Comprehensive DPR Calculator (v2.0!)

[Keravath]

Removed comment .. my mistake.

I was wondering if the number of decimal places for the DPR on the plots could be reduced? When reading the plots the numbers are centered over the AC which makes them harder to line up with all the decimals.

P.S. Really nice spreadsheet :)

[LudicSavant]

I was wondering if the number of decimal places for the DPR on the plots could be reduced? When reading the plots the numbers are centered over the AC which makes them harder to line up with all the decimals.

In Google Spreadsheets there's an option to decrease decimal places next to Font. Just hit CTRL+A, then click the icon that looks like ".0" with an arrow under it and it'll change the decimal places displayed for everything.

P.S. Really nice spreadsheet :)

Thanks!

[JonnyBolton16]

Why does the formula for L_adv have -1/400? I'm getting +1/400:

L_adv requires
- succeeding outright while advantaged, OR
- rolling a 1 with die a AND failing with die b, AND THEN succeeding the reroll, OR
- rolling a 1 with die b AND failing with die a, AND THEN succeeding the reroll, OR
- rolling two 1s AND THEN succeeding a reroll:

L_adv = P_adv + 1/20*(1−P)*P + 1/20*(1−P)*P + 1/400*P = P_adv + [2/20*(1−P) + 1/400]*P

[AureusFulgens]

Why does the formula for L_adv have -1/400? I'm getting +1/400:

L_adv requires
- succeeding outright while advantaged, OR
- rolling a 1 with die a AND failing with die b, AND THEN succeeding the reroll, OR
- rolling a 1 with die b AND failing with die a, AND THEN succeeding the reroll, OR
- rolling two 1s AND THEN succeeding a reroll:

L_adv = P_adv + 1/20*(1−P)*P + 1/20*(1−P)*P + 1/400*P = P_adv + [2/20*(1−P) + 1/400]*P

Thanks for the question! Briefly: The last case in your breakdown is a sub-case of the previous two, in the sense that rolling two 1's is also rolling a 1 with die a and failing with die b, and rolling a 1 with die b and failing with die a, since a natural 1 is always a failure. So the 1/400 chance of rolling two 1's isn't an additional case we need to add, but rather, a case that's already been counted twice by the previous cases that we need to compensate for.

Does that make sense? It's an application of a probability rule called inclusion-exclusion, which is used precisely to compute the probability of "at least one of these things happens," where "these things" are your second and third cases.

[JonnyBolton16]

Thanks for the question! Briefly: The last case in your breakdown is a sub-case of the previous two, in the sense that rolling two 1's is also rolling a 1 with die a and failing with die b, and rolling a 1 with die b and failing with die a, since a natural 1 is always a failure. So the 1/400 chance of rolling two 1's isn't an additional case we need to add, but rather, a case that's already been counted twice by the previous cases that we need to compensate for.

Does that make sense? It's an application of a probability rule called inclusion-exclusion, which is used precisely to compute the probability of "at least one of these things happens," where "these things" are your second and third cases.

Yup, makes sense. I overlooked the fact that I'd already counted it!

[LudicSavant]

Thank you for the calculator, you and your partner have obviously put a lot of work into it. I do have a question though. I can't get it to accurately calculate the average DPR when bonus damage is added to a damage roll. For instance, in the simplest example possible, I've made it impossible to miss the attack, there is no damage roll at all, and 1 bonus damage should be applied. The average DPH is 1. The average CPH is 1. But somehow, the average DPR is 0.95? I have found the same result even with damage die being rolled.

dropbox.com/s/c966i6nwfpwnfaa/Annotation%202020-06-02%20131541.png?dl=0

I believe the issue lies in the damage calculation below.

dropbox.com/s/wh5cllv31f5drzq/Annotation%202020-06-02%20131853.png?dl=0

Here, the damage is calculated as the 95% chance to hit minus the 5% chance to crit, making it only a 90% chance to hit, then you add in the 5% chance to crit. But that only adds up to 95% lol.

dropbox.com/s/inqaxnc355o0i1n/Annotation%202020-06-02%20132037.png?dl=0

Here the same calculation is made, making me believe that you guys did it intentionally, but I can't for the life of me figure out why. Once I change the formulas to what you guys have under Basic DPR in your documentation, it works perfectly. Is this an error or am I missing something?

You still have a 5% chance to miss because if you roll a natural 1, you automatically miss.

[Sassbearilla]

Makes sense. I thought I was isolating just the damage roll. If that's the case though, why not make the chance to hit 90%?

[JonnyBolton16]

Is there some option for two-weapon fighting (i.e. using your bonus action to make a second attack without the proficiency bonus)? I selected "# of Attacks = 2" but I think that applies the bonus to both damage rolls

[LudicSavant]

Is there some option for two-weapon fighting (i.e. using your bonus action to make a second attack without the proficiency bonus)? I selected "# of Attacks = 2" but I think that applies the bonus to both damage rolls

Use the bonus attack section at the bottom.

[ler.gan964]

this is great!

[ThePiGuy]

Is there a planned update for the oath of glory paladin feature? I can't for the life of me figure out how to calculate avg damage for a class that can choose to hit one time it would miss in a round. Additionally, although much lower priority, a slot calculator input option for artificer (which rounds up), would be appreciated. Thanks for the great tool! :)

[LudicSavant]

New Update!

Is there a planned update for the oath of glory paladin feature? I can't for the life of me figure out how to calculate avg damage for a class that can choose to hit one time it would miss in a round. Additionally, although much lower priority, a slot calculator input option for artificer (which rounds up), would be appreciated. Thanks for the great tool! :)

Function for the Artificer added!

Also, added a Spellbook calculator that makes it easy to sum up how much it'll cost to scribe spells / make backup spellbooks.

I have not added a function for the Glory Paladin because I don't have that book yet. Perhaps I'll do that in a future update.

Please let me know if there are any glitches with the new features and I'll be on it right away.

Link to new version here: Ludic & Aureus DPR Calculator Version 2.51

[Snownine]

This is crazy impressive, I have been messing with it a lot lately just for fun. How long did it take to put this thing together? It seems like a monumental task.

[q999]

How do I fix the " Unknown function: 'totalProb'. " problem? I have tried to see the other person who encountered this problem did, but it left me more confused than before. I do not delve that much into google code, so I would love if there was a simple solution that I could understand. The in-dept data I could get from these calculations would prove invaluable <3

[LudicSavant]

This is crazy impressive, I have been messing with it a lot lately just for fun. How long did it take to put this thing together? It seems like a monumental task.

Hard to say how long it took -- Aureus and I were working on it off and on, bit by bit, over quite some time. Definitely took a while, though!

[Voip]

This is amazing. Thank you.

I have a question. When I work DPR out on my own, my results are always a little different from yours. I put in a simple test case to see what the difference could be. Attack Bonus = 5. Target AC = 13. That should be 8/20 misses and 12/20 hits, right? But your "Chance of at least one hit: Normal" shows 0.65 which would be 13/20. (I notice something equivalent in the thumbnail on the original post.) Are you giving ties to the attacker? Or is there something more subtle happening here?

[Darthnazrael]

Are you giving ties to the attacker? Or is there something more subtle happening here?

That's how the game's rules work. Per the PHB, p. 194, "If the total of the roll plus modifiers equals or exceeds the target's Armor Class (AC), the attack hits."

[Frogreaver]

First of all, cool calculator.

Secondly, There is one important DPR increasing ability I make common use of that isn’t an option I can find. The Battlemaster’s precision attack. I realize this is a complicated option to model but it’s a powerful enough that it would make a great addition IMO. It’s also an ability that when used properly lasts most of the adventuring day.

[MaxWilson]

First of all, cool calculator.

Secondly, There is one important DPR increasing ability I make common use of that isn’t an option I can find. The Battlemaster’s precision attack. I realize this is a complicated option to model but it’s a powerful enough that it would make a great addition IMO. It’s also an ability that when used properly lasts most of the adventuring day.

You may find this Anydice tutorial helpful: https://www.reddit.com/r/3d6/comment..._great_weapon/ (hat tip: LudicSavant to posting this link a few days ago)

The example at the end of the article is this link: https://anydice.com/program/1b740 which you can tweak just by changing variable assignments like

AC: 13
PROF: 2

to whatever values you're interested in, and then re-running the outputs like

output
[battlemaster 4 superiority d8 precise {AC-8 .. AC-1} attacks 3 roll d20 plus PROF + 3 + 2 vs AC for 1d6 + 3 crit 1d6 on 20] named "[3] Variant human battlemaster crossbow expert"

[Frogreaver]

You may find this Anydice tutorial helpful: https://www.reddit.com/r/3d6/comment..._great_weapon/ (hat tip: LudicSavant to posting this link a few days ago)

The example at the end of the article is this link: https://anydice.com/program/1b740 which you can tweak just by changing variable assignments like

AC: 13
PROF: 2

to whatever values you're interested in, and then re-running the outputs like

output
[battlemaster 4 superiority d8 precise {AC-8 .. AC-1} attacks 3 roll d20 plus PROF + 3 + 2 vs AC for 1d6 + 3 crit 1d6 on 20] named "[3] Variant human battlemaster crossbow expert"

I read through the program but didn’t spend forever on it. So please correct me if I’m wrong but that program is having you use precision attack on any miss? Whereas the optimal case is to use it only when you miss by 3 or 4 or whatever (varies a bit depending on exact setup)

[MaxWilson]

I read through the program but didn’t spend forever on it. So please correct me if I’m wrong but that program is having you use precision attack on any miss? Whereas the optimal case is to use it only when you miss by 3 or 4 or whatever (varies a bit depending on exact setup)

It depends on what you pass in as PRECISE_RANGE, here in bold:

output
[battlemaster 4 superiority d8 precise {AC-8 .. AC-1} attacks 3 roll d20 plus PROF + 3 + 2 vs AC for 1d6 + 3 crit 1d6 on 20] named "[3] Variant human battlemaster crossbow expert"


If you want to use it only on a miss by 1-4, just change the "-8" to "-4".

[LudicSavant]

So please correct me if I’m wrong but that program is having you use precision attack on any miss?

It doesn't use Precision Attack on any miss. It uses Precision Attack if you miss by a given range, set by a variable.

[q999]

What options are there for actions such as the arcane archers' Curving Shot? If there are none, do you consider making any?

[LudicSavant]

What options are there for actions such as the arcane archers' Curving Shot? If there are none, do you consider making any?

I suppose what you're looking to calculate would be "if I miss at least once in a turn, get a bonus action attack"? There's no dedicated button for it, but you can basically do it piecemeal like so:

First, get the DPR of your Action attacks. That's your DPR against the first target.

Then, separately calculate the DPR of your bonus action attack. Multiply it by the chance that at least one of your attacks misses. That's your average DPR against the second target.

The chance of missing at least one attack is just 1-(chance to hit)^(number of attacks).

Spoiler: Note

Show

If you have some alternate bonus action that you would use whenever Curving Shot doesn't activate, then you would calculate the DPR of that bonus action, and multiply it by the chance that none of your attacks miss. (So, (chance of no misses)% of the time you'd use that bonus action, and the other (chance of at least one miss)% of the time you'd use the Curving Shot instead).

[nathan01]

So if you need an 11 to hit, why is it that attacking once with disadvantage has the probability of .25(.5*.5), but attacking twice with disadvantage only has a .4375 chance of hitting at least once? Shouldn't it be .5? Why is it only 1.75 times as likely to get at least once hit instead of twice as likely?

[MaxWilson]

So if you need an 11 to hit, why is it that attacking once with disadvantage has the probability of .25(.5*.5), but attacking twice with disadvantage only has a .4375 chance of hitting at least once? Shouldn't it be .5? Why is it only 1.75 times as likely to get at least once hit instead of twice as likely?

Because you can hit twice, once, or zero times. If the chance of missing once is 75%, then the chance of missing twice is 0.75 * 0.75, which is 56.25%. The chance of NOT missing twice is 100% - 56.25%, which is .4375 or 43.75%. On average you'll hit 0.5 times, but some of those hits are rolled into the parts of 43.75% where you hit twice in one round (25% * 25%, or 6.25%).

6.25% of the time you'll hit twice.
37.5% of the time you'll hit once.
(These add up to 43.75%.)

56.25% of the time you won't hit at all.

[nathan01]

Because you can hit twice, once, or zero times. If the chance of missing once is 75%, then the chance of missing twice is 0.75 * 0.75, which is 56.25%. The chance of NOT missing twice is 100% - 56.25%, which is .4375 or 43.75%. On average you'll hit 0.5 times, but some of those hits are rolled into the parts of 43.75% where you hit twice in one round (25% * 25%, or 6.25%).

6.25% of the time you'll hit twice.
37.5% of the time you'll hit once.
(These add up to 43.75%.)

56.25% of the time you won't hit at all.

Ah, ok, I see what I was getting hung up on now. Thanks!

[casualaf]

Hello. My math skill are pretty average. Would you be able to advise how to add the following Gloom Stalker lvl 11 skill into the calculator?

"At 11th level, you learn to attack with such unexpected speed that you can turn a miss into another strike. Once on each of your turns when you miss with a weapon attack, you can make another weapon attack as part of the same action."

Interested to see the numbers on this when combined with GWM and / or GWF.

[LudicSavant]

Hello. My math skill are pretty average. Would you be able to advise how to add the following Gloom Stalker lvl 11 skill into the calculator?

"At 11th level, you learn to attack with such unexpected speed that you can turn a miss into another strike. Once on each of your turns when you miss with a weapon attack, you can make another weapon attack as part of the same action."

Interested to see the numbers on this when combined with GWM and / or GWF.

It'd be similar to Curving Shot.

[cutlery]

I read through the program but didn’t spend forever on it. So please correct me if I’m wrong but that program is having you use precision attack on any miss? Whereas the optimal case is to use it only when you miss by 3 or 4 or whatever (varies a bit depending on exact setup)

You'll need a simulation to determine how many rounds (or how many attacks) it takes to deplete your superiority die; this will of course vary based on the rule you set for when you use them.

For example, attacking AC 17 at level 11 with a prof bonus of 4 and a main stat mod of 5; using GWM on every attack with a greatsword and only applying a d10 sup die on misses of 5 or less; You'll have on average (with 10,000 iterations)

14.01 hits (for 22 damage; ignoring fighting style)
22.01 swings
7.34 rounds (one less round if action surge used)
dpr: 42.02 (again, this changes with action surge; 42.02*7.34/6.34=48.65 with action surge used.)

You'll tend to have one crit occur during the 22 swings, and at least one bonus swing, this won't alter the number of swings until you deplete superiority die, only how few rounds it takes to do it. Easy enough to model but not that important for deciding what rule to use for when to use precision attack to match your rate of Sup die depletion to number of combat rounds between rests.