Need Help with Calculating Average Damage.

[Agrias]

Hi. I seen some Average Damage Per Round Calculators out there but they are missing some things and I wanted to make my own. I need some help checking if I'm getting the math right. Cause when I compared to "donjon power attack calculator site" I get the non critical damage the same but critical damage is off and I'm not sure if I made a mistake or if that site has a mistake.
So here is how I was thinking to calculate it. (it will be simplified version just to check the basics, aka no Power Attack, no Power Critical, no DR, no Sneak Attack, etc I wanna add those later)

Let's take these values:
Average Hit Damage = 20
Average Critical Damage = 40
Attack = 15
Critical = 19-20 (10%)
Critical Multiplier = x2
Number of Attack: 1
Enemy AC = 20


Step 1: Calculate Average Hit Chance (Min 5% Max 95%) <-- Because 1 is always miss and 20 is always hit
(100 - (AC - Attack) * 5) /100
(100 - (20 - 15) * 5) / 100 = 0.75

Step 2: Calculate Average Critical Chance
100 * Critical Threat * Hit
100 * 0.1 * 0.75 = 0.075

Step 3: Average Hit Damage
(Hit Chance - Critical Chance) * Average Hit Damage
(0.75 - 0.075) * 20 = 13.5

Step 4: Average Critical Damage
Critical Chance * Average Critical Damage
0.075 * 40 = 3

Step 5: Average Damage Per Round
Average Hit Damage + Average Critical Damage
13.5 + 3 = 16.5

[MisterKaws]

You forgot the crit confirmation rolls.

[JNAProductions]

So, you have three possibilities:

Miss on a 1-4, for 20% of the time
Hit on a 5-20, for 80% of the time minus whatever your crit chance is
Crit on a 19-20 (10%) followed by a 5-20 (80%) for 8% chance of crit

So, that leaves us with:

Miss 20%
Hit 72%
Crit 8%

Then, just multiply by the damage.

.2*0=0
.72*20=14.4
.08*40=3.2

And add them all together.

0+14.4+3.2=17.6

[Iku Rex]

It's been ages since I did this, but I think I remember.

As long as a crit threat is always a hit, your average damage on a hit is average regular damage * multiplier from crits. "Multiplier from crits" depends on crit range. x2 is 1.05. x3 or 19-20/×2 is 1.1 . x4 or 18-20/×2 is 1.15.

Then you just need to know how often you hit.

In this case, your average damage on a hit is 20*1.1 = 22.

You miss on a 1-4, or 20% of the time, so you hit 80% of the time.

22*0.8 = 17.6

Same result as JNAProductions, but this way is usually easier IMO.

[Agrias]

So, you have three possibilities:

Miss on a 1-4, for 20% of the time
Hit on a 5-20, for 80% of the time minus whatever your crit chance is
Crit on a 19-20 (10%) followed by a 5-20 (80%) for 8% chance of crit

So, that leaves us with:

Miss 20%
Hit 72%
Crit 8%

Then, just multiply by the damage.

.2*0=0
.72*20=14.4
.08*40=3.2

And add them all together.

0+14.4+3.2=17.6

Oh Right how did I mess that up. Hit would be 80% not 75% and then minus Crit.
Cheers now all is correct.