Damage Per Round

Dear Splart,

Thanks for your reply.

Splart said:

My guess is that WotC meant for Rain of Steel to do only weapon damage, not weapon damage plus WF, plus weapon enhancement, plus etc.

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Well, I can't take that into account here, I'm doing RAW.

Unfortunately, the PC doesn't get to choose to apply his quarry when the crit lands. If he rolls a normal hit on the first attack and crits on the second attack, he will only do normal quarry damage, not crit quarry.

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PHB104: under "Hunter's Quarry": "If you can make multiple attacks in a round, you decide which attack to apply the extra damage to after all the attacks are rolled."

Also, the chance of hitting with a normal attack is not a dependent probability on not hitting with a critical attack, so it should not be multiplied against the chance of not having a critical hit.

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I'll double check the formula in a minute, but the reasoning is this. If you crit on either attack, you get crit damage. However, if you hit on either attack, you don't necessarily get normal damage, because if you crit, then hit, you get crit damage already. So the probability of crit damage is simply the probability of at least one crit. However, the probability of normal damage is the probability of hitting at least once, but also not critting on the other attack.

The probability of critting thus has an effect on the regular damage component, but I may have got the wrong formula. I'll check it.

EDIT: I'll check the formula when I get home, I don't have my stuff at work.

loisel said:

PHB104: under "Hunter's Quarry": "If you can make multiple attacks in a round, you decide which attack to apply the extra damage to after all the attacks are rolled."

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Huh. I'm impressed with your deep knowledge of the books. So, this would apply even if the ranger used an action point to get 4 attacks in a round. Funky. So, is that a feature of the ranger only, or is that a feature of all "quarry-like" attacks? I.e. does the rogue/ranger get the same benefit from this, or does he have to name which dice is the "first" sneak attack, and only gets crit damage if rolled on that one?

According to RAW, I would say no, so the quarry probability formulas have to be made separate for the ranger versus the rogue/ranger.

In any case, for the ranger at least, the formula then becomes:

(1-(1-PCrit)^PCattacks)*crit quarry dmg + (1-(1-PHit)^PCattacks - 2 * PCrit * PHit) * average quarry dmg

loisel said:

I'll double check the formula in a minute, but the reasoning is this. If you crit on either attack, you get crit damage. However, if you hit on either attack, you don't necessarily get normal damage, because if you crit, then hit, you get crit damage already. So the probability of crit damage is simply the probability of at least one crit. However, the probability of normal damage is the probability of hitting at least once, but also not critting on the other attack.

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The problem with your reasoning is that the chance not getting a crit attack includes the chance of missing totally, which is not accurate when the rest of the calculation assumes at least one hit. It's like the old math problem -- I have two children and at least one boy: what is the chance I have two boys? According to the reasoning you used, the answer is 50% * 50% = 25%, but the correct answer is 33%, because there are three equal probability combinations that meet the 1 boy condition, boy-boy, boy-girl, and girl-boy. In this calculation, when you have already included the condition that one attack hits (1-(1-PHit)^PCAttacks), multiplying this by the chance that no crits hit (1-(1-PCrit)^PCAttacks) doesn't work because the no crit chance includes the chance that both attacks miss.

--Splart

I've not read all this carefully, but it looks like you assume things like fighter daily stances are being used for extra damage. How about flaming sphere for the wizard?

brehobit said:

I've not read all this carefully, but it looks like you assume things like fighter daily stances are being used for extra damage. How about flaming sphere for the wizard?

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It's only included as an example on the Level 20 chart. I will put a clearer warning.

Dear Splart,

Thanks for your reply.

Splart said:

deep knowledge of the books

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Well, I can't take credit. I originally had it that you used quarry on the first hit, but someone on the WotC forums pointed out that rule.

According to RAW, I would say no, so the quarry probability formulas have to be made separate for the ranger versus the rogue/ranger.

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Right, which doesn't affect me because my rogues only attack once per round, but you've got a twin strike rogue in there you might want to fix.

EDIT: actually, I do have a TS rogue I forgot about...

(1-(1-PCrit)^PCattacks)*crit quarry dmg + (1-(1-PHit)^PCattacks - 2 * PCrit * PHit) * average quarry dmg

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I think it's something like that, but I'm not 100% on the second part. I think the way I'm going to handle it is:

P(crit quarry) = (1-(1-PCrit)^n), like you suggest
P(no quarry) = PMiss^n
P(normal quarry) = 1 - P(crit quarry) - P(no quarry).

I think probably the P(normal quarry) in my spreadsheet is incorrect.

EDIT: which is, uh, P(normal quarry) = (1-PCrit)^n - PMiss^n

Sounds good to you?

loisel said:

Dear Splart,

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No need for formalities, especially with someone with a silly board name like "Splart."

Now, let's get down to brass tacks, shall we?

loisel said:

Right, which doesn't affect me because my rogues only attack once per round, but you've got a twin strike rogue in there you might want to fix.

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Yup. Sigh. I'll have to compare the probability matrices and add in the extra ranger quarry crits.

PCritQuarry=PCritSneakAttack + PCrit * (PHit + PMiss)

loisel said:

P(crit quarry) = (1-(1-PCrit)^n), like you suggest
P(no quarry) = PMiss^n
P(normal quarry) = 1 - P(crit quarry) - P(no quarry).

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Yes, that's all good, and more eloquent than what I had. Nice.

loisel said:

I think probably the P(normal quarry) in my spreadsheet is incorrect.

EDIT: which is, uh, P(normal quarry) = (1-PCrit)^n - PMiss^n

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Actually, this is fine too. In fact, it's mathematically equivalent to P(normal quarry) above, since (1-PCrit)^n - PMiss^n = 1 - P(crit quarry) - P(no quarry)

However, that's not what your spreadsheet uses. From cell DPR!B4, for normal quarry you have: (1-Pcrit!B4)^Toons!$C4*(1-(1-PHit!B4)^Toons!$C4), which simplifies down to (1-PCrit)^n * (1-(1-PHit)^n), which is neither here nor there.

Splart said:

However, that's not what your spreadsheet uses.

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I think you're looking at a previous version. I updated to 1.10 when I posted the formulae.

Right-o. I was looking at 1.8. I didn't realize you'd already fixed it while we were talking.

Splart said:

Huh. I'm impressed with your deep knowledge of the books. So, this would apply even if the ranger used an action point to get 4 attacks in a round. Funky. So, is that a feature of the ranger only, or is that a feature of all "quarry-like" attacks? (rest cut)

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It's a feature of the ranger only.

Rogues and Warlocks decide their extra damage after the -DAMAGE- is rolled, which is even later than the ranger.

DracoSuave said:

It's a feature of the ranger only.

Rogues and Warlocks decide their extra damage after the -DAMAGE- is rolled, which is even later than the ranger.

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Not clear that it's necessarily later than the ranger (does it say anywhere that you roll all attack rolls first, then all damage rolls?)

However, I think it's a reasonable reading that you can apply your sneak attack damage to any 1 attack you performed, so the effect for this thread is the same as the ranger's.