ISS space station you couldn’t have sucked out my enthusiasm faster.
But again, being Lawful Good, I realized that in order not to create a time paradox and destroy the universe, I had to write this article for him to retro-plagiarize. And it gave me something to compare against, and see if I have a legal case he read my thesis carefully. Apparently he has not. The Wand of Orcus attack he has does 4d8+33 damage. Mine is 5d8+29. His average and crit are 51 & 65, respectively, and mine are 51½ & 69.
“But Wait!” you cry, a pleading, desperate tone to your voice, “What about 50% higher damage? What about two or more targets? And minions? You haven’t completed the chart!” Well, yes I have. But you’ll have to wait until next time to get that succulent, juicy morsel. Like John Wick commands, I Play Dirty.
[tags]rpgs, dungeons and dragons, 4e, D&D, role playing games, math[/tags]