Sure Strike and Careful Attack [4e]

[Yakk]

These powers suck. I'll include a spoiler at the bottom of the post demonstrating that they do, indeed, utterly suck.

But the main question is -- how do we fix them?

The first idea is to have them grant full [W]+Stat damage.

That is pretty flavorless.

The second idea is to grant them an increase to-hit bonus. I find that the level of bonus needed to make them not-suck ends up being pretty ridiculous.

Another idea is to have them have a free attack reroll built into them. Ie, roll twice, take the best attack roll. Even then you need to increase their to-hit modifier above +2, or give them a chance (say, both attack rolls hit) to deal extra damage above [W], for them to suck.

Thoughts?

Evidence they suck:

Spoiler

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Let A be the average non-stat-based attack damage.
Let S be your stat-based attack damage.
Let P be your chance to hit.

Looking at the fighter first, and using reaving strike with a 1 handed weapon, we get:
RS = P*(A+S) + (1-P)*S/2
SS = (P+.1)*A
Subtracting:
RS-SS = P*S + (1-P)*S/2 - .1*A
= S/2 + P*S/2 - .1*A
Set it equal to zero, and solve for P:
A = S*5*(1+P)
(1+P) = A/(5S)
P = 1-A/(5S)
Chances to hit under this amount are better for sure strike. In particular, if
5S > A
then reaving strike is always better than sure strike against a non-minion.

Getting your non-stat based damage to average more than 5 times your stat-based damage is quite a feat.

So that leaves Sure Strike being a better attack against minions than reaping strike.

...

For Rangers, the situation is in a sense worse. Ranger twin strike does:
2AP
damage, plus (if Q is quarry damage),
(2P-P^2)Q
quarry damage.

Careful Attack meanwhile does A(P+.1) damage, with (P+.1)Q Quarry damage.

Subtract:
2AP-A(P+.1) = AP-.1*A
ie, careful attack does more damage on average if your P < .1 from your non-Quarry damage. Note that very shortly afterwards, the natural 20 rules kick in, which give advantage back to twin strike.

Quarry damage delta:
(2P-P^2)Q - (P+.1)Q
(-P^2+P-.1)Q
P = [-1+/-sqrt(1-.4) ] / -2
P = .89 or .11
ie, also in the "10% chance to hit" or "10% chance to miss" ranges.

And shortly thereafter, the natural 20 rules kick in...

Which basically reduces Careful Attack to doing more damage on average when you need exactly a 19 or 20 to hit the target. If you need an 18, twin strike is better...

[Yakk]

So, some explicit mechanics:

1> Roll twice at +2. If either roll hits, do [W] damage.

-- This ends up being worse than Twin Strike against a single target for the vast majority of to-hit rolls.

While some might say "that is the elf trick", elves don't give up stat-bonus to damage, and only an idiot of an elf would use their reroll on a basic attack.

Spoiler

Show

Careful: 2(P+.1)*A - (P+.1)^2*A
= 2PA + .2A - P^2A -.2PA -.01A
= -P^2A + 1.8PA +.19A
Set A = 10 we get:
= -10P^2 + 18P + 1.9
A basic attack does (S+A)*P, or 14*P with S=4, giving us a careful attack advantage of:
= -10P^2 + 4P + 1.9
which intersetcts 0 at:
P = (-4 +/- sqrt(92)) / (-20)
=~ 0.67958315233127195415974380641627

At P = 0.5, a basic attack does an average of 7 damage (with S=4, A=10).
At P = 0.5, a double-careful attack has a 84% chance of hitting, and does an average of 8.4 damage.

At P = 0.9, a basic attack does an average of 12.6 damage.
The double-careful attack does an average of 10 damage.

So with a 68% chance of hitting or below, the double-roll +2 to hit careful attack beats out a standard attack. At above 68%, the careful attack does less damage.

Note that this is not far out of line. And at low accuracies, double-careful attack matches twin strike. (at average accuracies it tends not to).

2> Roll once at +3. Considered a basic attack.

-- Good for Fighters, not so good for Rangers. With reasonable stat/other damage, beats a standard basic attack that needs a 13+ to hit for average damage/attempt.

Spoiler

Show

A = 10, S = 4 (non-stat attack is A, stat-damage is S). P is chance of hitting.

Basic is P(S+A). Sure is (P+.15)*A. Delta is:
.15*A-P*S
1.5-P*4
P=0.375

Better if you have a 35% chance of hitting or less, or a 14+ to hit.

3> Roll once at +5 to +7 to hit.

-- This could be implemented with "Add secondary stat to hit", like wisdom, dexterity, or the like.

Spoiler

Show

(P+.25)*A to (P+.35)*A
With A=~ 10 and S =~ 4, a basic attack does:
(A+S)*P

The delta is then:
.25*A to .35*A - S*P
2.5 to 3.5 - 4*P
P = 0.625 to 0.875
as the turn-over point where careful/sure matches basic attack in average damage. Ie, such an attack ends up being better than a basic attack.

4> Full damage is clearly better than a basic attack.

---

The next hurdle is how much it beats other at-will powers.

Reaping strike with a 2H weapon, and Twin Strike, are the two gold-standard single-target high-AC attack powers for the Fighter and Ranger respectively.

Reaping damage over a basic attack is:
(1-P)*S

Twin strike damage over a basic attack is (ignoring HQ)
P(A-S)
With HQ, it is:
P(A-S) + P(1-P)Q

As yet none of this analysis includes crits.

[AstralFire]

Yakk, I'm guessing you have a background in math.

Not that the math you use is particularly advanced so much as how you go about it and how often you do so.

(That is my contribution to this topic; I like 4e, but I haven't really gotten to play it much at all.)

[Holocron Coder]

Question: Does this bring into consideration enchantments, feat bonuses, etc?

As far as I've been able to tell, these AREN'T added to damages based exclusively on ability scores (as opposed to weapon rolls). Thus, getting the described damage out of your weapon roll over your ability is possible.

[Yakk]

That's in the A component -- average damage not based on a stat.

So a basic attack does (A+S) damage, while a Sure Strike does A, and twin strike makes two attacks for A damage.

Twin Strike is probably too good, so I'm a bit leery about building a power that is as good as Twin Strike.

[MartinHarper]

An interesting facet of the "roll twice, pick highest" option is that it increases the chance of crits too. This is nice, because if you are "trading damage for accuracy", it seems good to have a greater chance of hitting the weak spot for massive damage.

Reaping Strike and Sure Strike are competing for the same role: attacking things that are hard to hit, which makes things tricky. An alternative:
Str vs AC
Hit: [W] + Str damage
Effect: your next attack against this enemy gains a +3 bonus to hit

So Reaping Strike is for guaranteed damage, whereas Sure Strike is for setting up your encounter power. Different roles.