Improved Rapid Shot feat

[two]

I just think jgsugden is being contrary for the sake of being contrary - he has something against making "judgements" or something.

It would be easy enough (for him) to run the numbers in on of the spreadsheets (included in this thread), as I've done, and seen that a very "good case" scenario for an archer (10th level, always within 30', doing full attacks 75% of the time) results in:

Up to 5 "extra" points of damage a round when using IRS vs. not using it.

That's on average less than 2 points of damage per round (3 shots).

It's not that significant being a high-level feat.

For non-optimal situations (outside 30', less full attack possibilities) the average damage per round drops significantly. I also used a rather optimal weapon for the level (a +1 holy bow) in the example, it's better than a +3 bow by far for the archer.

This indicates to me that, across campaigns, the feat is balanced. Sometimes you will do more than 5 average per round (a ranger shooting at his most hated enemies), and lots of the time you will do less, it all evens out in the end.

At least, that's what the numbers indicate, and I believe them. It makes "sense" to me and the campaigns I've played in, as well.

I have no fear of making a judgement. I call "Improved Rapid Shot" fair ACROSS CAMPAIGNS and not game breaking; powerful, but as it should be for being a high-tier feat.

Done.

Out.

 

[jgsugden]

*Sigh*

Regarding IRS/WS, I was refuting Korak's statement that IRS was never more powerful than WS. I was not trying to establish that IRS is 'better' or 'worse' than WS. I showed two examples where his numbers had failed him because those numbers failed to incorporate reasonable variables/aspects of the game. I was not trying to prove IRS is too powerful. In fact, my original point is that you can't trust numbers to prove that IRS is too strong or too weak.

I've said my peace. I strongly believe in my advice: Don't trust the numbers, trust your experience. If you want to take my advice, I think it will serve you well. If you don't ... well ... I still hope things turn out nicely for you.

I'm now done with this thread. I have nothing further to add.

 

[Nail]

Huh. A bit of a flame war, eh? That's too bad.

Anyway, back On Topic:
It looks like IRS is probably balanced in a typical campaign, given the length of the feat chain and the increase in average damage over Rapid Shot. Still, it's a close thing, and I wouldn't blame anyone for removing IRS from their game. In a campaign with a lot of "mooks" (# of PCs << # of monsters), this feat is probably too good. In a campaign with lots of "boss monsters" (# of PCs >> # of Monsters), it's just an "okay" feat.

Note: The # of Monsters per PC is far more important than hp in the analysis. Think about that. Remember, in D&D, we assume that APL = EL, much of the time. So hp of monsters scale with APL. (APL = Average Party Level)

... I check for a natural 1 always failing at lower ACs, but don't bother checking for needing a natural 20 to hit the higher ACs.

Actually, the equation I gave above handles both the "always miss on a 1" and "always hit on a 20". At least...I'm pretty darn sure it does. I'd be willing to hear proof otherwise.

Here it is again:

P = Min[Max(21 - AC + Atk, 1),19]/20

where:

• "P" = probability to hit with an attack
• "AC" = opponent's AC
• "Atk" = attacker's total attack bonus (BAB, Str, Magic, Iterative Attack penalty, etc), and
• "Min" & "Max" = are functions within the Excel spreadsheet, finding either the smaller (Min) or larger (Max) of two numbers.

Just take that "P" and multiply it by your expected average damage per attack, and you've got it. Don't forget the criticals. [1 + Pc(M-1)] , where:

• "Pc" = percent chance to critcal (typically 5 - 10%), and
• "M" = critical multiplier

Anyone figure out how Power Critical (adds +4 to confirm a threat) would enter the calculations? Nail's provided the basic formula (sans feat) a page or two back, but how do you account for a 20% increased chance to confirm?

I'm still working on that. At higher threat ranges, my simple equation above breaks down. Surely someone else has already derived the formula? Here's your chance to show me up!

 

[Korak]

I'm still working on that. At higher threat ranges, my simple equation above breaks down. Surely someone else has already derived the formula? Here's your chance to show me up!

Here is my average damage formula for an attack. The logic part of it is expressed in an excel "if" statement, but I changed all the cell references to represent what each quantity is. Hopefully the logic of the formula will become apparent with that change.

=(IF((AC-(Attack Bonus-Power Attack))>2,(IF((AC-(Attack Bonus-Power Attack))>19,0.05,(1-((AC-(Attack Bonus-Power Attack))/20)))) ,0.95))*(Average Weapon Damage + Damage Bonus(Strength + Weapon Specialization + Divine Favor, etc) + Power Attack*Power Attack Multiplier + (Average Sneak Attack Damage and other types… e.g. elemental, if applicable) + (IF((AC-(Attack Bonus – Power Attack))>19,0.0025,(IF((AC-(Attack Bonus – Power Attack))<3,(0.95*(1.05-(Threat Range (expressed as the first number in the x-20 range e.g. 17 if the threat range is 17-20)*0.05))),((1-((AC-(Attack Bonus – Power Attack))/20))*((21-Threat Range)*0.05)))))*((Critical Multiplier - 1) * Subject_to_Crits? (1 if yes, 0 if no) * (Damage Bonus (as defined above) + Power Attack*Power Attack Multiplier + Average Weapon Damage)))

As for power critical, you need simply make the following changes...

=(IF((AC-(Attack Bonus-Power Attack))>2,(IF((AC-(Attack Bonus-Power Attack))>19,0.05,(1-((AC-(Attack Bonus-Power Attack))/20)))) ,0.95))*(Average Weapon Damage + Damage Bonus(Strength + Weapon Specialization + Divine Favor, etc) + Power Attack*Power Attack Multiplier + (Average Sneak Attack Damage and other types… e.g. elemental, if applicable) + (IF((AC-(Attack Bonus – Power Attack))>19,.05*.25,(IF((AC-(Attack Bonus – Power Attack))<3,(0.95*(1.25-(Threat Range*0.05))),((1-((AC-(Attack Bonus – Power Attack))/20))*((25-Threat Range)*0.05)))))*((Critical Multiplier - 1) * Subject_to_Crits? (1 if yes, 0 if no) * (Damage Bonus (as defined above) + Power Attack*Power Attack Multiplier + Average Weapon Damage)))

The bolded changes take care of the increased chance to confirm.

1.25-(Threat Range*0.05) is an equivalent expression to (25-Threat Range)*0.05 ...no real reason for having it appear in two different forms in the overall formula, I just felt like it, I suppose. That is what happens when you add new features to old formulas over time .

My formula runs an if statement to divide attack rolls into those that hit on a 2+, those that hit only on a 20, and those that require rolls of 3-19. Then it figures average damage for the basic hit. Next it figures the chance for a crit, and the increase in damage for that crit. It only applies the extra damage to the total if the user indicates that the target is subject to crits.

The basic flow of the equation is this:

=(IF ( ( AC - (Attack Bonus)) > 2 , (IF ((AC - (Attack Bonus)) > 19 , 0.05 , (1 - ((AC - (Attack Bonus)) / 20)))) , 0.95)) * (Average Damage + (IF ((AC - (Attack Bonus)) > 19, 0.0025 , (IF ((AC - (Attack Bonus)) < 3 , (0.95 * (1.05 -(Threat Range * 0.05))) , ((1 - ((AC - (Attack Bonus)) / 20)) * ((21 - Threat Range) * 0.05))))) * ((Critical Multiplier - 1) * Subject_to_Crits? * (Average Damage)))

Here it is in more simplified terms:

Avg Dmg = Chance to hit * Avg Dmg + Chance to Crit * Dmg on crit above a normal hit

*** To make the changes for power critical into something the user can toggle... you just need to add a 0,1 flag and change the following

.05*.25 to .05*((PowerCriticalFlag*.20)+.05)

1.25-(Threat Range*0.05) to (1.05+(PowerCriticalFlag*.2))-(Threat Range*0.05)

and

(25-Threat Range)*0.05 to ((21+(PowerCriticalFlag*4))-Threat Range)*0.05

***

 

[Nail]

Hey Korak!

Brute force, Excel style. Gotta love it.

Say, you might try Min and Max functions instead of all of those "if...then" statements. Less code.
Looks like you could get rid of some extra parentheses too...it would make bug squashing easier.

My brain hurts just looking over your code.

....it must be right!

 

[slingbld]

Hrmmm, Flame wars. Feels like home
(check my toon)
<--------

 

[DrSpunj]

P = Min[Max(21 - AC + Atk, 1),19]/20

Don't forget the criticals. [1 + Pc(M-1)]

<sigh> I miss math!

I really enjoyed doing stuff like this in undergrad, when I was actually using it near daily and could put that part of my brain to good use. Now it's only engaged once a month for doing bills (yes, that part of my brain is now lazy & stupid! )

Those are just...elegant, Nail. Damn. I would love to take the time to redo my spreadsheet with better functionality and slicker formulas, but I'm not an Excel wizard (I can't even figure out how to add a Yes/No menu choice for things like PBS) and don't honestly have the time to devote to a project like that.

Still, I might take time to tinker with it at some point.

 

[Korak]

Hey Korak!
Say, you might try Min and Max functions instead of all of those "if...then" statements. Less code.
Looks like you could get rid of some extra parentheses too...it would make bug squashing easier.

Excellent point. I usually start with If statements because that is the way my brain thinks best. Of course, depending on your available computing power, and other considerations, like bug checking; other functions are more elegant. I should strive to simplify in subsequent revisions, if not from the start. By the way, I do have some fun Min/Max functions on the second tab of my sheet, though . Check 'em out.

...and sorry about the mini-flame war. Sometimes I can get a bit more inflammatory than I should because most of my DnD rules "discussions" are with my good friends and roommates, and well, we don't mind the name calling and smacktalk. So, apologies for the incendiary that I lumped in with my points JGSugden. You aren't, perchance related to Molly Sugden are you?

 

[two]

Huh. A bit of a flame war, eh? That's too bad.

Anyway, back On Topic:
It looks like IRS is probably balanced in a typical campaign, given the length of the feat chain and the increase in average damage over Rapid Shot. Still, it's a close thing, and I wouldn't blame anyone for removing IRS from their game. In a campaign with a lot of "mooks" (# of PCs << # of monsters), this feat is probably too good. In a campaign with lots of "boss monsters" (# of PCs >> # of Monsters), it's just an "okay" feat.

[other stuff snipped]

This rather confuses me, and goes against the numbers I ran. IRS is ok but not great when the AC of the enemy is rather low (from 15-20). That's because removing the -2 is not that important, since you hit the mooks most of the time anyway. There is an increase in damage, but it's on the order of 2-3 per round (total hitpoints).

Where IRS, in my little sample, really shines in vs the high AC opponents. Removing the -2 penalty when attempting to hit AC30 or 35 is very significant, and makes a much bigger increase in damage per round (around 5 or so).

So, my number indicate that IRS is best against the guys you really care about (high AC BBEG's) and only so-so vs. the mooks.

(I mean, what level 10 archer is going to miss an AC15 mook even on an iterated shot, even with rapid shot up? +5bab +5 dex +3 bow +1 bracers - 2 rapid shot = +12 to hit, i.e. hit on a 3 or less on your worst shot. +13 to hit within 30', etc.).

 

[Nail]

This rather confuses me, and goes against the numbers I ran.

Sorry, 'bout that. I'm already on to the "next part" of this subject.

It's true IRS is excellent against high AC opponents. We've all agreed on that.

In addition, an archer has an inherent advantage over the melee monster. He may take a full attack each round, whereas the melee monster might have to spend some move actions getting from bad guy to bad guy.

The archer can switch targets whenever he kills an opponent; the melee monster may or may not have that chance. Thus my statement above.