"DPR" is a phrase that I see thrown about in Op/advice discussions around here relatively consistently, or at least with enough consistency that I would like to inquire about it further. Often the totals are extravagantly large, and this has given me some question of whether people aren't properly calculating a Damage Per Round, or that I am really rusty and out of practice when it comes to building damage dealing characters these days.
So yeah, how do you calculate DPR?
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The damage formula is h(d+s)+tchd
h = Chance to hit, expressed in a decimal 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 assumed
t = Chance to roll a critical threat, expressed as a decimal percentage
c = Critical hit bonus - 1. For example, x2 = 1, x3 = 2, x4 = 3
There ya go.
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If you want to go insane with permutations and possibilities, I've put a Damage Calculator spreadsheet in the PFS GM Shared Prep folder:
You can just use the Excel file as a calculator and just plug in values (it covers two-handed, one-handed, TWF, flurry, and up to 3 iterative attacks).
The Word file explains all the cells and formulas, and there's a section that explains the math behind the formulas (dice averaging, to hit calculations, and probability distribution for expected value on damage).
Rynjin covered it pretty well. But that is technically Damage Per Attack.
I do DPR based on full attacks with iteratives/TWF/rapid shot/etc.
I made a table for "to hit on first attack" = 2,3,...,20,20+ in rows and attacks in columns, cells are average damage for each attack, add up the averages of the attacks in the first column and that is my DPR for the target AC. And I used to take the average of all target ACs, but that doesn't give a better overview than just looking at it.
I have BAB, bonuses and penalties elsewhere in the file so they can be changed without major efforts.
I remember wanting to expand it to turn power attack and similar on and off, but I never got around to it, and checking just now: I must have left the spreadsheet without finishing it, because it doesn't seem to work :)
Before the spreadsheet using probability I did pretty much the same in programmed simulations.
Now: I don't really do DPR calculations, but I might try and rebuild the spreadsheet.
The damage formula is h(d+s)+tchd
h = Chance to hit, expressed in a decimal 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 assumed
t = Chance to roll a critical threat, expressed as a decimal percentage
c = Critical hit bonus - 1. For example, x2 = 1, x3 = 2, x4 = 3There ya go.
Chance to hit = Avg D20 roll + all mods correct? So for example a ranger 1 with 16 Str 2h with a shield bash + Power Attack would be 14? How do I express this as a decimal?
Well, you pick an AC (typically this is done at level 10, vs AC 24 which is the average AC of CR 10 bestiary creatures) and then see your percentage chance of hitting that target AC.
So if you need a 10 to hit, you have a 50% chance to hit. If you need a 20, that's 5%, etc.
So yeah, how do you calculate DPR?
I try not to.
But if I do, Rynjin's formula works.
Percentage chance to hit as a decimal = d20 roll needed to hit, converted into percentage chance to hit, converted into decimal (1.00 = 100%).
How do I express this as a decimal
So if you would hit your target AC on a roll of 6-20 with your first attack, 11-20 with your second attack, and 16-20 with your third, that's a 75%, a 50%, and a 25% chance of hitting respectively. In decimal form, that is .75 + .5 + .25. You'd add those together to get an average of 1.5 hits per round (if you were doing DPR for a full attack). That's chance to hit as a decimal.
...
Now that the calculation is explained... for the love of God, don't assume that this is the same thing as your actual average damage per round at the table.
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To further Coriat's last point, all this calculation does is get you the amount of damage you'd likely do over the course of 1000 or 10000 attacks. It is important to max the hit chance.
Your goal is generally to max out your To-Hit percentage for your target AC before you max out damage. Once you get 95% chance to hit, you can start dumping the extra bonuses into damage. Unless you can trade that +1 for a staggering amount of extra damage. Of course, your target AC may not be the average AC of monsters with CRs equal to your level; maybe your GM favors large number of low level mobs or a few higher level mobs.
Why? Because 50% chance to do 100 damage averages to 50 damage while 55% chance to do 91 damage averages to 50.05 damage... So that single +1 to hit is worth about 9 damage AND also affects your crit damage (can't crit if you can't hit) and means special abilities go off more often and you get a better chance to end the fighter sooner and so on.
Well, you pick an AC (typically this is done at level 10, vs AC 24 which is the average AC of CR 10 bestiary creatures) and then see your percentage chance of hitting that target AC.
So if you need a 10 to hit, you have a 50% chance to hit. If you need a 20, that's 5%, etc.
Nitpick: If you need a 10 to hit, you actually have a 55% chance to hit.
I would also suggest that while CR 10 is a good average number to work with, it would probably be more accurate to use that class's level/CR.
So yeah, how do you calculate DPR?
Personally, I usually break out pencil/paper or a spreadsheet. I calculate attack and damage bonuses first, then percentage chance of miss, normal hit, crit, and hit via unconfirmed crit threat. Figuring in the average damage of normal and critical hits, it is usually easy to compute. Including power attack, critical focus, and oddities like twin thunders add complication, but nothing insurmountable.
OMG so avg AC is 14 or 17 + CR??? My ranger is never going to hit anything. He has a Str 16, Power Attack and a trait granting +1 to shield bash damage. Here's his attack at level 1:
Melee 2h PA shield bash +3 (1d6 +8)
As he leveled my idea was to have him take the 2 weapon style. This will impose even MORE penalties on his already weak attack bonus. Since I'm still only level 1 I MAY have to rethink this build...
The median AC of a CR=1 monster is 14 in Pathfinder. The maximum AC of a CR=1 monster is 18.
It looks like you would have a 50% chance of hitting an average CR=1 monster at level 1, while using Power Attack.
The median hit points of a CR=1 is 13. On a normal hit (with power attack), you do between 9 and 14 damage, often dropping the creature. On a crit, your shield squashes the enemy's skull into a bloody pulp.
In general, power attack is pointless unless you have a 2h weapon. The trade-off of hit chance is just not going to be worth it.
I think Power Attack acts the same when someone has a 2h weapon and when they simply wield a weapon in 2 hands (as Mark's ranger plans to do).
Yeah, it does. But you also don't see many people power-attacking with a 16 strength since it does hurt the to-hit number by a noticeable amount.
I did a quick calculation and it seems that using Power Attack has more average damage here. Against an average CR=1 monster, a ranger with 16 strength using a shield bash 2-handed will do more average damage with power attack than without.
Fairly sure you need to distinguish between hit chance and criticals.
So if you are hitting on a 12 with a 19-20 crit range then your chance to hit is 35% and chance to crit is 10%.
Well, your chance to threaten a critical hit there would be 10%. Your chance to crit would then be (10%)*(45%)=4.5%, and your chance to do normal damage would be (35%) + (10%)*(55%) = 40.5%. (assuming no bonuses to critical confirmation rolls)
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Well, your chance to threaten a critical hit there would be 10%. Your chance to crit would then be (10%)*(45%)=4.5%, and your chance to do normal damage would be (35%) + (10%)*(55%) = 40.5%. (assuming no bonuses to critical confirmation rolls)Fairly sure you need to distinguish between hit chance and criticals.
So if you are hitting on a 12 with a 19-20 crit range then your chance to hit is 35% and chance to crit is 10%.
Everyone knows that your chance to score a critical hit is not measured by the probability of rolling a certain number on a die, but rather on the dramatic weight of the encounter.
Modified, of course, by the number of giants you have slain, on whose corpses you build a new Dwarven empire.
Modified, of course, by the number of giants you have slain, on whose corpses you build a new Dwarven empire.
...aaaaand, you're my favorite person ever!
Nitpick: If you need a 10 to hit, you actually have a 55% chance to hit.Well, you pick an AC (typically this is done at level 10, vs AC 24 which is the average AC of CR 10 bestiary creatures) and then see your percentage chance of hitting that target AC.
So if you need a 10 to hit, you have a 50% chance to hit. If you need a 20, that's 5%, etc.
That's not a nitpick: that's really important information, and a very, very common error.
Miss percentage = (20-MissThreshold)/20
Hit percentage = (21-HitThreshold)/20.
Where
MissThreshold = the highest number you can roll on the die and still miss
and
HitThreshold = the lowest number you can roll on the die and still hit
I'm also not a fan of calculating DPR at a fixed point in time, because my characters never spontaneously poof into existence at level 10 with every magic item they could possibly want at their absolute maximum wealth per level, as if they've never spent a copper piece before now.
I try to look at how well the characters are likely to do across their careers.
For example, I've used the damage calculator mentioned earlier in the thread to compare career averages of different types of archer builds. The Zen Archer out-damages an archer fighter until level 6, assuming the fighter doesn't trade out Weapon Training I and the fighter picks up Manyshot. If the GM rules that shooting through other creatures is Soft Cover instead of Partial cover, the Zen Archer can pick up Improved Precise Shot at level 6 and be pretty comparable with the fighter until level 10.
However, if you look at level 10 as an isolated snapshot, the fighter completely blows away the Zen Archer, no questions asked. If you're playing a game that tops out around level 7, though, that information doesn't help you much.
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I've created a new DPR Calculator for everyone to use.
how do you edit that RD?
Glutton, you save a copy for yourself. You don't want to edit the master document in the link.
It evens out to being an insignificant DPR increase since it's an unreliable source of damage. DPR is more a general measure of how much damage you're dealing across all the rounds in a given day, not just each individual round in a combat, and so on.
Basically, if you're not getting an AoO every round, it doesn't matter.
If you are guaranteed to (or always do in your game) get an AoO every round...just input that as an extra attack, ala TWFing without the -2. It'll calculate that just fine.
DPR is more a general measure of how much damage you're dealing across all the rounds in a given day, not just each individual round in a combat, and so on.
Is not.
Why is that, Coriat?
I made a DPR calculator that my boyfriend calls "the depressing spreadsheet," because it tells him things like "take weapon focus, not power attack," and "enchant your sword for pluses, not flaming shocking acid."
Like others, it can't tell you what ACs your DM will throw at you, how you're doing with AOOs, or, for that matter, whether you're able to get full attacks or if you're usually limited to single attacks, all of which are usually more significant to DPR than whether you should take Power Attack or Weapon Focus for your next feat.
I would like a spreadsheet that could graph DPR vs a small range of target ACs, in order to better compare "I can hit ANYTHING!" builds to "I can pounce lowish AC guys to DEATH!" type builds. But I haven't figured out how to do that with google docs.
PS: My spreadsheet agrees with Kkazrandir that power attack helps a 2WF ranger at first level... also 5th level.
Why is that, Coriat?
Because DPR has no stable relationship to X where X = (Total damage inflicted by the character over the course of a suitably large number of combats / (Number of turns taken in said combats), at all. At all. At all.
(or if it does: what is it? x ~= .4 x DPR? X ~= .75 x DPR? x ~= 1.25 x DPR?)
I made a DPR calculator that my boyfriend calls "the depressing spreadsheet," because it tells him things like "take weapon focus, not power attack," and "enchant your sword for pluses, not flaming shocking acid."
These are the sorts of things DPR is actually a reasonably accurate tool for. Limited scope comparisons between things intended to do almost exactly the same thing in slightly different ways, such as +2 sword and +1 flaming sword.
I'm sorry, I guess I'm just really not grasping the % to hit part.
Assuming the following AC's, what number would I use: (I should be able to figure it out from there)
AC: 5
AC: 10
AC: 15
AC: 18
AC: 20
AC: 25
I'm sorry, I guess I'm just really not grasping the % to hit part.
Assuming the following AC's, what number would I use: (I should be able to figure it out from there)
AC: 5
AC: 10
AC: 15
AC: 18
AC: 20
AC: 25
You have to calculate it based on your attack bonus.
Let's say for instance, you have a +22 to hit on your main attack, against an average AC of 24 (which is the assumed AC based on the Bestiary, but you really should base it off the actual average AC of the encounters you face which may be a difficult figure to obtain which is why for purposes of internet forums we assume 24 which has its own set of problems) means you have to roll a 2 or better on the die, or rather, you cannot roll a 1. This is your optimal statistic here, and it means you have a 95% chance to hit something. Why is this? Because on a d20 every face represents a 5% chance probability. You can take the number of faces that will yield a result that will let you hit an AC of 24 and multiply that number by 5 and you will have the percentile figure that you need.
This method however is slightly flawed in execution beyond theorycrafting online characters mainly due to the fact that in most home games (at least the ones I run and the ones I play in) the DM adjusts the average AC of enemies based on the party. If this method held true, you would never need to get your attack bonus for your lowest attack below a 22 because the status quo established only requires that meaning in practice the highest attack roll you will ever need is a 37.
The actual usage and validity of DPR I have found to be more important on the DM side of things when designing encounters to determine how strong to make the bad guys. The real downside to using it is that if you become too comfortable with it, all your encounters end up getting trashed once the players hit the goalpost.
I'm sorry, I guess I'm just really not grasping the % to hit part.
Assuming the following AC's, what number would I use: (I should be able to figure it out from there)
AC: 5
AC: 10
AC: 15
AC: 18
AC: 20
AC: 25
You have to calculate it based on your attack bonus.
Let's say for instance, you have a +22 to hit on your main attack, against an average AC of 24 (which is the assumed AC based on the Bestiary, but you really should base it off the actual average AC of the encounters you face which may be a difficult figure to obtain which is why for purposes of internet forums we assume 24 which has its own set of problems) means you have to roll a 2 or better on the die, or rather, you cannot roll a 1. This is your optimal statistic here, and it means you have a 95% chance to hit something. Why is this? Because on a d20 every face represents a 5% chance probability. You can take the number of faces that will yield a result that will let you hit an AC of 24 and multiply that number by 5 and you will have the percentile figure that you need.
This method however is slightly flawed in execution beyond theorycrafting online characters mainly due to the fact that in most home games (at least the ones I run and the ones I play in) the DM adjusts the average AC of enemies based on the party. If this method held true, you would never need to get your attack bonus for your lowest attack below a 22 because the status quo established only requires that meaning in practice the highest attack roll you will ever need is a 37.
The actual usage and validity of DPR I have found to be more important on the DM side of things when designing encounters to determine how strong to make the bad guys. The real downside to using it is that if you become too comfortable with it, all your encounters end up getting trashed once the players hit the goalpost.
Okay, so let me just make sure I'm doing this right.
If I have a +6 to hit, my chances would be the following for the AC's I listed.
95%
80%
65%
50%
35%
10%
I'm sorry, I guess I'm just really not grasping the % to hit part.
Assuming the following AC's, what number would I use: (I should be able to figure it out from there)
AC: 5
AC: 10
AC: 15
AC: 18
AC: 20
AC: 25
You have to calculate it based on your attack bonus.
Let's say for instance, you have a +22 to hit on your main attack, against an average AC of 24 (which is the assumed AC based on the Bestiary, but you really should base it off the actual average AC of the encounters you face which may be a difficult figure to obtain which is why for purposes of internet forums we assume 24 which has its own set of problems) means you have to roll a 2 or better on the die, or rather, you cannot roll a 1. This is your optimal statistic here, and it means you have a 95% chance to hit something. Why is this? Because on a d20 every face represents a 5% chance probability. You can take the number of faces that will yield a result that will let you hit an AC of 24 and multiply that number by 5 and you will have the percentile figure that you need.
This method however is slightly flawed in execution beyond theorycrafting online characters mainly due to the fact that in most home games (at least the ones I run and the ones I play in) the DM adjusts the average AC of enemies based on the party. If this method held true, you would never need to get your attack bonus for your lowest attack below a 22 because the status quo established only requires that meaning in practice the highest attack roll you will ever need is a 37.
The actual usage and validity of DPR I have found to be more important on the DM side of things when designing encounters to determine how strong to make the bad guys. The real downside to using it is that if you become too comfortable with it, all your encounters end up getting trashed once the players hit the goalpost.
Okay, so let me just make sure I'm doing this right.
If I have a +6 to hit, my...
Looks right to me.
Except that it also doesn't produce an entirely accurate figure as you need to include the chance to crit as well.
Chance to crit is a completely separate figure to be included in the final calculation.
How dare you calculate DPR? Filthy, filthy metagamers!
;P
How dare you calculate DPR? Filthy, filthy metagamers!
;P
Go ahead and calculate DPR. Just don't wildly misuse and misinterpret the resulting statistic.
The forum's track record on the second is... poor.
DPR calculations should be used as a way to compare different builds and not used as an actual, in game, expectation.
With that said I find the best standard for ACs to be Bestiary Table1-1. While people can argue that it may be high/low/whatever at least it is a standard that does not change.
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DPR is a useful, so long as the person calculating it remembers that it's only a single small factor in an overall character. Knowing your average damage on a full attack, and whether ability A improves that more than ability B can be useful. Where the problem tends to come up is if people focus on DPR to exclusion of all else.
Things DPR does not account for:
Situational Factors: Like TheWiz mentioned, things like Attacks of Opportunity can't really be accounted for in a DPR formula. About the best you could manage is average damage per AoO.
Non-Damage Effects: There are plenty of options for trading off average damage to inflict a debuff on the enemy, give yourself a positive benefit, or something else. DPR calculations can't tell you if doing 10% less damage, but leaving your opponent shaken and sickened, is a good trade.
Every other aspect of your character: DPR only calculates raw average damage. It doesn't account for stuff like your characters defenses, other combat options, and special abilities. Not to mention all the of the many non-combat options in the game.
Bottom line, I think DPR is useful, but one should never forget that it's only a calculation of average HP damage on a full attack.
Keep in mind that for purposes of determining the CR of a creature, its DPR is the average of its damage assuming all of its attacks are successful.
Just thought I'd throw that out there.
How dare you calculate DPR? Filthy, filthy metagamers!
;P
My question is how do you pronounce DPR?
Is it D-P-R?
Is is a word Dpr? If so is it deeper or diaper or dapper or dipper or duper or doper? I find it funny about people bragging about how big their DPR pronounced 'diaper' is.
So just how do you pronounce DPR?
