Skip to main content

Revisiting Expected Damage

So after more thought I have decided to revisit expected damage.

Consider the case with a 20/x2 critical, which is reasonably standard.

Probability of Hit (No Critical) ~=  (20-(AC of target - attack of attacker))/20
Minimum is always 1/20, maximum is always 19/20

The probability of a critical hit is always 1/20

Mean Damage = (Max Damage + Min Damage)/2

Expected Total Damage = Prob of Hit * Mean Damage + Prob of Crit  * Mean Damage

In our 20/x2 case:

Expected Total Damage = Mean Damage * (21-(AC-Attack)/20


Consider 3 undead (+3 attack, 2d6+2 damage) attacking an AC 14 PC

Expected Total Damage = (14+4)/2 *(21-(14-3)/20 = 9*10/20 = 4.5

With 3 undead, this means expected damage of 3* 4.5 = 14 damage per round

If we ignore criticals, the answer would be only 12 damage per round, a 17% difference!


Generically we can expand the formula for any critical hit as follows:

Expected Total Damage = Mean Damage *((20+Critical Rolls*(Critical Damage Multiplier-1))-(AC-Attack))/20

Where Mean Damage = (Max Damage + Min Damage)/2
And Critical Rolls are the number of dice values for a critical (i.e. 18-20 => 3)
And Critical Damage Multiplier is factor that damage is multiplied by for a crit


Labels:

Comments

Post a Comment

Popular posts from this blog

5E Starting Gold and Equipment for Higher Levels

The DMG has a rough recommendation for starting gold and equipment for higher levels, but with my groups running one-shots, we wanted to nail it down to level by level. Here's my DMG-inspired table. Generally I allow equipment to be traded in during character creation for half book value, where applicable. I also, as a GM, offer to make custom magic items for players who can't choose. A list of magical items by rarity can be found here  with stats available in the DMG. I also generally allow players to buy healing potions (2d4+2) for 50gp and greater healing potions for 250gp (4d4+4). PHB items are available at book cost at creation. I do not allow other equipment to be purchased except in game. This is generally based off the "high magic" campaign. Level Starting Gold Starting Equipment / Magic Items 1 - 160gp  OR Standard starting equipment 2 210gp Standard starting equipment 3 285gp Standard starting equipment 4 365gp Standard sta...
3 comments
Read more

Rules for Flying Creatures in 5E

I'm not one for just throwing my players willy-nilly into something new without an idea of how it would work.  Flying races are on the horizon for one of my games, so here are my clarifications for flying creatures: A flying creatures requires a minimum space of at least 3 times their height in all directions in order to flight. For example, a 6 ft tall flying creature requires a room to be at least 18 ft in all dimensions before they can fly in it. A flying creature can attempt to grapple a creature.  If the the target or grappler are flying, grapple attempts are at disadvantage. If neither are flying, grapples are per RAW.  The state of flying or walking is determined by the last square you have moved.  To change between walking and/or flying, you must use at least 1 space of movement.  Movement rules per RAW apply (PHB pg 190 "Using Different Speeds") A successful grapple check by a flying creature can allow the flying creature to potentially carry th...
Post a Comment
Read more

An Analysis of Tasha's Caldron of Everything: Spells

 I am going to be evaluating "Tasha's Cauldron of Everything" for incorporation into my own games. I figured I would go ahead and record this analysis on my blog here so other folks can follow along and glean some useful information from the time I spent. I tried to find an in-depth analysis elsewhere, but at this time none so detailed as this seems to be available. You will not find any of the text in its entirety in this blog. I will be referencing the first printing of the book, so please refer to that as you read along. There are no released errata for the book at the time of writing, although there are errata from other books that affect some of this content. There are 21 spells in Tasha's Cauldron of Everything. This includes Booming Blade, Green-Flame Blade, Lightning Lure, and Sword Burst cantrips that were originally published in Sword Coast Adventurer's Guide. There are 9 spells that allow you to summon creatures of various types. Three spells are notabl...
Post a Comment
Read more