The math of GWM/SS

[Keravath]

I recently posted a thread on the math of Advantage and Disadvantage which includes formulas and tables on Advantage, Disadvantage and Elven Accuracy on your chances to hit/save/skill check. For most cases Advantage is the equivalent of +4 to +5.

http://www.enworld.org/forum/showthread.php?654979-The-math-of-Advantage-and-Disadvantage

However, another question that comes up is when is it better to use the -5/+10 feature of the feats Great Weapon Master and Sharpshooter. The challenge with this is that it requires looking at both the chances to hit and the average damage your weapon can do.

(Keep in mind these are not "white room analyses" ... the game uses the same math ... unless you feel like you or your dice are either blessed or cursed (which I admit many seem to ) ... the chances to hit and average damage are mathematically defined. They aren't theory crafted or made up. If you need to roll a 10 or more to hit on your d20 then you will make that roll 11/20 times and fail 9/20 on average and that has NOTHING to do with whether we are working it out on a forum or playing the game ).

So, how DO we figure out whether it is better to use GWM/SS or not?

We find the to hit die roll where the average damage when you roll using GWM/SS (and its -5 to hit and +10 damage) will be greater than the average damage from rolling a straight hit.

Average damage = (damage done) * (chance to hit)

Damage done = (weapon damage + stat)

The higher the damage done, the more you lose if you miss using GWM. As a result, as the base damage goes up, the number where you want to use GWM goes down.

The following is a picture illustrating this for a d10 weapon damage +5 stat ... say a glaive or heavy crossbow with 20 str or 20 dex. The axis on the bottom is the number you need to roll TO HIT. This is AC - to hit modifier. So if the AC of your target is 18 and you have a +8 to hit (or if the AC is 15 and you have a +5) ... you need to roll 10 or more ... so you look at the plot (if you have d10+5 weapon) and see the following:

If you are attacking normally ... use GWM/SS if you will hit on a 10 or less without it
If you are attacking with advantage ... use GWM/SS if you will hit on a 12 or less without it
If you are attacking with elven accuracy ... use GWM/SS if you will hit on a 12 or less without it.




You can create a picture like this for every combination of weapon damage and stat. However, we can also just tabulate the results.

Use GWM/SS when the base required to hit roll without GWM/SS is less than or equal to the following.

[TABLE="width: 500"]
[TR]
[TD]Weapon Damage[/TD]
[TD]Normal[/TD]
[TD]Advantage[/TD]
[TD]Tri-vantage[/TD]
[/TR]
[TR]
[TD]d12+5[/TD]
[TD]10[/TD]
[TD]11[/TD]
[TD]12[/TD]
[/TR]
[TR]
[TD]d12+4[/TD]
[TD]10[/TD]
[TD]12[/TD]
[TD]12[/TD]
[/TR]
[TR]
[TD]d12+3[/TD]
[TD]11[/TD]
[TD]12[/TD]
[TD]13[/TD]
[/TR]
[TR]
[TD]d10+5[/TD]
[TD]10[/TD]
[TD]12[/TD]
[TD]12[/TD]
[/TR]
[TR]
[TD]d10+4[/TD]
[TD]11[/TD]
[TD]12[/TD]
[TD]13[/TD]
[/TR]
[TR]
[TD]d10+3[/TD]
[TD]11[/TD]
[TD]12[/TD]
[TD]13[/TD]
[/TR]
[TR]
[TD]d8+5[/TD]
[TD]11[/TD]
[TD]12[/TD]
[TD]13[/TD]
[/TR]
[TR]
[TD]d8+4[/TD]
[TD]11[/TD]
[TD]12[/TD]
[TD]13[/TD]
[/TR]
[TR]
[TD]d8+3[/TD]
[TD]12[/TD]
[TD]13[/TD]
[TD]13[/TD]
[/TR]
[TR]
[TD]d6+5[/TD]
[TD]11[/TD]
[TD]12[/TD]
[TD]13[/TD]
[/TR]
[TR]
[TD]d6+4[/TD]
[TD]12[/TD]
[TD]13[/TD]
[TD]13[/TD]
[/TR]
[TR]
[TD]d6+3[/TD]
[TD]12[/TD]
[TD]13[/TD]
[TD]13[/TD]
[/TR]
[TR]
[TD]2d6+5[/TD]
[TD]10[/TD]
[TD]11[/TD]
[TD]12[/TD]
[/TR]
[TR]
[TD]2d6+4[/TD]
[TD]10[/TD]
[TD]11[/TD]
[TD]12[/TD]
[/TR]
[TR]
[TD]2d6+3[/TD]
[TD]11[/TD]
[TD]12[/TD]
[TD]12[/TD]
[/TR]
[/TABLE]


IF you need to roll the number in the table OR less in order to hit your target on a d20 with the weapon damage listed THEN the average damage will be higher when using GWM. Keep in mind that you WILL miss more often (obviously) but over time you do more damage.

If the target only needs one more hit to go down .. you might not want to use GWM/SS .. that is a judgement call.

Also, if you need to roll a 20 to hit ... you might as well use GWM/SS since a 20 always hits anyway. In addition, if you have any sort of advantage and need a 19+ to hit ... it is better to use GWM and go for the crit.

General observations:
- if you need to roll a 10 or less to hit - it is always better to use GWM/SS
- if you need to roll a 14 or more to hit - it is never better to use GWM/SS

When you are close to the target number in the table, the average damage from normal vs GWM are typically close ... so it isn't too far off to use this rule of thumb:

normal: if you need to roll 11 or less to hit (without the -5) use GWM/SS
advantage: if you need to roll 12 or less to hit (without the -5) use GWM/SS
tri-vantage: if you need roll 13 or less to hit (without the -5) use GWM/SS

When the average weapon damage is large ... bump these down by 1.

If you are doing any additional damage like hex/hunters mark etc ... also bump them down. The more damage the weapon does on a hit the less attractive it is to use GWM/SS (this is why the -5/+10 feature of SS is usually a very bad idea for rogues).

Please let me know if I made any obvious mistakes

 

[Asgorath]

Interesting, I had been using this thread as my guide:

http://www.giantitp.com/forums/showthread.php?472938-Great-Weapon-Mastery-How-to-5-10-Like-a-Pro

The image showing the formula is here, since it normally doesn't load for me:

https://i.imgur.com/zEQKq6w.png

which just says "Maximum AC = attack bonus - (average damage / 2) + 16".

 

[UngeheuerLich]

A good analysis. And it is still some white room involved:
You don't take enemy hp into account or the chance to cleave through on a hit. Nor do you account for spells like armor of agathys where you rather want a big hit instead of many small ones.

 

[Keravath]

Interesting, I had been using this thread as my guide:

http://www.giantitp.com/forums/showthread.php?472938-Great-Weapon-Mastery-How-to-5-10-Like-a-Pro

The image showing the formula is here, since it normally doesn't load for me:

https://i.imgur.com/zEQKq6w.png

which just says "Maximum AC = attack bonus - (average damage / 2) + 16".

Cool. Thanks.

The formula gives the same results as my normal column in the table. However, the formulae for advantage and tri-vantage are too unwieldy to use. So, if you want some insight into when to use GWM/SS in conjunction with advantage/elven accuracy, the table is a useful source of information.

 

[CapnZapp]

Without looking at your numbers specifically, I find that this type of analyses are usually misleading, grossly underestimating what a minmaxer can do with the -5/+10 mechanism, thus severely underestimating the power of these feats.

In short: these feats are completely broken but white-room analysis generally doesn't see it.

Again, I haven't looked at this particular set of numbers. But I can ask you all - do they crunch the numbers for the following scenario? (If so I will be impressed, no other similar analysis have even come close, and I will happily admit that my previous statements then do not apply in this specific case But I am not holding my breath, the math gets complicated, much more so than most white-room analysts are prepared to deal with.)

Case in point (and please excuse any mistakes with details; I'm doing this from memory here): Battlemaster Fighter using a -5/+10 feat in conjunction with advantage, possibly a bonus such as Bless, and the Precision maneuver.

Obviously no serious analysis would make the error of computing average damage without taking into account that using GWM/SS is voluntary. Lots of flawed efforts add in the negative impact of using -5 when enemy AC is too high - I am assuming this is not the case here.

You should then use Precision to turn near-misses into hits. Rolls of perhaps 1 thru 5 will be left alone (accepted as misses), with advantage this happens much less often than 25%.

You will find two things: a) the miss rate is really low, despite -5 b) you don't use nearly as many superiority dice as for other maneuvers (you don't need to spend a superiority die on a hit or a clear miss, only near misses)

This makes you come close to the full potential of +10 damage per attack, and good sustainability of the tactic (you can expect to use it for a large portion of the day's important battles).

If this poster's analysis shows that GWM/SS grants between +30 and +50 damage at medium- to high levels for a properly minmaxed character, congratulations - that matches my actual play experience.

It also proves beyond a shadow of a doubt that these feats are completely broken in expert hands. Nothing else in the game comes close to granting you a potential +10 damage, and the -5 can be played around, as shown. WotC's designers must be less than expert, or they would have caught and stopped this.


Have a nice day.
Zapp

PS. If you have any questions, there are very many and very long threads about the subject. Every piece of data you might require is there. DS

 

[ccs]

Oh goody, let's beat this dead horse again....

 

[Oofta]

Oh goody, let's beat this dead horse again....

Since we probably only miss the horse on a 1 if we're next to it, at least we'll get +10 to damage.

 

[Asgorath]

Cool. Thanks.

The formula gives the same results as my normal column in the table. However, the formulae for advantage and tri-vantage are too unwieldy to use. So, if you want some insight into when to use GWM/SS in conjunction with advantage/elven accuracy, the table is a useful source of information.

Agreed, their recommendation had basically boiled down to "if you have advantage, always use GWM/SS" so it's nicer to see a bit more detail in your analysis. I do like the way you broke it down to the number you had to roll on the dice, rather than specific AC values. The graphs make it really easy to visualize how they impact the probabilities.

 

[Zardnaar]

Without looking at your numbers specifically, I find that this type of analyses are usually misleading, grossly underestimating what a minmaxer can do with the -5/+10 mechanism, thus severely underestimating the power of these feats.

In short: these feats are completely broken but white-room analysis generally doesn't see it.

Again, I haven't looked at this particular set of numbers. But I can ask you all - do they crunch the numbers for the following scenario? (If so I will be impressed, no other similar analysis have even come close, and I will happily admit that my previous statements then do not apply in this specific case But I am not holding my breath, the math gets complicated, much more so than most white-room analysts are prepared to deal with.)

Case in point (and please excuse any mistakes with details; I'm doing this from memory here): Battlemaster Fighter using a -5/+10 feat in conjunction with advantage, possibly a bonus such as Bless, and the Precision maneuver.

Obviously no serious analysis would make the error of computing average damage without taking into account that using GWM/SS is voluntary. Lots of flawed efforts add in the negative impact of using -5 when enemy AC is too high - I am assuming this is not the case here.

You should then use Precision to turn near-misses into hits. Rolls of perhaps 1 thru 5 will be left alone (accepted as misses), with advantage this happens much less often than 25%.

You will find two things: a) the miss rate is really low, despite -5 b) you don't use nearly as many superiority dice as for other maneuvers (you don't need to spend a superiority die on a hit or a clear miss, only near misses)

This makes you come close to the full potential of +10 damage per attack, and good sustainability of the tactic (you can expect to use it for a large portion of the day's important battles).

If this poster's analysis shows that GWM/SS grants between +30 and +50 damage at medium- to high levels for a properly minmaxed character, congratulations - that matches my actual play experience.

It also proves beyond a shadow of a doubt that these feats are completely broken in expert hands. Nothing else in the game comes close to granting you a potential +10 damage, and the -5 can be played around, as shown. WotC's designers must be less than expert, or they would have caught and stopped this.


Have a nice day.
Zapp

PS. If you have any questions, there are very many and very long threads about the subject. Every piece of data you might require is there. DS

This we have used the -5/+10 feats up to AC 20-22. If you can hit 50% of the time with the -5 using crossbow expert you use it all of the it me even if you miss 50% of the time you will still deal more damage.

 

[Shiroiken]

In short: these feats are completely broken but white-room analysis generally doesn't see it.

Two quick things.

The OP's analysis is somewhat white-room, but as he focuses on the actual die roll required, it can take additional bonuses into consideration. The primary aspect that was ignored (as almost always is during these discussions) is the actual amount of damage required. If using GWM allows you to kill something in 2 hits instead of 3, then the benefit is useful, but if the actual amount of hits required doesn't change, then it's not (this makes it hard to figure out, as most DMs do not tell the players how many HP each enemy has). The post, however, was not an analysis of the power of the feats, but merely the mathematical determination on when you gain the greatest statistical benefit for using it, similar to the equations for Power Attack back in 3E.

Secondly, I see GWM and SS in use all the time, both as a player and a DM. Even with players utilizing Powergamer strategy to maximize the benefit, I still just don't see it as OP. I believe that it is powerful (top of the curve tbh), but I consider the resources used to maximize it and accept that as part of the cost. If your issue with is Powergamers, well they've existed in every edition, but IME in 5E the difference between the average character and a powergamed character really isn't as large as it's been in every other edition I've played (everything but OD&D).