# Thread: Comprehensive DPR Calculator (v2.0!)

1. ## Comprehensive DPR Calculator (v2.0!)

An example of what you can do with this sheet.

Ever wanted to know just how much Elven Accuracy was really helping you? How about the exact AC you should stop using -5 to hit/+10 damage? Or how many rounds it'd take on average for a Hold Person to wear off? Or just how much the party's DPR goes up from the Cleric casting Bless? Well, now you can easily calculate all of this and much, much more!

Some time ago, I posted a DPR calculator which has since apparently become the #1 result for such on Google. It factors in a wide variety of things that many DPR formulas posted around here do not, such as advantage/disadvantage, great weapon fighting, elemental adept, riders, DoTs, rounding effects, critical hit chance / damage, when you should power attack (such as with Heavy Weapon Master or Sharpshooter), and so forth. It also will produce a chart showing DPR against enemies of every AC value. Two sheets are currently included; one for attack rolls, and one for saving throw effects.

In collaboration with mathematician AureusFulgens, I have upgraded the calculator even further with numerous additional functions, such as Elven Accuracy, the Lucky feature of halflings, multiple sources of Bless-like bonuses, bonus actions, checkboxes, dropdown menus, custom scripts, etc. Additionally, we have included thorough documentation for the formulas we use and how to accurately calculate probability for just about everything in D&D (including the nitty gritty bits such as "how do you calculate the odds of success with Triple Advantage, Bless, and Bane active at the same time?")

The documentation can be found here: https://docs.google.com/document/d/1...it?usp=sharing

Just make a copy, enter your basic information like attack bonus and damage dice, and get all the information you want printed out.

Please let me know if you find this useful, if you have any questions, if there is anything even slightly inaccurate, or if there is additional functionality you would like to see provided. Note that this runs a little bit slower than the old calculator, since the new one uses Javascript in order to perform more complex calculations (you'd be surprised at how complex probability math can get for certain rules interactions).

This took a while to put together, so I hope you guys enjoy. And if you do, spread the word!

-Ludic

2. ## Re: Comprehensive DPR Calculator (v2.0)

Good day! I'm AureusFulgens, the other developer on this project. A lot of the more esoteric formulas on this sheet sprang out of the twisted eldritch depths of my mathematician brain, so I'm also on call to answer questions or complaints or corrections about the calculator!

(And if anything is wrong, then we seriously want to know. Every time a math error is published, Carl Friedrich Gauss rolls over in his grave, ad we don't want to do that to him.)

I'm on GitP a little less frequently than Ludic, so my responses might be a little more delayed than his, but I do promise to respond.

Hope this is of help to you!
Cheers,
Aureus

(Seriously, just call me Aureus. "Mr. Fulgens" just feels so formal, y'know?)

3. ## Re: Comprehensive DPR Calculator (v2.0)

Many thanks to the both of you for this update! I especially enjoy the fact that the bonus attack field is overrided (edit: that it takes into account a bonus attack is still made if no crit is scored) upon checking the GWM crit bonus check-box. Speaking of, check-boxes are a fantastic quality of life improvement. Issues I had with the previous iteration all seem to have been dealt with so a 10/10 from me.

4. ## Re: Comprehensive DPR Calculator (v2.0)

Originally Posted by AureusFulgens
Good day! I'm AureusFulgens, the other developer on this project. A lot of the more esoteric formulas on this sheet sprang out of the twisted eldritch depths of my mathematician brain, so I'm also on call to answer questions or complaints or corrections about the calculator!

(And if anything is wrong, then we seriously want to know. Every time a math error is published, Carl Friedrich Gauss rolls over in his grave, ad we don't want to do that to him.)

I'm on GitP a little less frequently than Ludic, so my responses might be a little more delayed than his, but I do promise to respond.

Hope this is of help to you!
Cheers,
Aureus

(Seriously, just call me Aureus. "Mr. Fulgens" just feels so formal, y'know?)
To be clear, if Gauss turns in his grave every time a maths error is published, wouldn't we have a perpetual energy machine? 🤔

5. ## Re: Comprehensive DPR Calculator (v2.0)

I'm simultaneously amazed by the amount of thought and math that went into this, and amazed that nobody implemented such an obviously useful tool at this level before. This is great stuff.

I'm currently playing a archer rogue/ranger in a game with some crazy house-rules, so this is perfect for understanding what to expect from my character in combat.

The real trick for me is going to be converting it to Microsoft Excel - I tried that briefly and the monitor screamed and leaked blood.

6. ## Re: Comprehensive DPR Calculator (v2.0)

Originally Posted by GreyBlack
To be clear, if Gauss turns in his grave every time a maths error is published, wouldn't we have a perpetual energy machine? 🤔
His spinning induce gauss projectile propulsion, making it far too deadly to get near.

7. ## Re: Comprehensive DPR Calculator (v2.0)

Awesome work!

8. ## Re: Comprehensive DPR Calculator (v2.0)

You make all my math look like child's play. Good show.

9. ## Re: Comprehensive DPR Calculator (v2.0)

Oh, wow! I'm sadly not well up enough on my 5e to really understand what's going on here, but I know enough to know that this is really impressive! I've long wished there was something like this for... almost every system I've used, really. Great work!

10. ## Re: Comprehensive DPR Calculator (v2.0)

Thank you very much for this. I was a big fan of the old calculator and used it to calculate good effective damage numbers for classes I was interested in and these quality of life changes that have been made are most welcome.

11. ## Re: Comprehensive DPR Calculator (v2.0)

Nice! I'm a fan of the first one, and I'm sure I'll like this one, too.

12. ## Re: Comprehensive DPR Calculator (v2.0)

I'm loving this! Great work!

Minor detail thingy: I used it to calculate the tipping point in AC to do a power attack yes or no, and while it nicely indicates the intersection between the two attack modi, it can be difficult to really read out what the AC is at that point. Is it possible to calculate this point and display its value either on the graph or in a separate box?

It is only because the calculator works extremely well that these kind of quality of life changes are the only remarks I can make, well done!

13. ## Re: Comprehensive DPR Calculator (v2.0)

Thanks for the feedback thus far, everyone!

Originally Posted by Crucius
I'm loving this! Great work!

Minor detail thingy: I used it to calculate the tipping point in AC to do a power attack yes or no, and while it nicely indicates the intersection between the two attack modi, it can be difficult to really read out what the AC is at that point. Is it possible to calculate this point and display its value either on the graph or in a separate box?

It is only because the calculator works extremely well that these kind of quality of life changes are the only remarks I can make, well done!
Try clicking on the graph in question, then mousing over any given point. It should have a popup display the AC for that point, as well as some other information.

14. ## Re: Comprehensive DPR Calculator (v2.0)

This is wonderful. I am especially fond of the "When to Powerattack" charts. Thank you kindly.

15. ## Re: Comprehensive DPR Calculator (v2.0)

Where do you add extra damage from hunters mark / hex? I can only find an option for first hit bonuses like sneak attack.

16. ## Re: Comprehensive DPR Calculator (v2.0)

Originally Posted by Halabalousa
Where do you add extra damage from hunters mark / hex? I can only find an option for first hit bonuses like sneak attack.
You can add any damage dice that apply on a per-attack basis (such as Hunter's Mark and Hex) in the "Damage" section, right under "Target AC."

17. ## Re: Comprehensive DPR Calculator (v2.0)

So this actually settled a debate at the table I play at.

My DM felt that another player's use of Sharpshooter was unbalanced, and wanted to ban or nerf it. I sent him a link to this spreadsheet, and we played around with some numbers. This led to a very nerdy conversation about why Sharpshooter isn't actually that great for PCs like Rogues that get a lot of damage from single attacks, and discussion about how the flanking & ranged flanking rules he used were resulting in everyone rolling with Advantage and thus doing more damage than intended.

May all future rules debates be this easy to solve with math and spreadsheets.

18. ## Re: Comprehensive DPR Calculator (v2.0!)

This is quite useful, thanks for all the great work.

I like to play a lot of Archer types and this helped tremendously in figuring out which ones had better dps at each tier, and what could be done to optimize for that. I think the biggest surprise was the Rogue Assassin keeps up very well.

19. ## Re: Comprehensive DPR Calculator (v2.0!)

Originally Posted by Makorel
Thank you very much for this. I was a big fan of the old calculator and used it to calculate good effective damage numbers for classes I was interested in and these quality of life changes that have been made are most welcome.
Originally Posted by Telesphoros
This is quite useful, thanks for all the great work.

I like to play a lot of Archer types and this helped tremendously in figuring out which ones had better dps at each tier, and what could be done to optimize for that. I think the biggest surprise was the Rogue Assassin keeps up very well.
Originally Posted by Connington
So this actually settled a debate at the table I play at.

My DM felt that another player's use of Sharpshooter was unbalanced, and wanted to ban or nerf it. I sent him a link to this spreadsheet, and we played around with some numbers. This led to a very nerdy conversation about why Sharpshooter isn't actually that great for PCs like Rogues that get a lot of damage from single attacks, and discussion about how the flanking & ranged flanking rules he used were resulting in everyone rolling with Advantage and thus doing more damage than intended.

May all future rules debates be this easy to solve with math and spreadsheets.
It's always great to hear about people testing their intuitions or builds and learning something new!

Indeed, my motivation for creating this in the first place was noticing how consistently certain abilities were over- or under-valued in forum discussion. My hope is that people will take advantage of this calculator in order to make such discussions more evidence-based. Let us know your results!

20. ## Re: Comprehensive DPR Calculator (v2.0!)

Does this include any sort of data for typical ACs and save bonuses by level? If so, how is "typical" defined?

21. ## Re: Comprehensive DPR Calculator (v2.0!)

Originally Posted by Chronos
Does this include any sort of data for typical ACs and save bonuses by level? If so, how is "typical" defined?
No; the calculator does not make any assumptions about what is "typical," precisely because that would require making an assumption. The user inputs the target's AC or saving throw (or can get a graph of their DPR against every AC).

That said, you might find the table on page 274 of the DMG helpful.

22. ## Re: Comprehensive DPR Calculator (v2.0!)

1.) Great work! I believe that you may very well have achieved the goal you mentioned to me of making your previous work look... <ahem> shoddy.
2.) Many thanks to Aureus. Anyone that was actually able to provide assistance to Ludic gets major cred in my book.
3.) I notice that there are some non-obvious tabs listed. Can either of you explain, in brief, what differences, if any other than formatting, there are b/w the Simple Attack Calculator v/s the Advanced Calculator?

Thanks to you both. You do good work.

23. ## Re: Comprehensive DPR Calculator (v2.0!)

3.) I notice that there are some non-obvious tabs listed. Can either of you explain, in brief, what differences, if any other than formatting, there are b/w the Simple Attack Calculator v/s the Advanced Calculator?
I see you've found the hidden sheets! That's an earlier, incomplete draft of the UI that we didn't end up using. It doesn't do anything in the current version, which is why it was a hidden sheet (along with a few others that were basically just used as scratch pads by Aureus and I). I probably should have just deleted it. In fact, I'll do that right now.

Following that little bit of cleanup, here is a summary of the function of each tab (both the public ones, and the hidden ones):

Visible Tabs:
The "Attack Calculator" is for anything that targets AC. The "Saves Calculator" is for anything that targets a saving throw.

Hidden Tabs:
The "Data Validation" sheet is necessary for the dropdown menus to work and look pretty. Don't edit it.

24. ## Re: Comprehensive DPR Calculator (v2.0!)

Glad people seem to be finding this useful! As always, keep us posted about any questions, concerns, or suggestions you have about the calculator. We want to make sure this thing is as accurate and useful as it can be.

1.) Great work! I believe that you may very well have achieved the goal you mentioned to me of making your previous work look... <ahem> shoddy.
2.) Many thanks to Aureus. Anyone that was actually able to provide assistance to Ludic gets major cred in my book.
3.) I notice that there are some non-obvious tabs listed. Can either of you explain, in brief, what differences, if any other than formatting, there are b/w the Simple Attack Calculator v/s the Advanced Calculator?

Thanks to you both. You do good work.
You're very welcome! And thank you for your kind words :)

25. ## Re: Comprehensive DPR Calculator (v2.0!)

I am aware that in D&D 5E, RAW, the damage multiplier on a crit is 2. That being said, if we wanted to play around with items doing triple (or other) damage on a crit, would it be valid to add an input at, say, E14 on the DPR sheet, then, going down to B208, F208, & J208 and replace the number "2" in all instances to the value of E14? It *seems* to work as intended at first glance. Without being intimately familiar with the inner workings of your mathematical wizardry I don't want to presume too much.

Can either of you confirm that my clumsy toying around with your delicate machine will or will not have the desired effect and not cause any... imbalances in the force?

26. ## Re: Comprehensive DPR Calculator (v2.0!)

I am aware that in D&D 5E, RAW, the damage multiplier on a crit is 2. That being said, if we wanted to play around with items doing triple (or other) damage on a crit, would it be valid to add an input at, say, E14 on the DPR sheet, then, going down to B208, F208, & J208 and replace the number "2" in all instances to the value of E14? It *seems* to work as intended at first glance. Without being intimately familiar with the inner workings of your mathematical wizardry I don't want to presume too much.

Can either of you confirm that my clumsy toying around with your delicate machine will or will not have the desired effect and not cause any... imbalances in the force?
Oooh, now this is interesting.

Yes, on looking over our sheet again, this should work. The six cells you'd want to edit would indeed be the ones in row 208. (Don't forget the ones on the Bonus Action Attack table: Q208, U208, Y208.) Everywhere else that references or depends on crit damage ties back to those cells.

The precise mechanic is that dice are doubled, so if we were a fairly average 1st-level Fighter (16 STR) with the Dueling style wielding a longsword, then you'd expect your damage on crit to change to:
1d8 + 5 --> 2d8 + 5, 3d8 + 5, etc.
depending on your multiplier. Things like the Half-Orc's extra die are added in separately, so that would be unaffected, as I assume you'd desire.

Hope this helps. Glad you're getting into modding our sheet :D

EDIT: Oh, there's one other thing. The sheet handles Sneak Attack damage in a somewhat awkward way, and you'd want to factor that in.
In this little formula from Y9, under Damage per Round:

=B202+Q202+IF(I19,B232*(B223-Q202))+AZ167*Y21+(AZ167-Q22)*Y21*(Y18/Y6)

the highlighted term adds in the damage from a potential crit while Sneak Attacking, by adding in the averages of the damage dice *again* without the static bonus. Just modify it to multiply by E14 (or whatever) minus one, to add in that damage the right number of times. Like so:

=B202+Q202+IF(I19,B232*(B223-Q202))+AZ167*Y21+(E14 - 1)*(AZ167-Q22)*Y21*(Y18/Y6)

Make that edit in Y9, AC9, and AG9.

27. ## Re: Comprehensive DPR Calculator (v2.0!)

Originally Posted by AureusFulgens
Oooh, now this is interesting.

Yes, on looking over our sheet again, this should work. The six cells you'd want to edit would indeed be the ones in row 208. (Don't forget the ones on the Bonus Action Attack table: Q208, U208, Y208.) Everywhere else that references or depends on crit damage ties back to those cells.
So doing this would mean that the Bonus Action Attack would utilize the same multiplier for critical hits that the "Standard Action" Attack uses. If the Bonus Action Attack were to utilize (for purposes of computation) some mechanic that provided a different (lesser or greater, whatever) multiplier for crits then we'd want to insert *another* input field for Bonus Action Attack crit multiplier... say at E42 and then have E42 replace the 2 in all instances for fields Q, U, & Y 208, yes?

Originally Posted by AureusFulgens
The precise mechanic is that dice are doubled, so if we were a fairly average 1st-level Fighter (16 STR) with the Dueling style wielding a longsword, then you'd expect your damage on crit to change to:
1d8 + 5 --> 2d8 + 5, 3d8 + 5, etc.
depending on your multiplier. Things like the Half-Orc's extra die are added in separately, so that would be unaffected, as I assume you'd desire.

Hope this helps. Glad you're getting into modding our sheet :D

EDIT: Oh, there's one other thing. The sheet handles Sneak Attack damage in a somewhat awkward way, and you'd want to factor that in.
In this little formula from Y9, under Damage per Round:

=B202+Q202+IF(I19,B232*(B223-Q202))+AZ167*Y21+(AZ167-Q22)*Y21*(Y18/Y6)

the highlighted term adds in the damage from a potential crit while Sneak Attacking, by adding in the averages of the damage dice *again* without the static bonus. Just modify it to multiply by E14 (or whatever) minus one, to add in that damage the right number of times. Like so:

=B202+Q202+IF(I19,B232*(B223-Q202))+AZ167*Y21+(E14 - 1)*(AZ167-Q22)*Y21*(Y18/Y6)

Make that edit in Y9, AC9, and AG9.
So Y9, AC9, and AG9 factor in potential sneak attack damage with regards to average damage yield/round as well as potential Bonus Action Attack(s), yes? And my ham handed tinkering STILL shouldn't break the machine. Correct?

Also, thank you VERY much for your prompt reply to my last question. :)

EDIT: For those of you playing along on the home version of this game, YES! I am tinkering about with this with the thought of crit multipliers as they existed in legacy versions of D&D (such as 3.5) for various weapons.

Post post scriptum: Aureus or Ludic, the "crits on" value at E13 applies across all attacks, Standard & Bonus alike. Is there a field that can be edited that would change the Crits On value for JUST bonus action attacks? I'd search it out myself for a bit but there's this muscle relaxer kicking in that I took for my back a short while ago and I feel I'm losing the edge on my focus.

28. ## Re: Comprehensive DPR Calculator (v2.0!)

So doing this would mean that the Bonus Action Attack would utilize the same multiplier for critical hits that the "Standard Action" Attack uses. If the Bonus Action Attack were to utilize (for purposes of computation) some mechanic that provided a different (lesser or greater, whatever) multiplier for crits then we'd want to insert *another* input field for Bonus Action Attack crit multiplier... say at E42 and then have E42 replace the 2 in all instances for fields Q, U, & Y 208, yes?
Yes, precisely. That should work.

So Y9, AC9, and AG9 factor in potential sneak attack damage with regards to average damage yield/round as well as potential Bonus Action Attack(s), yes? And my ham handed tinkering STILL shouldn't break the machine. Correct?

Also, thank you VERY much for your prompt reply to my last question. :)

[…]

Post post scriptum: Aureus or Ludic, the "crits on" value at E13 applies across all attacks, Standard & Bonus alike. Is there a field that can be edited that would change the Crits On value for JUST bonus action attacks?
My pleasure! :D

The three row-9 cells are pretty much the tying-it-all-together cells. I'll bring back that formula from my last post, from Y9 (the other two are analogous):

B202+Q202+IF(I19,B232*(B223-Q202))+AZ167*Y21+(AZ167-Q22)*Y21*(Y18/Y6)

B202 and Q202 reference the tables down at the bottom - the total average damage from the action and bonus-action attacks, respectively.

The IF(...) statement handles the Great Weapon Master crit bonus.

And the last two terms handle, respectively, Sneak Attack damage from normal hits and crits.

The issue with having separate crit multipliers and crit thresholds for Action and Bonus Action attacks is probably going to be that the last term might not work quite right. You'd have to split it into two terms to factor in the separate cases where the Sneak Attack is triggered by the Action attacks vs. the Bonus Action attacks. As I'm writing this, I'm wondering if perhaps we should be doing that already - the probability of crit-given-hit on the Action vs. Bonus Action attacks might already be different if the probability of a hit is different.

Issue detected:There's a minor issue with Sneak Attack crit damage that would come up in the case that Action and Bonus Action attacks have different probabilities of hitting and once-per-round damage is nonzero and nonconstant. I'll address that ASAP (grad school has demands on my time today, so this will likely be tomorrow or Saturday) and announce again once it's been repaired. Thanks to Outcast_Shadow for giving me the context to notice this; this is why I keep asking for people to test it and giving feedback!

I'd search it out myself for a bit but there's this muscle relaxer kicking in that I took for my back a short while ago and I feel I'm losing the edge on my focus.
Hope you recover quickly!

You're certainly pushing our limits, and I love that. Keep fiddling with this thing and let us know any questions you have or things you notice.

29. ## Re: Comprehensive DPR Calculator (v2.0!)

Originally Posted by AureusFulgens
Issue detected:There's a minor issue with Sneak Attack crit damage that would come up in the case that Action and Bonus Action attacks have different probabilities of hitting and once-per-round damage is nonzero and nonconstant. I'll address that ASAP (grad school has demands on my time today, so this will likely be tomorrow or Saturday) and announce again once it's been repaired. Thanks to Outcast_Shadow for giving me the context to notice this; this is why I keep asking for people to test it and giving feedback!
The issue described here should be resolved. To explain briefly: Damage from Sneak Attack and similar effects is now split into three terms (instead of two as previously), since this lends itself to the correct formula for the probability that the effect is triggered by a critical hit. The documentation has also been edited to explain the new, correct formula.

(The following deals with editing the sheet to reflect rules outside of standard 5E, as do a couple previous posts)

As a nice side benefit to correcting our formula, the alternate rules Outcast_Shadow is working with are now relatively natural to include. In order to implement potentially different critical hit thresholds and dice multipliers for the regular attacks and bonus action attacks, do the following:
• In the tables at the very bottom, the formulas for "probability of a critical hit" are the same in the Attack and Bonus Action Attack tables (this is in row 211), as both depend on the cell E13 that gives the crit threshold. If you want to make this value different for bonus action attacks, just replace the text "E13" in cells Q211, U211, Y211 with whatever cell the new crit threshold comes from.
• Edit the cells that read Damage Per Crit (row 208) to replace the 2* multipliers with the appropriate new multipliers.
• Edit the cells Y9, AC9, AG9 up at the top to add crit multipliers to the last two terms. I explained how to do that in a previous post; just be sure to do it for both of the last two terms of the sum.

In general, if you're interested in modding the sheet, give the documentation a good read-over. I've tried to make it as accessible to those unfamiliar with probability theory as possible.

30. ## Re: Comprehensive DPR Calculator (v2.0!)

Originally Posted by AureusFulgens
The issue described here should be resolved. To explain briefly: Damage from Sneak Attack and similar effects is now split into three terms (instead of two as previously), since this lends itself to the correct formula for the probability that the effect is triggered by a critical hit. The documentation has also been edited to explain the new, correct formula.

Is this something I'm going to need to go in and correct manually on my particular version of the calculator or am I "good" now?

Originally Posted by AureusFulgens

(The following deals with editing the sheet to reflect rules outside of standard 5E, as do a couple previous posts)

As a nice side benefit to correcting our formula, the alternate rules Outcast_Shadow is working with are now relatively natural to include. In order to implement potentially different critical hit thresholds and dice multipliers for the regular attacks and bonus action attacks, do the following:
• In the tables at the very bottom, the formulas for "probability of a critical hit" are the same in the Attack and Bonus Action Attack tables (this is in row 211), as both depend on the cell E13 that gives the crit threshold. If you want to make this value different for bonus action attacks, just replace the text "E13" in cells Q211, U211, Y211 with whatever cell the new crit threshold comes from.
• Edit the cells that read Damage Per Crit (row 208) to replace the 2* multipliers with the appropriate new multipliers.
• Edit the cells Y9, AC9, AG9 up at the top to add crit multipliers to the last two terms. I explained how to do that in a previous post; just be sure to do it for both of the last two terms of the sum.

In general, if you're interested in modding the sheet, give the documentation a good read-over. I've tried to make it as accessible to those unfamiliar with probability theory as possible.
As long as you're sharp while you're doing this it's REALLY quite easy and not an issue (Super easy, barely and inconvenience).

Keep up the good work fellows!

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