Note: the damage here is generally trivial, and this question is mostly silly, but now I'm curious and would like to see if anyone knows of any specific rules or official rulings on this.
Imagine the following scenario:
A character with a spear (2H Simple Weapon, 1d6, x2), 12 Strength (+1 Str Modifier), and no other damage bonuses. They roll a crit. How high is the total flat modifier for the damage on this crit?
Theory 1: Round immediately.
This seems to be the common camp, where one rolls 1d6 (base weapon damage) + 1.5 (1 Str modifier * 1.5 for wielding two-handed), rounds down to 1d6+1, then rolls a second time for another 1d6+1, total of 2d6+2.
Theory 2: Round at the end.
While apparently unusual, this case is perfectly valid by the rules, and may be closer to RAW, though not RAI. Here, you roll 1d6 + 1.5 + 1d6 + 1.5, then add them together for the total crit damage of 2d6+3.
The rule is clearly round down when you must (in the PRD, that's actually "are must", but I'll let that go for now). That isn't a problem. The rules for adding up multiple "damage rolls" for a crit (rather than "multiplying") is also not a problem. The question is: when must you round down? Specifically, can someone find a direct quote from the rules that state you should be rounding down before determining final damage on a crit?
Ok, now the above character is: Wizard 3 / Magus 1 using Evocation's Intense Spells on a Shocking Grasp delivered through that spear, without getting a crit against an enemy with no resistance or DR.
This yields: 1d6 + 1.5 (physical damage) + 1d6(3d6 if cast with wizard slots) + 1.5 (electric damage)
Rounded down immediately because they are separate types of damage with a +2 flat modifier, or added together for a +3 flat modifier on the rolled damage from the attack?
#1 is correct.
The rules say 'whenever you wind up with a fraction', which to me says 'at the moment you have a fraction, round it down'.
| 1 person marked this as a favorite. |
*facepalm*
#1 is correct.
The rules say 'whenever you wind up with a fraction', which to me says 'at the moment you have a fraction, round it down'.
Where do they say that? I only see that line in the d20pfsrd third-party site, not in the Official PRD.
That's the source I use for everything. Frankly, I think it's better than the official PRD.
While I might agree with you (I certainly prefer the d20pfsrd formatting), the Table of Average Die Rolls in the Bestiary disagrees with you, Zhayne (and may be one of the few spots where fractional values appear in the books).
Of great value is the note on this table:
"*Always round down after multiplying. For example, treat the average of 1d4 as 2, and the average of 2d4 as 5."
The section on Damage defines "Multiplying Damage" - and this note specifies that you always round down after multiplying.
Unless someone comes up with evidence to the contrary, this has been solved -- you keep the fractional value to the end when multiplying damage (e.g. on a crit).
Since you multiply the number of times you roll damage, not the damage itself, the question doesn't apply to critical hits.
It seems to me that in all cases you use standard mathematical orders of operation. So, before you add you multiply and, as a special rule, after you multiply you round if you have a fraction.
Fractions are therefore NEVER used in any mathematical operation that occurs after you get the fraction.
Since you multiply the number of times you roll damage, not the damage itself, the question doesn't apply to critical hits.
It seems to me that in all cases you use standard mathematical orders of operation. So, before you add you multiply and, as a special rule, after you multiply you round if you have a fraction.
Fractions are therefore NEVER used in any mathematical operation that occurs after you get the fraction.
Not true. Those fractional favored class bonuses would never work if you rounded them down to zero at each level where you received them before adding them up.
Fractional favored class bonuses also follow this rule. After you multiply them by the number of times you have taken the bonus you drop any fraction and that tells you how much of a modifier/bonus whatever you have.
You don't lose that you have taken that bonus 1 time, even when the rounding makes it have no effect.
Fractional favored class bonuses also follow this rule. After you multiply them by the number of times you have taken the bonus you drop any fraction and that tells you how much of a modifier/bonus whatever you have.
You don't lose that you have taken that bonus 1 time, even when the rounding makes it have no effect.
This is correct.
There are several Favored Class Bonuses that specifically state they do not receive the benefits of choosing X Favored Class Bonus Y times because of fractal division, right in the D20PFSRD site under some of the race's Favored Class Bonuses.
@ OP: I agree with Zhanye in that it would be when you immediately get a numerical result.
Let's take an Empowered Fireball against a Water/Ice Elemental. You deal 10D6 worth of damage on that Fireball; average 35 damage. Following the rules of Empower, you then multiply that total by 1.5, equating to an actual increase of 17.5. You can't deal half a hit point of damage, meaning you shouldn't multiply the .5, since it effectively does nothing; so it should be rounded down to 17 to accomodate those rules, resulting in a total of 52 damage. Since the Elemental has a Vulnerability to Fire, that total (52) is multiplied by 1.5, equalling 78 damage. However, the Elemental did make his Reflex Save, reducing that total damage down to 39.
Fractions are therefore NEVER used in any mathematical operation that occurs after you get the fraction.
This is what I was disagreeing with. With favored class bonuses, you get the fraction right from the beginning.
So let's say that you have a favored class bonus of 1/3 and you have taken it 3 times. I think everyone agrees that the total bonus is 1/3 + 1/3 + 1/3 = 1.
But if you never use fractions in any operation after you get the fraction, then each of those +1/3 bonuses would have to be rounded down to zero, and your total bonus would be 0 + 0 + 0 = 0. That is clearly wrong.
I think people are over thinking this.
The key here is when does a bonus get rounded? The answer? When it becomes a bonus.
Take Strength for example. You calculate the Strength bonus to damage by multiplying the strength modifier by a multiplier and then rounding down. That is your Strength bonus to damage.
Favored Class bonuses that are fractional are added up and then become the bonus. For example, if you have taken the Half-Orc Alchemist favored class bonus three times you have 3*0.5 = 1.5. The Favored Class bonus is +1.5 damage to bomb which, when rounded down, is +1 damage to bombs.
The point is that the rounding is occurring at each kind of bonus. Calculate the bonus, round down. Do not calculate the sum of all different types of bonuses and then round down.
Fractions are therefore NEVER used in any mathematical operation that occurs after you get the fraction.This is what I was disagreeing with. With favored class bonuses, you get the fraction right from the beginning.
So let's say that you have a favored class bonus of 1/3 and you have taken it 3 times. I think everyone agrees that the total bonus is 1/3 + 1/3 + 1/3 = 1.
But if you never use fractions in any operation after you get the fraction, then each of those +1/3 bonuses would have to be rounded down to zero, and your total bonus would be 0 + 0 + 0 = 0. That is clearly wrong.
Nobody is saying that. He might appear to be saying it, but that's because he's not saying it correctly.
What we're saying it fractions aren't used for a final result of an equation for damage rolls, attack rolls, healing, etc.
The rule is that yes, +1/3 + 1/3 = 2/3, but you can't factor that in to, say, equating an extra round of Rage or Bardic Performance from a Favored Class Bonus, because the calculations for those abilities (or anything similar for that matter) don't parse fractals. Since they cannot be parsed, they are effectively 0 due to the rule that the result of an equation ending in a fraction is rounded down, regardless of the number (unless stated otherwise).
Im pretty sure that if my 12 str person has a 2h weapon for all in tents i have a ... +1 strength bonus. Ive never seen it treated as a +15 to damage.
Part of the goal of rounding down is to ensure most math in the game is as simple as possible.