I need a number cruncher for DPR

[Kane0]

Hullo all.

I admit I'm not the best mathematician out there. Could I trouble someone to help me crunch some numbers for SCIENCE?

We have Warren the Warrior, Sue the Scout and Garry the Gish. These three are putting their money where their mouth is and betting that their damage output is competitive if not superior to each of the other two.

Warren is a typical GWM + PAM fighter. He hasn't decided whether he wants to go Champion or Battlemaster yet but he's looking for damage output to make sure he puts the others in their place.

Sue is taking up a TWF approach and gets these abilities: Level 1 she gets +1d4 to damage on each hit which increases in die size each time her proficiency bonus goes up. She also gets access to hunter's mark and a fighting style (TWF) at level 2, extra attack at level 5 and at level 11 can reroll a miss once per turn. Finally at level 20 her attack stat increases by 2 to a max of 22.

Garry is a sword and boarder and gets some neat stuff of his own. Relevant to us he gets a fighting style (dueling) at level 1, access to Firebolt at level 2 and the ability to add it's damage to a weapon attack. At level 5 he gets extra attack though he can't use this in conjunction with his firebolt add-on until level 11.

So my question is how do Warren, Sue and Garry compare to each other throughout their careers? For argument's sake we can say that they are wailing on training dummies with an AC of 12 + their prof bonus at levels 4, 8, 12 and 20.

Edit: Oh and they each start with 16 in their attack stat.

[Kane0]

So here's what I have so far.

Level 4 (AC 14, +2 prof):
Warren takes PAM with his ASI and deals 1d10 +3 rerolling 1s and 2s and 1d4 +3 with an attack bonus of +5. Champion gets him crits 10% of the time.
Sue take TWF with her ASI and deals 1d8 +1d4 +3 twice with an attack bonus of +5
Garry takes +2 STR with his ASI and deals 1d8 +1d10 +5 with an attack bonus of +6

Level 8 (AC 15, +3 prof):
Warren takes GWM and +2 STR using his ASIs for 1d10 +4 rerolling 1s and 2s twice plus 1d4 +4 with an attack bonus of +7. Champion crits 19-20 and has the option to take -5 to hit for +10 damage with each attack
Sue takes +2 dex for 1d8 +1d6 +4 three times with a +7 attack bonus
Garry takes +2 Str again for 1d8 +2d10 +6 or 1d8 +6 twice with an attack bonus of +8

Level 12 (AC 16, +4 prof):
Warren takes +2 STR and another feat for 1d10 +5 rerolling 1s/2s three times plus 1d4 +5 with an attack bonus of +9. Champion crits 19-20 and can choose to take -5 to hit for +10 damage on each of his four attacks.
Sue takes +2 dex and deals 1d8 +1d8 +5 three times with a +9 attack bonus, rerolling one miss per turn
Garry takes elemental adept for 1d8 +7 twice, one of those adding +3d10 turning 1s to 2s with an attack bonus of +9

Level 20 (AC 18, +6 prof):
Warren takes some other feats cause he has ASIs to burn. His final attack routine is 4x 1d10 +5 rerolling 1s/2s plus 1d4 +5 with an attack bonus of +11 or +6 if he wants to add +10 damage per hit. He crits on 18-20 now.
Sue is up to 22 dex for three attacks at 1d8 + 1d12 +6 each with a +12 attack bonus, rerolling one miss each turn.
Garry gets two attacks at +11 for 1d8 +7 each, plus 4d10 turning 1s to 2s if one of those hits.

Does anyone know the calculations to turn these into hits and damage per round?

[Kryx]

You could copy and modify my dpr of classes sheet. It's fairly understandable to others I hear.
The core setup is close to what you're looking for: standard progression at all levels which can be used to compare the fighting style options.

[qube]

Not really sure on the numbers you give (GWF also applies to the d4 of PAM; no clue how scout works, and no clue where the d10 comes from for a sword and board flameblader)

(disclaimer: no clue how scouts work)


Level 4 (AC 14, +2 prof):
Warren takes PAM with his ASI and deals 1d10 +3 rerolling 1s and 2s and 1d4 +3 with an attack bonus of +5. Champion gets him crits 10% of the time.
Sue take TWF with her ASI and deals 1d8 +1d4 +3 twice with an attack bonus of +5
Garry takes +2 STR with his ASI and deals 1d8 +1d10 +5 with an attack bonus of +6
(I've also calculated a Fourth guy (Ford, if you will), namely a Warren variant who uses great sword & took GWM as first feat, dispite AC 14 being already relatively high to take a -5 attack dump on, And Bob the barbarian, reckless GWM greatsword )


W = +5 vs 14 = 8 misses, 10 hits, 2 crit (out of 20)
S = +5 vs 14 = 8 misses, 11 hits, 1 crit (out of 20)
G =+6 vs 14 = 7 misses, 12 hits, 1 crit (out of 20)

F = +0 vs 14 = 13 misses, 5 hits, 2 crit (out of 20)

B = +0 vs 14 with advantage means 13 misses on a d20, meaning (X-1)² = 12² = 144 misses when advantage
the number of crits is 20 (first die is a 20) + 19 (second die is a 20 whiel the first is not) = 39
and the rest of the 400 are hits, so that makes: 144 misses, 217 hits, 39 crits

d4* = (2.5+2.5+3+4)/4 = 3
d10* = (5.5+5.5+ 3+4+...+10)/10 = 6.3

Wdam4 = 3+3 = 6
Wdam10 = 6.3+3 = 9.3
Wcrit4 = 3+3+3 = 9
Wcrit10 = 6.3+6.3+3 = 15.6

Sdam = 4.5+2.5+3 = 10
Scrit = 4.5+4.5+2.5+2.5+3 = 17

Gdam = 4.5+5.5+5 = 14.5
Gcrit = 4.5+5.5+5.5+5 = 19.5 (I seem to recall an errata stating greenflame doesn't multiply on crit)
1d8 +1d10 +5

d6* = (3.5+3.5+3+4+5+6)/6 = 4.166...
2d6* = 8.33...

Fdam = 8.33 +3+10 = 21.33
Fcrit = 8.33 + 8.33 + 3 +10 = 29.66

Bdam = 7+3 +10 = 20
Bcrit = 7+7+3 +10 = 27
rBdam = 7+3+2 +10= 22
rBcrit = 7+7+3+2 +10 = 29


Damage per round = { (hit chance * damage) + (crit chance * crit damage) } for every attack

Warren: ( 10*9.3 + 2*15.6 ) + ( 10*6 + 2*9 ) = 124.2 + 78 = 202.2 ~~> 10.11 DPR
Sue: (11*10 + 1*17) x 2 = 127 x2 = 254 ~~> 12.7 DPR
Garry: (12*14.5 + 1*19.5) = 193.5 ~~> 9.68 DPR

Ford & Bob take the -5/+10, and gets a bonus attack when he crits:
Damage per round = { (hit chance * damage) + (crit chance * (crit damage + the extra attack )

Ford: (5*21.33 + 2* (29.66 + ((5*21.33 + 2*29.66)/20) ) = (5*21.33 + 2* (29.66 + 8.3 ) = 182.6 ~~> 9.13 DPR
Bob: (217*20) + 39*(27+ ((217*20 + 39*27)/400) ) = (217*20) + 39*(27+ 13.4825 ) = 5918.82 ~~> 14.80 DPR
Raging Bob: Bob: (217*22) + 39*(29+ ((217*22 + 39*29)/400) = 6480,74 ~~ > 16.20 DPR



Warren: 10.11 DPR
Sue: 12.7 DPR
Garry: 9.68 DPR
Ford: 9.13 DPR
Reckless Bob: 14.80 DPR
Reckless Raging Bob: 16.20 DPR