D&D General DPR Calculations Wut?

[EzekielRaiden]

Of course I can figure out average damage per round (1 attack, 1d6+2, average 5.5).

But I see people with equations like : 65% chance to hit.

Where's that coming from? I feel like there are some assumptions I am missing. The % to hit would come from the AC of the target right?

Spell out DPR and explain it for me as a process, like I was in high school. (I do have a degree but somethings not clicking)

65% is what the designers aim for the typical fight being. Naturally, you cannot perfectly predict AC, and thus AC will vary up and down--some things will be fragile, other things hella sturdy.

If you are going to reject the idea that we can estimate typical long-run behavior, then you're fundamentally rejecting the concept of mathematical analysis in the first place. The game cannot be designed, then, because there's no way for us to analyze it; all we can do is present totally individual experiences and hope we can glean something from them...which is going to be extremely difficult, if not impossible.

I'm not saying qualitative data has no place, it absolutely does; nor am I saying that DPR is the only metric, it isn't. Hell, it isn't even the best metric in a lot of ways. But in order to do mathematical analysis of things, that is, in order to know that the designs we make are effective in addition to being evocative and compelling, we have to be able to do some degree of benchmarking.

If you know what your DPR is against an expected "average" AC, then you are at least better-prepared to predict what your damage output will be when reality diverges from those assumptions. That's why we do safety drills, right? We practice when there is no problem, so that we are prepared to deal with the times that there are problems.

 

[Zardnaar]

65% is what the designers aim for the typical fight being. Naturally, you cannot perfectly predict AC, and thus AC will vary up and down--some things will be fragile, other things hella sturdy.

If you are going to reject the idea that we can estimate typical long-run behavior, then you're fundamentally rejecting the concept of mathematical analysis in the first place. The game cannot be designed, then, because there's no way for us to analyze it; all we can do is present totally individual experiences and hope we can glean something from them...which is going to be extremely difficult, if not impossible.

I'm not saying qualitative data has no place, it absolutely does; nor am I saying that DPR is the only metric, it isn't. Hell, it isn't even the best metric in a lot of ways. But in order to do mathematical analysis of things, that is, in order to know that the designs we make are effective in addition to being evocative and compelling, we have to be able to do some degree of benchmarking.

If you know what your DPR is against an expected "average" AC, then you are at least better-prepared to predict what your damage output will be when reality diverges from those assumptions. That's why we do safety drills, right? We practice when there is no problem, so that we are prepared to deal with the times that there are problems.

It doesn't always reflect reality.

Smites come to mind. White room you have XYZ crit chance, smites deal XYZ average damage.

But smites tend to get used more when you smite.

White rooms also really bad at tactics and strategy. The old -5/+10 feats I identified very early. People here said youre an idiot. Not if you build around them.

Same thing with how we were getting massive danage boosts out of paralyzed. Cant do that but when stuff fails wisdom saves 75-95% of the time (common tbh) yes you can guarantee crits.

Hell Ive had people argue you cant auto crit with ranged attacks vs paralyzed foes without disadvantage.

 

[M_Natas]

To add everything that is said:
The DPR is the average amount of damage per Round if you hit 100% of the time.
1d6+2 is 5,5, so a hit does on average 5,5 Damage.

Now you have to adjust for Hitchance.

What are the hit chances ... the numbers for 5E are that:

A Level 1 to 3 Character has, on average, a bonus to hit of +5 (+2 Prof, +3 from Abilitiy Bonus)
A Level 4 Charater +6 (+4 from Ability),
a Level 5 Character +8 (+3 Prof Bonus and if you roll randomly on the magic item table according to the 5E DMG, your party will probably have a +1 magic weapon at that point in the game)
A Level 6 to 8 Character has an attack bonus of +9 and so on.

Now you need the monster AC and deriviate the HP from it.
And now it gets silly, because the base assumption for 5e is, that a fight lasts on average 3 rounds and that a party has on average 4 members.
So, the damage output of the party for a complete combat is DPR of party member * 4 party memeber *3 rounds.
So lets say 5,5 * 4 * 3 = 66 - not accounting for special abilities.

Which is quite bad ... in my calculations, that includes spells an special abilities, a first Level Party has a DPR of 8 to 12 per Member, depending on the length of the adventuring day (DPR of 11,6 if you have one battle between long rests, DPR of 8 if you have 24 battles between long rests) - if they Party fights against 1 Monster. If they fight against 3 or more monsters, the DPR range for a first level party changes to 8 to 15 because of AOE damage from casters.

So we have to make even more assumptions. How long is the adventuring day? What is the party composition? A first level all Champion Fighter Party is way stronger against a single big monster and an all wizard party is way stronger against hordes of creatures.

The DMG2014 says, the adventuring day should have 3 to 6 encounters (which translates to combats or things that have combat like effects on the party resources).

So, now we dialed that in ... our average party of 4 (2 Fighters, 2 Wizards) first level characters has a DPR of 36,45 (100% Hitchance) fighting against a single monster during an adventuring day of 4 encounters, account for Spells and special abilites. The party has a +5 to hit bonus.

So, an AC6 Monster needs somewhere between 73 and 109 HP to Last for 3 rounds against the party. Because with an attack bonus of +5, the party hits 100% of the time (not accounting for critical failures with critical failures, any Monster AC automatically becomes the hit bonus of the party +2 if it is lower than that). So AC7 is actually the lowest AC our Monster should have, which gives the party a 95% hit chance, so it can have HP anywhere from 70 to 103, to last on average 3 rounds. With critical hits (which are accounted for in my calculations of the DPR), there is always a 5% hit chance, so the highest AC for a hit bonus of +5 is always 20 + Hitbonus = 25 for our Level 1 party. With a 5% hit chance, the Monster should have 4 to 5HP to a last three rounds.

You can see this play out in the monster manual on average again: A monster with a lower AC usually has a higher HP amount for monsters of the same CR.

But: There are always exceptions. Because "evil" WotC has also monsters that are definitely designed to last shorter than 3 rounds.

A CR1 Brass Dragon Wyrmling with AC16 and HP16 will last one round against a 4 member level 1 party or it will TPK the party with it's breath weapon.

But interestingly, at Level 1 I don't see a monster that would last longer than 3 rounds on average. The highest AC/HP Monster at CR 1 is the Dread Warrior with AC18 and HP 37 which is dead center in the HP range to die in 3 rounds of AC18 against a Level 1 party with +5 Hit Bonus. The HP Range would be 30 to 43.

Now, how does WotC adjust for that? For lower number of rounds? When the Monsters AC/HP combo says, that on average it would only last 1 round or 2 rounds, WotC is making the Damageoutput of that Creature higher.

Our Animated Amor has a DPR of 2d6+4, 11 at a 100% Hitchance, Attackbonus is +4, against an average Party AC of 15, that is a 50% hitchance, so the Mosnter makes 5,5 damage per round on average, doing 16,5 damage during the whole combat.
Our Brass Dragon Wyrmling, who will only last on average one round, can probably hit 2 characters on average with its breath weapon. DC11, so lets say 65% success chances of the party to make the save (now we are again in assumption land, because while the attack bonus is usually close to the average, saving throw boni can range wildey). So, 14 Damage 2 0,65 =18,2 damage dealt.

So, while the fight with the dragon Wyrmling only lasts 1 round, it deals roughly the same damage as the 3 rounds fight of the Animated Amor.


So if you want to simulate combat or create monsters you have to account for:

• Hit Bonus of the Party (Abilitiy mods, prof. bonus, magic items, special circumstances, special abilities)
• Damage dealt of the party (Spells, Weapon Damage, special abilities, Magic Items ect.)
• Number of expected combat rounds for that one battle
• number of battles/combat rounds in the adventuring day
• Number of Monsters
• Number of Party Members ...
• Combat strategy of the party
• optional rules (Flanking for free advantage)
• Oh, and environment

which all have an influence on the

• AC of the Monster
• HP of the Monster
• abilities that Adjust AC and HP (hide, regeneration ...)
• Damage output of the Monster

 

[tetrasodium]

I don't know if anyone linked it already but I threw together this spreadsheet on google docs for crunching these kinds of numbers during the covid shutdown. Fill in the grey bar at the top & relevant dr/resist numbers. everything else will automagically calculate below . The numbered sheets (ie 25/75 50/50 etc) will show the round by round breakdown at those hit/bypass save percentages). FAQ is self explanatory, it explains sgugg. I think spell doodles along with sheet9&10 were an attempt to build some not particularly complete data & functionality I quit working on for various reasons (ie tedious & impossible to assume variables plus general garbage core math that stacks the deck for an agenda under analysis).

You probablt need to open it on a computer, the sheet is just too data dense to realistically use on a phone