Penny arcade pvp - battlerager

[Bow_Seat]

I'm interested in looking at average damage comparisons for when it does max damage for taking disadvantage. What is the probability of hitting with disadvantage compared to the probability of critting without disadvantage?

 

[The Shadow]

I'm interested in looking at average damage comparisons for when it does max damage for taking disadvantage. What is the probability of hitting with disadvantage compared to the probability of critting without disadvantage?

I looked at this some yesterday. Let's say you do die-type + bonus in damage, abbreviated d and b respectively.

Then the average damage you do is d/2 + b + 1/2. (Technically, it'd be 19/20 times that plus 1/20 times (d + b), but the difference is negligible for the amount of effort it adds. Do note that including crits would inevitably make Battlerager just a tiny bit worse, though.)

If the chance of hitting an opponent is p, then the chance of hitting with disadvantage is p^2.

So with Battlerager, your average damage is (d + b)*p^2.

Whereas without the feat, you deal maximum damage with a probability of 1/20 + 19/(20*d). Or just 1/20 if you're only interested in crits.

So for Battlerager to make a difference for you, you'd need:

(d + b)*p > d/2 + b + 1/2

Unfortunately, there are three solutions, depending on whether p is >, <, or = to 0.5:

p=0.5: b < -1. In other words, if you have even odds to hit, Battlerager gives you a net benefit only if your bonus is negative. Since this is extremely unlikely for a melee combatant who takes this feat, Battlerager is a net loss under realistic circumstances.

p<0.5: d < [1 + 2(1-p)b]/[(2p-1)]. Assuming b is positive, d has to be a negative number, which is impossible. So for this case also, Battlerager is a net loss.

p>0.5: d > [1 + 2(1-p)b]/[(2p-1)]. Here at last we have a case where Battlerager has a net benefit. Let's take the worst-case scenario of p=0.55 and assume a bonus b of +3.

Then d has to be greater than 37, which is impossible in D&D.

Now take the best-case scenario, with p=0.95.

Then d has to be greater than 0.072, which is true of all D&D weapons.

Where's the breakeven point? If d is 12 (a greataxe, say), then p has to be 0.633, or in other words, you need to hit on a 7. This doesn't change significantly if your damage bonus is 4.

If d is 8, you have to hit on a 6.

In short, maximum-damage Battlerager is a losing proposition on average, except for easy-to-hit opponents. One could argue that this is realistic - that berserking is a losing proposition on the whole against armored opponents - but it doesn't make the feat look all that attractive.

However, Battlerager gets a lot more attractive if your bonus goes negative - in other words, if you've been debuffed. That's something to take into consideration. And of course, if you're at a disadvantage for any reason, the feat suddenly gets completely awesome.

 

[The Shadow]

Double post somehow, sorry.

 

[GMforPowergamers]

I want to play a drunk battlerager now...

+2d6 damage and 1d6 dr and disadvantage

 

[The Shadow]

It just occurred to me to run the same analysis taking Combat Superiority into account. The following will assume the use of only one expertise die for Deadly Strike.

Max damage is now d + c + b, and average damage is now d/2 + c/2 + b + 1. (Where c is the expertise die type.)

So Battlerager would be a net benefit if:

(d + c + b)*p > d/2 + c/2 + b + 1

(2p-1)(d + c) + (p-1)b > 1

(2p-1)(d + c) > 1 + (1-p)b

Once again, there are three cases:

p=0.5: b < -2. Even worse than before.

p<0.5: d + c < [1 + (1-p)b]/(2p-1). Once again, this is impossible, so there is no net benefit.

p>0.5: d + c > [1 + (1-p)b]/(2p-1). Here there is a ray of hope!

In the worst case scenario, p=0.55 (and assuming b=3), d + c must be greater than 23.5. This is actually achievable, if expertise dice ever go up to d12's. (For b=4, it goes up to 28.)

The breakeven point for d=12 and c=6 (ie, a 1st level fighter with a greataxe) is 0.564, only barely better than 0.55. In other words, hitting on a 9.

At 4th level, with c=8, it's 0.558. (9 again.) With b=4, it's not significantly different.

With d=8, c=6, the breakeven is 0.594, or still a 9, though barely.

So: Combat Superiority makes maximum-damage Battlerager more attractive. With realistic melee stats and a halfway decent weapon, a fighter will get a net benefit from it against foes he can hit on a 9 or better. If his dice ever go up to d12, he can raise that to 10 or better. For that matter, if he uses more dice, he can likewise get it to 10. But he seemingly can't get it any higher than that, though I haven't analyzed it in detail.

Still, if he has an 18 Str, a roll of 9 will hit AC 16 even at first level, so it doesn't seem that bad.

 

[pemerton]

Math: let's say you hit with probability p, and roll a dX. With no disadvantage you need to hit once and get average damage, with disadvantage you need to hit twice, but get max damage. To break even you need
p*p*X >= p*(1+X)/2 or
p >= 1/2 + 1/2X

Hm, quick calculation time:

If you hit on a 10+, disadvantage takes you from 55% hit to 30.25% hit.
An ordinary sword attack goes from 1d8+3 (average 7.5) to 11 damage. That's 4.125 vs. 3.3275.
A bigger attack goes from 1d12+3 (average 9.5) to 15 damage. That's 5.225 vs. 4.5375.
An awesome fighter attack goes from 1d12+3+1d6 (average 13) to 21 damage. That's 7.15 vs. 6.3525.

It only breaks even when you hit on lower numbers, or if you're drunk I suppose.

As has been noted, the flat bonuses make a big difference and tend to make rage worthless.

I did some similar calculations for orc raging and worked out that it is basically never worthwhile.

 

[the Jester]

That all looks pretty good to me- it seems that a fighter is going to hit on a 9+ a lot of the time, with the lower ACs in 5e.

 

[the Jester]

Also, I notice very little of the new stuff on the character sheets matches with what [MENTION=697]mearls[/MENTION] says in the podcast.

 

[ZombieRoboNinja]

I want to play a drunk battlerager now...

+2d6 damage and 1d6 dr and disadvantage

Actually this is a pretty nice use for it... Anytime you're attacking an invisible enemy, or a fey warlock, or are drunk or blind or have disadvantage for whatever other reason, might as well go crazy and add a few d6 of rage damage, since disadvantage doesn't stack!

 

[GMforPowergamers]

Actually this is a pretty nice use for it... Anytime you're attacking an invisible enemy, or a fey warlock, or are drunk or blind or have disadvantage for whatever other reason, might as well go crazy and add a few d6 of rage damage, since disadvantage doesn't stack!

Yea and when you gain any 1 advantage you cancel all the disadvantage