Another math request


Pathfinder First Edition General Discussion

Grand Lodge RPG Superstar 2012 Top 32

I have another task for those forumites who enjoy mathy stuff. :)

So let's say I have a character named Alice. She attacks once per round at +15 to hit and deals 2d6+20 damage on a hit. (For my reference: 10+5+5)

Now let's say I also have a character named Bob. He can attack twice per round. Each attack is at +11 to hit for 1d6+14 damage.

Now suppose I have a third character, this one named Charlene. She can attack four times per round. Each attack is at +11 to hit and deals 1d6+8 damage.

Against target ACs of 15, 20, and 25; what is the average damage per round for each of these characters? Please do not factor in crits.

Thanks in advance!

Grand Lodge RPG Superstar 2012 Top 32

Eh?

Sczarni

I'm not great at Math, but I do have a spreadsheet I could drop these numbers into - problem is I don't know how to exclude the crits. I could try zeroing them out but I don't know if that would skew the numbers.


Alice a) 27 * .95 = 25.65
b) 27 * .8 = 21.6
c) 27 * .55 = 14.85

Bob a) 2 * 17.5 * .85 = 29.75
b) 2 * 17.5 * .6 = 21
c) 2 * 17.5 * .35 = 12.25

Charlene a) 4 * 11.5 * .85 = 39.1
b) 4 * 11.5 * .6 = 27.6
c) 4 * 11.5 * .35 = 16.1

Sczarni

^There you go. I came up with the exact same numbers for Alice. Didn't bother doing the others as it looks good.


(Edit: Ninja'd, but at least it's confirmation)

If I did this wrong, someone will likely point it out.

---
Alice (+15, 2d6+20)
Expected damage per hit = 27
Number of attacks: 1
---
AC 15:
Hits on a 2 or better
Chance to hit = 95%
Expected damage per attack = 25.65
Expected damage per round = 25.65

AC 20:
Hits on a 5 or better
Chance to hit = 75%
Expected damage per attack = 20.25
Expected damage per round = 20.25

AC 25:
Hits on a 10 or better
Chance to hit = 55%
Expected damage per attack = 14.85
Expected damage per round = 14.85

---
Bob (+11, 1d6+14)
Expected damage per hit = 17.5
Number of attacks: 2
---

AC 15:
Hits on a 4 or better
Chance to hit = 85%
Expected damage per attack = 14.875
Expected damage per round = 29.75

AC 20:
Hits on a 9 or better
Chance to hit = 60%
Expected damage per attack = 10.5
Expected damage per round = 21.0

AC 25:
Hits on a 14 or better
Chance to hit = 35%
Expected damage per attack = 6.125
Expected damage per round = 12.25

---
Charlene (+11, 1d6+8)
Expected damage per hit = 11.5
Number of attacks: 4
---

AC 15:
Hits on a 4 or better
Chance to hit = 85%
Expected damage per attack = 9.775
Expected damage per round = 39.1

AC 20:
Hits on a 9 or better
Chance to hit = 60%
Expected damage per attack = 6.9
Expected damage per round = 27.6

AC 25:
Hits on a 14 or better
Chance to hit = 35%
Expected damage per attack = 4.025
Expected damage per round = 16.1


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The damage formula is h(d+s)+tchd.

h = Chance to hit, expressed as a percentage
d = Damage per hit. Average damage is assumed.
s = Precision damage per hit (or other damage that isn't multiplied on a crit). Average damage is again assumed.
t = Chance to roll a critical threat, expressed as a percentage.
c = Critical hit bonus damage. x2 = 1, x3 = 2, x4 = 3.

To exclude crits, just remove the +tchd part.

For h, we need to assume an AC. Let's assume AC 20.

Alice needs a 5 to hit AC 20, so she has a 75% chance to hit.
0.75(26) = 19.5 DPR

Bob needs a 9 to hit each time, so he has a 60% chance to hit.
0.60(17) x 2 = 26.4 DPR

Charlene aslo needs a 9 to hit, so she has a 60 % chance to hit.
0.60(11) x 4 = 24.2 DPR

Percent chance to hit is based on adding up 5% for each qualifying number on a d20 roll. if you need a 9, that's 12 different numbers you could roll (9-20); 5 x 12 = 60.


Damn. Ninja'd.


Note that Charlene will always do more expected damage than Bob since she has the same hit bonus, twice as many attacks, and more than half the damage per hit as Bob.


Blahpers is more correct than mine, since he assumed 3.5 average roll on a d6, whereas I assumed an average roll of 3. His is more precise.


blahpers wrote:


If I did this wrong, someone will likely point it out.
---
Alice (+15, 2d6+20)
Expected damage per hit = 27
Number of attacks: 1
---
AC 20:
Hits on a 5 or better
Chance to hit = 75%
Expected damage per attack = 20.25
Expected damage per round = 20.25

Minor error here: hitting on a 5 or better = 80% hit chance. Thac20's average DPR = 21.6 was correct.

Grand Lodge RPG Superstar 2012 Top 32

Thanks all! Hm, that formula makes sense. Maybe now I can do this stuff myself. :D


Just for you, Jiggy A little webpage of my own creation.

You can set the CR with the drop down box and it will change the AC, or you can just type in the AC. But if you type it in, then you will have to refresh the page before the dropdown box works again. :)

EDIT: If you dont want it to factor crits, then make the "crit multiplier" box = 1. That will remove all crit damage from the calculation.


Matthew Downie wrote:
blahpers wrote:


If I did this wrong, someone will likely point it out.
---
Alice (+15, 2d6+20)
Expected damage per hit = 27
Number of attacks: 1
---
AC 20:
Hits on a 5 or better
Chance to hit = 75%
Expected damage per attack = 20.25
Expected damage per round = 20.25
Minor error here: hitting on a 5 or better = 80% hit chance. Thac20's average DPR = 21.6 was correct.

Good catch. I checked that one three times and still missed it.

Grand Lodge RPG Superstar 2012 Top 32

BigDTBone wrote:

Just for you, Jiggy A little webpage of my own creation.

You can set the CR with the drop down box and it will change the AC, or you can just type in the AC. But if you type it in, then you will have to refresh the page before the dropdown box works again. :)

EDIT: If you dont want it to factor crits, then make the "crit multiplier" box = 1. That will remove all crit damage from the calculation.

Okay, that's pretty spiffy. Thanks!


BigDTBone wrote:

Just for you, Jiggy A little webpage of my own creation.

You can set the CR with the drop down box and it will change the AC, or you can just type in the AC. But if you type it in, then you will have to refresh the page before the dropdown box works again. :)

EDIT: If you dont want it to factor crits, then make the "crit multiplier" box = 1. That will remove all crit damage from the calculation.

BigDTBone, the page hasn't been working for a little while now. Dunno if you were already aware or not.


ZanThrax wrote:
BigDTBone wrote:

Just for you, Jiggy A little webpage of my own creation.

You can set the CR with the drop down box and it will change the AC, or you can just type in the AC. But if you type it in, then you will have to refresh the page before the dropdown box works again. :)

EDIT: If you dont want it to factor crits, then make the "crit multiplier" box = 1. That will remove all crit damage from the calculation.

BigDTBone, the page hasn't been working for a little while now. Dunno if you were already aware or not.

I made a post about it here. Shoot me a PM with you email address and I'll send you the excel sheet. Alternatively stay tuned to the other thread and I'll post when I get the new page up. Probably in about 2 weeks or so.

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