A new damage calculator...

[Nefarii]

*edit - This has nothing to do with DPR

The Calculator can be located: Here

I was bored at work yesterday and normally when Im bored I will look at new character builds, build new characters, or something else to that nature. Well when I was building my last character I was trying to decide what weapon to use and I couldnt find any solid charts or graphs that explained weapon damage with relation to brutal and high crit. Which got me thinking that I should build my own damage calculator that factored in Versatile, Brutal, High Crit (at different levels), Crit, Enhancement, Proficiency, and Magic Weapon Crit damage. So that's what I did.

This calculator that Im posting takes every weapon property under consideration and spouts out the Raw damage (the average amount of damage you will do on every hit) and the projected damage over 10 hits which factors in the weapon's proficiency and the enhancement bonus to hit (This is not as simple as damage*10).

This calculator calculates everything on the randomness of rolls, right now the default is 250,000 hit rolls (this can be modified by the user, but as it is it only takes a second to calculate; obviously more rolls are better). To repeat this, this calculator assumes that you hit 250,000 times and rolls the damage to find the average damage over those rolls.

I will share a little bit about how everything is calculated first because I know I will get asked and probably flamed by the people that don't get it right away.

Most people are taught that a 1d6 damage on average is 3.5, it is not, the average damage is actually 3.625 because on roll's of 20 you do max damage. This makes a bigger difference in comparing a d6 to a d12.

To solve this yourself:
19 x 3.5 = 66.5
1 x 6 = 6.0
---------------
72.5 / 20 = 3.625

or with a d12:
19 x 6.5 = 123.5
1 x 12.0 = 12.0
------------------
135.5 / 20 = 6.775

I feel that brutal and versatile are pretty self explanatory, one gives you a +1 to damage and the other will reroll a 1 or 2 depending on what brutal you choose (brutal 2 and versatile on a d6 will make the Raw damage roughly 5.57).

High Crit adds 1w, 2w, or 3w on every crit (this weapon damage is also rolled randomly). Enhancement bonus is also added to the damage as well as the Magic weapon crit bonuses (also rolled randomly). Its very interesting to throw high crit into the mix, most people completely dismiss it when factoring it into the damage equation (The fights over Mordenkrad and Executioner's axe rings a bell; everything considered the ExAxe is superior).

Now comes the part I feel I should explain myself because a few of you will fight with me on this until it makes sense.

The average damage over 10 hits (10 hits being a short combat).

This factors in weapon proficiency and the to hit part of the enhancement bonus. You might ask: How can you figure out damage from the to hit without know the monsters AC or the to hit bonus and level of the PC?

Very easily.

The best weapon proficiency in the game is +3. Meaning, that if you cant hit with a +3 weapon, you will not hit with a +2 weapon, and you will not hit with +1 weapon regardless of your level or your BaB. To repeat that, if the same character has the choice between a +3 weapon and a +2 weapon he will hit 10% more often with the +3 weapon then the +2 weapon because it has a net of +1 to hit. He will always have to roll one less on a d20 because of this +1.

So this calculation assumes that a +3 proficiency will hit 100% of the time because if it can't hit, no other weapon in the game will be able to hit either. This makes the chart look like this:

+3 = 100%
+2 = 90%
+1 = 80%
+0 = 70%

Every step lower results in you having to roll one number higher regardless of everything else.

Now to add on Enhancement it is simply (Bonus * .10). So a +2 magic weapon will give you a 20% better chance to hit. So if you combine that with a +2 prof weapon you will have a 110% chance of hitting which makes sense because you need one less number then a +3 prof weapon.

So how the second number works is that it factors in the to hit part of the equation to show how much damage you will do over 10 hits if a +3 proficiency is a 100% hit chance over those 10 hits.

I hope you guys enjoy my calculator. Im posting it because Im a min/maxer through and through and I know a few of you are as well, and I havent seen anything on the net this comprehensive. I did all the calculations with pen and paper beforehand and I havent seen any errors in my math but I suppose that does not mean that they do not exist. I look forward to your feedback and I think you guys will actually see some surprising results especially when it comes to high crits and the projected 10 hit number.

 

[Mengu]

Not to inflate your blimp, but all this has been done by char op years ago... It's called DPR (damage per round) calculations. Basic formula is:

DPR = (miss chance x miss damage) + (hit chance without crit x hit damage) + (crit chance x crit damage)

The assumed defenses of what is affectionately known as a tofu monster are: AC = Level + 14, F/R/W = Level + 12. These defenses are used for the calculation of miss/hit/crit chances.

These are the basis of all you need for DPR calculations. More in depth explanations are posted on the WotC char op boards, and I believe there are a few calculators floating around, though I find it easier just to use Excel, since many factors can modify the results from avenger double rolls, to ranger twin strikes and quarry damage, to crit based attacks such as barbarian rampage or two weapon opening.

 

[Nefarii]

DPR is not the same as what im doing. This calculator is solely for the purposes of comparing two weapons.

It doesnt matter your class, race, or special abilities. It takes into account all weapon properties and shows what weapon will do the most damage over time.

Edit* And i know for a fact that this is not common knowledge. I can pull up 10 threads right now where everyone agrees that the mordenkrad is better then the executioner's axe and at every level I can prove that the axe does more damage (this was actually the main reason I built the calculator).

 

[Mengu]

I build a character with a Mordenkrad, then I build the same character with an Execution axe, compare DPR, whichever is higher, is the better weapon for that character, for the purposes of dealing damage against equal level opponents.

I'll quickly zip through some calculations for a level 2 dwarf fighter with Mordenkrad vs Execution axe using brash strike, assuming Str 20, Con 16, DWT, Expertise, +1 magic weapon:

Mord: +13 vs AC, 2d6[b1]+11
DPR: 0.85*19 + 0.05*26.5 = 17.475

Exec: +13 vs AC, 1d12[b2,hc]+11
DPR: 0.85*18.5 + 0.05*34 = 17.425

Mord > Exec by a very slight margin in this case. You can't generalize that one weapon is better than another, without taking into account all the contributing factors from hit chance to static damage modifiers to crit damage contributions depending on the pluses of the weapon, feats, and a hundred other factors. For instance at high levels, the contribution of the high crit property to critical hit damage will be rather minimal, compared to all the other critical hit dice you are getting, making the mordenkrad's higher average dice damage matter more. But if you build an avenger with a higher crit chance, the numbers may swing in favor of the execution axe.

DPR is far from perfect for making judgement about a character's performance, but it is a pretty fair comparison tool keeping its assumptions in mind. It takes most factors into account. I'd hesitate to use anything more ad hoc.

 

[GreyICE]

You've screwed up the hit math.

If your attack would normally hit on an 11 and you get an extra +1 to hit, the damage increase is .55/.5-1 = 10% (ignoring crits)

Your math assumes 5%. That's just wrong. You'll heavily undervalue the +3 prof bonus.

 

[Nefarii]

This should solely be used as a tool for comparing two weapons. If a character is solely invested into hammer feats, then sure, go Mordenkrad.

I just find it fascinating when you get into comparisons like this: What weapon is better?

+4 Enhancement, +3 Prof, Versatile, 1d8
or
+3 Enhancement, +2 Prof, Highcrit(2W), 1d12

Everyone should say that the second one does more damage (it does). However, it will only take a few swings for the first one to do more damage over time because if the exact same character wields both, the first one hits 10% more often then the second one resulting in more damage over time. This is why I built the calculator.


[MENTION=6684526]GreyICE[/MENTION] - Im not exactly getting your math.

Say a character hits on an 11-20 with a +1 enhance +3 prof weapon. Which means that he would hit on a 12-20 with an ordinary +3 prof weapon. If a guy rolls to attack 20 times he should hit 10 times with the +1 weapon and 9 times with the +0 weapon. If the weapon does a 1d10, lets say 5.5 average to make it easy, then he would do 55 damage compared to 49.5 which equals 10% like you said. But this is over 20 swing chances, Im only doing this for 10 swing chances which would be half of 10% which would be 5%. The first guy would hit 5 times and the second guy would hit 4.5 times.

 

[Mirtek]

[MENTION=6684526]GreyICE[/MENTION] - Im not exactly getting your math.

Say a character hits on an 11-20 with a +1 enhance +3 prof weapon. Which means that he would hit on a 12-20 with an ordinary +3 prof weapon. If a guy rolls to attack 20 times he should hit 10 times with the +1 weapon and 9 times with the +0 weapon. If the weapon does a 1d10, lets say 5.5 average to make it easy, then he would do 55 damage compared to 49.5 which equals 10% like you said. But this is over 20 swing chances, Im only doing this for 10 swing chances which would be half of 10% which would be 5%. The first guy would hit 5 times and the second guy would hit 4.5 times.

Which is still a 10% increase.

 

[Nefarii]

lol touche sir, definitely an oversight

where did you get .55?

and the link was updated above to reflect the new values

 

[Ferghis]

Every time I click on the link it gives me a message that "all downloads are in use." Not really a complaint, but it seems that the thing is pretty popular.

 

[Fanaelialae]

Most people are taught that a 1d6 damage on average is 3.5, it is not, the average damage is actually 3.625 because on roll's of 20 you do max damage. This makes a bigger difference in comparing a d6 to a d12.

To solve this yourself:
19 x 3.5 = 66.5
1 x 6 = 6.0
---------------
72.5 / 20 = 3.625

Perhaps I'm missing something, but it seems to me that the fact that a natural 1 is an automatic miss (0 damage) should cancel out the natural 20 and skew the average to just below 3.5.

So, effectively:
18 x 3.5 = 63.0
1 x 6 = 6.0
1 x 0 = 0.0
---------------
69.0 / 20 = 3.45