# Thread: Highest DPR on Forums! (Math silliness for min-maxing)

1. ## Highest DPR on Forums! (Math silliness for min-maxing)

A friend of mine is a bit of a math wiz, and a huge fan of statistics.
Together (mostly just him) we crafted a series of equations for your character's "damage per round" or DPR. DPR is 6 times your DPS, if you must know.

The variables:
AC: Armor Class of the enemy in question. (for calculating damage to an average AC, assume 14 + character level)
AB: Attack Bonus with the selected weapon. Remember to factor in "unusual size" penalties, and tower shield penalties.
PA: Amount your charater power attacks for (count this variable as zero for the purposes of characters who do not power attack)
DA: Average Damage with selected weapon. To calculate average damage divide the max value of the die in question by two and add 0.5 to it. Multiply this value by the number of dice. Then add all other bonuses, such as strength, sneak attack etc etc. Example: a half-orc fighter with a strength of 20 and a 3d6 large greataxe deals an average damage (on a hit) of 17.5, (((6+1)/2)*3) + 1.5 * str (5).
DC: is not Difficulty Class. Damage per crit is the multiplier you apply on a crit. ex: a large greataxe deals *3 damage on a crit.
CC: 25 miligrams of critical chance, stat! CC is the critical chance. 1/20 for a weapon that crits on a 20. 2/20 for a (19-20) weapon. For quick reference: 1/20 is 0.05. 2/20 is 0.1. 3/20 is some ridiculous repeating decimal (just use the fraction) If a creature doesn' take critical damage, count the crit chance as 0.
DR: Damage Reduction of enemy. DR Sucks. Carry a silvered weapon at all times. Alternitevely, use the caster as an improvised greatclub, magic bypasses a lot of creatures' DR.

The equation for a melee fighter (not necissarily the "fighter" class):

(((21-AC+AB-PA)/20)*(DA+PA) + ((DC-1)*CC*(DA + PA)*((21-AC+AB-PA)/20))) -DR

There is also a specific equation for our ranged rogue who uses a repeating crossbow and uses rapid shot. Factoring in that he needs to reload. You really don't want to know.

Example: a 4th level Half-Orc Fighter with 20 strength, wielding a large-sized greataxe (3d6 and x3 critical) not power attacking deals an average DPR of

((21-18+8)/20)*17.5 + ((3-1)*.05*17.5*((21-18 + 8)/20))) or 10.58 DPR (1.76 DPS, if you must)

I guess I could post the ranged equation, but it causes insanity upon extended viewing.

2. ## Re: Highest DPR on Forums! (Math silliness for min-maxing)

nice.

small pedantic nitpick: i'd come up with a different acronym rather than DC for crit damage.

it's only going to lead to endless confusion.

/minor pedantry

3. ## Re: Highest DPR on Forums! (Math silliness for min-maxing)

This doesn't account for extra damage dice, effects that proc on crits, power attack multiplication. You also forgot to multiply power attack on the critical side.

4. ## Re: Highest DPR on Forums! (Math silliness for min-maxing)

I did forget power attack.

The other concerns:
Extra effects on criticals: simply slap this harmless equation on the end of it for each effect: + (CC*(Damage of Effect))
Extra Damage Dice: as previously noted in the entry for DA add any extra damage dice to the DA value after calculating the average dammage of your base dice.

What is this "power attack multiplication" of which you speak?

These equations are ludicrously fun for players, and endlessly useful for me as a DM, because I love to homwbrew, but before now I couldn't check balance. They're also terrific for checking if taking a large weapon is for your character! Simply plug in the numbers and check your DPR!

The first few days of having these equations we staged a purely hypothetical fight between the Half-Orc Fighter 4 (Borgackackle the Brave) and the Dwarven fighter 5 (Grok).

Borgack has 20 STR and 17 AC
Grok has 20 CON and 24 AC
Borgack wins by ~5 HP after ~6 rounds.

MinMaxxing is AWESOME.

5. ## Re: Highest DPR on Forums! (Math silliness for min-maxing)

It was added in 3.5 - power attack does more damage when used with a two-hander, or with Leap Attack, or the like.
Adding damage dice into DA is a mistake because extra damage dice such as Flaming weapons are not multiplied on critical hits.
In the case of things like Flaming weapons, it might be wise to add a separate elemental column to account for Fire Resistance or Vulnerability to Fire or whatever.

IMO without some average target ACs this is largely irrelevant for min/maxing. And collecting accurate average AC data is going to be a pain (I'm not sure I trust your 14+level thing)

PS: This does not account for Tactical Feats/Manevers and their attached opportunity costs (nor should it, IMO, that's way too much work), nor does it account for multiple attacks per round.

6. ## Re: Highest DPR on Forums! (Math silliness for min-maxing)

Originally Posted by Foryn Gilnith
It was added in 3.5 - power attack does more damage when used with a two-hander, or with Leap Attack, or the like.
Adding damage dice into DA is a mistake because extra damage dice such as Flaming weapons are not multiplied on critical hits.
In the case of things like Flaming weapons, it might be wise to add a separate elemental column to account for Fire Resistance or Vulnerability to Fire or whatever.
Bah, logic is fail.
This equation attacks for 17.4 DPR against your flaming weapon.
It gets no save.

I guess that you could remed that by adding ANOTHER variable, called ED, or erecti-- erm, extra dice, and that would add only to the first DA, hence:

(((21-AC+AB-PA)/20)*(DA+PA+ED) + ((DC-1)*CC*(DA + PA)*((21-AC+AB-PA)/20))) -DR

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