New weapon damage calculator

[Nefarii]

This is not a DPR calculator. This evaluates and compares two weapons in both their raw damage and their damage over time. These are absolute numbers and will easily show which weapons are better. Look at the calculator before you flame.

The Calculator can be located Here
(http://d01.megashares.com/dl/3UnYtUH/DamageCalculator.zip)

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.

[WickerNipple]

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.


This is not a good way to do this. All DPR calculations include crit rate for factoring in final DPR, but they do it at the end for a reason - people have variable crit rates. Unless a 20 is always and the only way for max damage to occur, it can't be a part of one of your fundamental variables.

[Gillric]

Not to mention that you left out the fact that a 1 is an auto miss for 0 damage.

[Snowbody]

And also you can't ever have over 100% hit rate, nor ever less than 5%. These will throw your numbers off.

[Nefarii]

The 0 as an automiss is a non factor because the 250,000 rolls all represent hit rolls - not attack rolls. So it doesnt matter if you hit 2-20 or just 19-20, you still hit 250,000 times.

Also, you can have over a 100% hit rate through enhancement bonuses. If you have a +2 longsword you will hit 10% more often then if you just had a longsword. So if your character can hit with a longsword 100% of the time then +2 would hit 110% of the time. Dont get stuck on this, if my level whatever basket weaver is holding a longsword and I swing at a rat, and I hit 11-20, then that is my 100% range. I will hit the rat 100% of the time 11-20. So if all of a sudden I pick up a +2 longsword, I will start hitting the rat 9-20, I will hit 10% more often then my already determined 100% range. Remember, all 250,000 rolls are all hit rolls, they are not attack rolls.

This calculator is a weapon's calculator. It doesnt matter what level, race, or build you are. It assumes that the same character is holding up both weapons to compare them.

The reason I built it is to figure out problems 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.

[Nefarii]

Someone found a small error in the program, so I just updated the version in the link above.

[Mando Knight]

Also, you can have over a 100% hit rate through enhancement bonuses. If you have a +2 longsword you will hit 10% more often then if you just had a longsword. So if your character can hit with a longsword 100% of the time then +2 would hit 110% of the time. Dont get stuck on this, if my level whatever basket weaver is holding a longsword and I swing at a rat, and I hit 11-20, then that is my 100% range. I will hit the rat 100% of the time 11-20. So if all of a sudden I pick up a +2 longsword, I will start hitting the rat 9-20, I will hit 10% more often then my already determined 100% range.
First: That makes no intuitive sense. The absolute hit percentage is more useful in 4e since it's more readily available, and won't introduce any mathematical errors compared to this... (a relative scale?)

Second, you are mathematically wrong (http://www.youtube.com/watch?v=tRVUOGUmxJI). A 50% hit rate (that is the actual hit rate of your example) upgrading to a 60% hit rate is seeing a relative increase of 20%... you are getting a total of 120% relative accuracy.

Third... a numerical solver, for a problem in which an analytic solution already exists? Really?

[Ashdate]

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

This doesn't really work because it doesn't make sense why you would roll "19" times for average damage, but only once for full damage, if a need to "hit" requires a 20.

For example, assume you need an 11 or higher to hit an opponent, and 20 is a crit for max damage. Assume an even distribution of rolls, to hit 20 times you need to roll 40 times, such that half the time you would miss (you roll 1-10), you hit 18 times (11-19) and crit (20) twice.

Thus your average damage (on a hit) would be (18 x 3.5 + 2 x 6) / 20 = 3.75 (the same as (9 x 3.5 + 1 x 6) / 10).

This is also why assuming a +2 proficiency weapon hits "95% of the time" is perilous too; assuming (again) that you hit 50% of the time with a +3 proficiency weapon, then you'll hit 45% of the time with a +2. Thus to "hit" 10 times with a +3 proficiency weapon will require (assuming an even distribution) 20 rolls, then a +2 weapon (45% hit rate) will require ~ 22.2 rolls (assuming a relatively equal distribution). Thus you should really be reducing your "average damage" for a +2 weapon by over 10%! These numbers obviously change depending on what the "to hit" bonus and target AC is of course, but i hope it illuminates some issues with your model.

I think I understand why you wanted to model just "hits" (as defense numbers and magic items are so variable) but I think it's important to recognize that the scaling defenses (+1 for every monster level) means that magical items aren't really a +5% bonus to hit.

Much like how attack bonus scales (level / 2), magic items (and expertise) are simply helping the player stay on par. The difference in defenses between a level 1 monster (+1) and a level 30 monster (+30), is typically made up from a combination of raw level (+15), prime stat (~ +7 to 8), expertise (+3), and magic items (+6).

Certainly, a +3 weapon will hit more often than a +2 weapon, but in terms of 4e math you're probably not hitting 5% more often with a higher level weapon as the number your trying to hit has risen with your magic item bonus. Likely, when you get the +2 weapon up until you get the +3 one, you will be experiencing a period where you're to hit percentage exceeds average, is on par with, and then dips below average before you claim your shiny new +3 weapon (mitigated by your own rise in level and stats).

Not to discourage you, but given that defense estimates are relatively easy to figure out (the DMG has them), a calculator that compares the bonus to hit (taking into account level, stats, class features etc.), to monster level and uses that for relative damage makes more sense.

[Nefarii]

That was the small error that someone else already found in the program.

If the proficiency at +3 is 100%
then +2 = 90%
+1 = 80%
+0 = 70%

and each enhancement bonus gives a 10% better chance to hit

This can be seen in the fact that if a +3 hits 11-20 and a +2 hits 12-20 and we are using a d10 for an average of 5.5 damage and the +3 hits 10 times over 20 rolls then the +2 would hit 9 times. The plus +3 would do 55 damage and the +2 would do 49.5 damage. Or 10% less

The link was updated for this error yesterday.

[Ashdate]

and each enhancement bonus gives a 10% better chance to hit

As I mentioned, this assumes a static defense that you're aiming to hit. A +1 weapon against a monster with an AC of 11 has the same chance at hitting against a +2 weapon against a monster with an AC of 12. Similarly, a +6 weapon isn't going to give you a "higher" hit percentage against a monster with an AC of 16; you're simply treading water. If your calculations are assuming that monster AC is static (i.e. a roll of 11 will always hit) then you're going to end up over-representing the amount of damage you deal. I would encourage you to remove item bonuses from everything but damage; I can see the value of keeping proficiency (as that it is weapon based and static) but given the scaling nature of AC, if you're modeling "hits" then to me, it makes sense to simply assume the weapon bonus (along with expertise and level scaling) has no effect on the chance to hit.

[Snowbody]

Unless you know the appropriate defenses of the monster you're fighting (and any other factors like CA, cover, concealment, etc.) there is no way to know in advance which weapon is better.

Suppose you're fighting a way overleveled monster, so that you need to roll a 20 to hit with one weapon, but a 19 or 20 to hit with the other. Your hit rate is DOUBLED by using the more accurate weapon -- not increased by 5% or 10%.

[Mando Knight]

Unless you know the appropriate defenses of the monster you're fighting (and any other factors like CA, cover, concealment, etc.) there is no way to know in advance which weapon is better.

Suppose you're fighting a way overleveled monster, so that you need to roll a 20 to hit with one weapon, but a 19 or 20 to hit with the other. Your hit rate is DOUBLED by using the more accurate weapon -- not increased by 5% or 10%.

Alternately, if you're frequently hitting a 65% or so absolute accuracy, the relative accuracy increase of switching to a battleaxe from a greatsword is much lower than if you were only at 50%. (1/13 rather than 10%)

[Gralamin]

Unless you know the appropriate defenses of the monster you're fighting (and any other factors like CA, cover, concealment, etc.) there is no way to know in advance which weapon is better.

Suppose you're fighting a way overleveled monster, so that you need to roll a 20 to hit with one weapon, but a 19 or 20 to hit with the other. Your hit rate is DOUBLED by using the more accurate weapon -- not increased by 5% or 10%.

You don't need to know more then the baseline, and then the progression for +2 to hit mods (Which is usually, except in extreme cases, linear, since it decreases the miss percent and increases the hit percent). Then some quick math of baseline + bonuses = Approximate DPR is enough in play to switch between weapons rapidly. Factoring In +Damage bonuses is harder, but not unreasonably so.