Huh? Theory on what?
Greg
You mean this?
h(d+s)+tcvd
h = Chance to hit, expressed as a percentage (min 0.05, max 0.95)
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 (min 0.05 for natural 20 only, up to 0.3 for 15+, cannot be greater than your Chance to hit)
c = Critical hit bonus damage. x2 = 1, x3 = 2, x4 = 3.
v = Chance to Confirm a Critical Threat, expressed as a percentage (min 0.05, max 0.95, cannot be greater than your Chance to hit +0.05/+1 bonus to confirm)
Kierato, don't you count critical hits double?
shouldn't it be like
h = chance to hit, but not critical
so h1:= h-t*v
replace h by h1.
I got this off of a forum a while back, never used it...
hd+tchd is a short hand that doesn't work in a few corner cases. Full formula below.
h(d+s)+ft(cd+cb+r)
h = Chance to hit, expressed as a percentage. This will never exceed .95 or go below .05, obviously.
d = Normal damage. This is any damage that happens any time you hit.
s = Damage which isn't multiplied on a crit. S stands for sneak attack, but this includes elemental/alignment properties on weapons, manyshot damage, and so on.
t = Chance to roll a threat. This is the threat range of your weapon or your chance to hit, whichever is lower.
f = This is your chance to confirm a threat. Most of the time, this is equal to h. If you have Critical focus, it's (h+.2) or .95, whichever is higher. If you auto-confirm crits, as with a level 20 fighter or Bless Weapon, this is 1.
c = This is the number of bonus multiples you get from a crit. A 2x crit weapon is 1, a 3x crit weapon is 2, etc.
b = This is elemental burst damage, such as from fiery burst weapons and thundering. Such enhancements self-multiply based on your crit multiplier; if they don't, then they're added to r and not b.
r = This is fixed bonus damage dealt on a crit. No such abilities exist in PF core, to my knowledge.
Edit: Added shorter formula.
r = This is fixed bonus damage dealt on a crit. No such abilities exist in PF core, to my knowledge.
Killer: You made your first kill at a very young age and
found the task of war or murder to your liking. You eithertake particular pride in a well-placed blow, or find vile
pleasure in such a strike as you twist the blade to maximize
the pain. You deal additional damage equal to your
weapon’s critical hit modifier when you score a successful
critical hit with a weapon; this additional damage is added
to the final total, and is not multiplied by the critical hit
multiple itself. This extra damage is a trait bonus.
EDIT: Not core, APG trait...
Okay, I'm probably going to get hate/rage/flames for this...
But I want the math for theorycraft. I have googled it and found none - do I need a special term, or what?
I wish to examine this math and see if mine can match it at all.
So, if anyone can give me this fabled Holy Grail of All Things D&D/Pathfinder, I'd love to see it.
It is not that simple though. The math needed depends on what you are trying to compare. The formula above is the formula used for the DPR competition. There is even a premade spreadsheet in that forum.
It is not that simple though. The math needed depends on what you are trying to compare. The formula above is the formula used for the DPR competition. There is even a premade spreadsheet in that forum.
I probably should have specified that this was for DPR. Either way I assumed that was the formula he was referring to. I could be wrong though. You are also correct in that it really isn't that simple. Just because you squeeze the highest DPR out of a character doesn't mean the characters any good, or fun to play. It really only goes to set a certain benchmark on how the damage potential compares to other classes.
Thank you for your replies.
I see that the subject is more complex than I first thought - I was thinking in all honesty that someone had made a unified theory that "proved" that Wizards at 1st level were superior to everyone at 2nd level or whatever.
Nonhelpful reply. I honestly do not think you will have an universal constant, because everyone's games are different. I think someone coined the term "theorycraft" because it is all just conjecture that looks good on paper. The whole caster vs melee thing often (not always) revolves around versatility is better. Sometimes it isn't.
It happened that the cat met Mr. Fox in the woods. She thought, "He is intelligent and well experienced, and is highly regarded in the world," so she spoke to him in a friendly manner, "Good-day, my dear Mr. Fox. How is it going? How are you? How are you getting by in these hard times?"
The fox, filled with arrogance, examined the cat from head to feet, and for a long time did not know whether he should give an answer. At last he said, "Oh, you poor beard-licker, you speckled fool, you hungry mouse hunter, what are you thinking? Have you the nerve to ask how I am doing? What do you know? How many tricks do you understand?"
"I understand only one," answered the cat, modestly.
"What kind of a trick is it?" asked the fox.
"When the dogs are chasing me, I can jump into a tree and save myself."
"Is that all?" said the fox. "I am master of a hundred tricks, and in addition to that I have a sackful of cunning. I feel sorry for you. Come with me, and I will teach you how one escapes from the dogs."
Just then a hunter came by with four dogs. The cat jumped nimbly up a tree, and sat down at its top, where the branches and foliage completely hid her.
"Untie your sack, Mr. Fox, untie your sack," the cat shouted to him, but the dogs had already seized him, and were holding him fast.
"Oh, Mr. Fox," shouted the cat. "You and your hundred tricks are left in the lurch. If you had been able to climb like I can, you would not have lost your life."
Greg
+1 to hit is equal to +.05 to your probability to hit in the DPR formula. Keep in mind that is the DPR from 1 attack, so for multiple attacks you add them together.
The 2.47 number is fairly accurate. It assumes an average base damage of ~50 and your primary attack not being an auto-success. Its actually a little less since the 50 is not including crit chance. This is a completely reasonable number that one would see somewhere arround 6th-8th level on a primarily martial character.
Using a simple 2 handed fighter at level 6 (falchion, 22 str, +2 weapon, power attack, weapon spec, weapon training) hitting over his entire crit range:
h(d+s)+ft(cd+cb+r)
d=5+9+2+6+2+1 = 25
f=.15
c=1
s,b,r=0
an increase of +1 to hit is equivalent to +.05h
.05*25 +.15*.05*25 = 1.4375
DPR increases by 1.4375 per attack, and you have 2. This is a 2.875 increase for this character.
Now to equate that to a static + to damage, you need to assign a target AC for the monster. Your hit probability alters the weight that base damage counts for.
Assuming hit on 11 with primary, a +2 to damage equals:
(First Attack) + (Second Attack)
(.5*25 + .15*.5*25) + (.25*25 + .15*.25+25) = 21.5625
(.5*27 + .15*.5*27) + (.25*27 + .15*.25+27) = 23.2875
A 1.725 increase in DPR
Assuming a 2+ with the primary (rare at this level), a +2 to damage:
(.95*25 + .15*.95*25) + (.7*25 + .15*.7+25) = 47.4375
(.95*27 + .15*.95*27) + (.7*27 + .15*.7+27) = 51.2325
A 3.795 increase in DPR.
Its hard to gauge how much both of these are worth, because they will be worth different ammounts to different characters. Generally, I weight a +1 to hit as slightly more than +2.5 to damage because after running DPR for many characters I have found that a +1 enhancement bonus has increased DPR more than the 3.5 damage increase from a bonus damage die like flaming. Keep in mind that you get wierd things at the extremes.