Superior Xbow/Greatbow dpr

[oakbriar]

So every resource I've seen for ranger (and other twig tossing classes too) say the Superior Crossbow is what you want. Enchantments aside (yeah bow enchants are much more controllerish), it's still said that the +1 on attack rolls beats out the (average) +1 damage.

But I've just been running a bunch of DPR tests at various levels for Twin Strike and RBAs and the Greatbow has come out on top each time. It isn't a large difference (around 5%), but it's still there in the numbers.

So what DOES make the superior X bow apparently better?

For the record, the into I was using:
A starting 20 score in the stat, bumped every time.
Weapon Expertise feat (obviously)
NOT using prime shot
And a +X ench increase after each half tier (ie: 6, 11, 16, 21 etc)

The only thing I can think of is if you have a whole load of static bonuses? I've had my fill of math for the afternoon already so I'm not going to jump into it all over again loaded with all the static dmg.

Thought it was interesting.

 

[DracoSuave]

So every resource I've seen for ranger (and other twig tossing classes too) say the Superior Crossbow is what you want. Enchantments aside (yeah bow enchants are much more controllerish), it's still said that the +1 on attack rolls beats out the (average) +1 damage.

But I've just been running a bunch of DPR tests at various levels for Twin Strike and RBAs and the Greatbow has come out on top each time. It isn't a large difference (around 5%), but it's still there in the numbers.

So what DOES make the superior X bow apparently better?

For the record, the into I was using:
A starting 20 score in the stat, bumped every time.
Weapon Expertise feat (obviously)
NOT using prime shot
And a +X ench increase after each half tier (ie: 6, 11, 16, 21 etc)

The only thing I can think of is if you have a whole load of static bonuses? I've had my fill of math for the afternoon already so I'm not going to jump into it all over again loaded with all the static dmg.

Thought it was interesting.

The easy way to compare the math is quite simple.

Take the number of outcomes where the bow hits. Multiply that by 1 in pre-epic, and 2 in epic. This is how much more damage those outcomes would generate if you used a bow instead of a xbow.

Take the average damage on a hit of a xbow. This is how much damage that extra outcome (the +1 to hit) grants you.

Divide both by 20 to get the DPR. This gives you the equation:

(p = number of outcomes, x = 1 or 2 depending on tier, d = average damage of the great bow)

GreatBow is superior if and only if:

px/20 > d/20

or

px > d

Really simple math to do, actually.

So, let's take level one, with a 20 dex.

1d10+5+1d6 = 7-21 damage = 14 damage on an average hit.

1p > 14

p > 14

Now p is equal to 21 minus what you need to roll on the d20 to hit. Well call that number t for target number.

21 - t > 14

7 > t

Which means the greatbow is only superior if you can hit with anything less than a 7 with it. So:

Your attack bonus is +7, so that would mean the AC would have to be less than 14.

How many level 1 monsters have an AC less than 14? Most 'theorycraft' around D&D 4th edition revolves around the 50% attack assumption, which doesn't apply in practical use. A more practical examination looks at the AC break-even point, and considers whether or not you encounte that AC often.

In this case, the AC in question -never happens- and SupXBow is superior across all monsters. However, if examination shows the AC break point occurs often, then either weapon is good. And if the breakpoint is above what you normally shoot at, greatbow is better for damage.

EDIT: The math actually works out to AC 15 because of the extra point of critical damage. But the rest is still as much a wash.

EDIT2: Load minor is only a concern to characters who use minor actions to do their shtick....

...oh wait... Hunter's Quarry...

EDIT3: I flipped xbow and gbow around. It's correct now: The more accurate wepaon does more damage even at level 1. More static bonuses favor accuracy over damage.

 

[Mengu]

At low levels, the extra damage from greatbow will eek out the superior crossbow. As static modifiers are piled on, the d10 vs d12 becomes insignificant, and +1 to hit plays a much bigger role. It does cost an extra feat (or an item property) to make the superior crossbow work without the minor action cost though, so that can be consideration. Also Steady Shooter is a nice boost to damage if you can afford the Con.

 

[Mort_Q]

How many level 1 monsters have an AC less than 14?

20 out of 88 (in the compendium)... including the camel.

 

[DracoSuave]

20 out of 88 (in the compendium)... including the camel.

How many monsters you'll reasonably -fight-?


It's kinda like Power Attack in that, the higher the damage you deal before Power Attacking, the less you actually want to power attack. In 3rd edition, if you were doing 1d10+5+1d6 damage, would you want to power attack for 1 in anything but where you absolutely outclassed their AC?

The answer is no, you would not. But in 3rd edition, there was a lot more of an AC deviation than in 4th, which made Power Attack useful for clearing certain types of encounters. In 4th, however, you'd rarely want to Power Attack for 1 with that level of damage.

This situation is no different. Twin Strike only changes the situation -slightly-, because the average damage of a hit has to be normalized for Hunter's Quarry only applying once.

p > d + q

Where d is the damage without quarry, and q is the normalized quarry damage. Q will be the average quarry damage.

Half of situations, it's the first hit, and in the other half of situations, you only apply the quarry damage if you missed in the first half.

So... q = Q/2 + Q(21-p)/40
=20Q/40 + (21Q-Qp)/40
=41Q-Qp/40

p > d + 41Q/40 - Qp/40

p + Qp/40 > d + 41Q/40

40p + Qp > 40d + 41Q

(40+Q)p > 40d + 41Q

p > (40d + 41Q)/(40+Q)

Okay. this is a lot more complicated an equation. But we just need to plug in the variables:

d=avr(1d10+5)=9.5
Q=3.5

p > (40[9.5]+41[3.5])/[40+3.5)
> (380 + 143.3) / (43.5)
> 12.03

As p is an integer, that means it must be >= 13.

21 - t >= 13
8 >= t
And with a +7 to hit
AC <= 15.

If AC <= 15, long bow does more DPR.

Again, this is not common at level 1.

 

[oakbriar]

Which means the greatbow is only superior if you can hit with anything less than a 7 with it. So:

Your attack bonus is +7, so that would mean the AC would have to be less than 14.

That's where my problem was right there. I was calculating with a +1 weapon and the weapon expertise feat, so I was always fitting in the greatbow=better range.

Thanks for the mathemagics Draco!

(Ps, I dont know what kind of campaigns you guys are playing, but my party is always getting ambushed by camels!)

 

[Mengu]

(Ps, I dont know what kind of campaigns you guys are playing, but my party is always getting ambushed by camels!)

I stick with toxic acid spitting undead llamas.

 

[blargney the second]

Cool analysis, Draco. Wish I could give you XP for that.

 

[DracoSuave]

One thing to consider tho is that different levels/campaigns/parties have different attack bonuses. So one that has a leader constantly handing out attack bonuses may find their greatbow/supxbow math a bit different.

It's a lot easier to just figure out the AC threshhold then to look at a 50/50 based analysis in a vacuum. The reality is, sometimes the greatbow pulls a head... if you have a lot of +1[W] powers, for example, then static damage has a LOT less of an effect.

 

[BobTheNob]

Put the damage aside (and yes, I know the ranger is a striker, its his job) and consider that the bulk of powers attacks carry riders of some form. Splintering shot (lvl 5 daily) imposes a -2 to hit till end of encounter, or a -1 on miss. Now, if it was me, that extra point of damage I would do here and there would count for squat when compared to landing that hit. If I were using the greatbow and missed by 1 (and it happens, it really does happen) I reckon all the gains in damage would pale into insignifigance compared that that one roll missing.

Its even worse for encounter powers, which generally dont have on miss conditions.

What if a power reduces the enemies defence by 2(hyperthetical) till end next round and the +1 from Xbow over the GreatBow made a miss into a hit? Follow that up with an action point to attack again and your attack in the next round as well so you get two attacks with the now reduced defences. What sort of a difference did that make on your DPR? Mathematical models almost never take these things into account.

To me, in the whole "accuracy vs damage" debate, I would gladly drop damage to gain to-hit every single time, and the math can go to hell. Landing effects is king to me.