Careful Attack/Sure Strike: A mathematical analysis

[Starbuck_II]

Someone on the another board suggested: adding bonus to defenses (+1 or 2) until end of next turn if hit.

So careful Strike makes you better and more careful (hence the name).

It is a original fix.

 

[eamon]

eamon: Upping the to hit chance does nothing to improve the situation: probability to hit and damage done are inextricably linked via expected damage (see the first post in this thread). What this means is that Careful Attack and Twin Strike are competing in the same space since they both do damage only (currently Careful Attack is a distant, distant second in this race). Careful Attack needs to differentiate itself by having a secondary effect.

The only situation in which Sure Strike is worth considering is when taking Heavy Blade Opportunity, so at least this power has a (very limited) redeeming feature.

Whoops, I didn't see this post, so I missed replying.

It is NOT the case that Careful attack and Twin strike are inextricably linked such that upping Careful Attack's bonus will simply either leave Careful attack worse or make it absolutely better. Even in terms of expected damage, there exist bonuses such that high AC creatures will be more usefully hit with careful attack and low AC creatures with twin strike.

Image a creature you hit on all attacks unless you roll a one. Against such a creature, and arbitrary Careful attack bonus would not suffice to make careful attack competive with Twin Strike. Conversely, consider a creature which twin strike cannot hit (i.e. a natural 20 is a non-crit hit). Clearly, a +20 careful attack bonus would make careful attack much more attractive against such a creature. In other words, if careful attack's bonus is high enough, then vs. difficult to hit creatures it will deal more damage than twin strike, and vs. low-AC creatures twin strike will deal more damage.

Where is the crossover point? Well, that depends on a number of factors.
Without hunter's quarry it's pretty readable:

P = B - cM * C

where P is the non-crit hit probability (excl. careful attack's bonus) such that careful attack is balanced with twin strike, B is the bonus granted by careful attack, cM is the crit-multiplier (i.e. crit avg damage divided by non-crit avg damage) and C is the crit chance.

This formula assumes that the bonus B+P+C < 1, i.e. that natural 1 rolls don't need to be taken specially into account for careful attack and that similarly the critical chance for careful attack and twin strike are identical (per strike), which is the case when twin strike and careful attack both hit the AC on any critical roll (20,19-20,18-20 depending on the situation). In short, this formula assumes that twin strike hits normally at least on a crit and careful attack misses normally on a 1.

The formula gets a lot more complicated when you take hunters quarry into account, but it's not truly relevant; the conclusion remains the same.

It is possible to balance careful attack and twin strike by raising careful attack's bonus sufficiently far; if you do so, careful attack will be good vs. high-AC targets and twin strike vs. low-AC targets (which seems to make sense to me).

 

[Nifft]

Even in terms of expected damage, there exist bonuses such that high AC creatures will be more usefully hit with careful attack and low AC creatures with twin strike.

But there are no such creatures.

Image a creature you hit on all attacks unless you roll a one. Against such a creature, and arbitrary Careful attack bonus would not suffice to make careful attack competive with Twin Strike. Conversely, consider a creature which twin strike cannot hit (i.e. a natural 20 is a non-crit hit). Clearly, a +20 careful attack bonus would make careful attack much more attractive against such a creature.

Seriously, there are no such creatures any more. 4e nails down the range of acceptable defenses to such an extent that you can actually say: the PCs will always have a chance of hitting. You can even intelligently discuss how likely any given PC is to hit against an average foe of any given level.

Within this context -- and I assert that this is the context presented in 4e -- there is no bonus for Careful Attack which makes it worthwhile.

Cheers, -- N

 

[Ulorian - Agent of Chaos]

But there are no such creatures.

@eamon: Nifft just saved me a lot of typing! The cases you describe are addressed in my analysis, but they are imaginary/academic: any creature requiring a 20 to hit is that way because its level is far above yours, so will not participate in any encounter you have until you are of a suitable level, at which time the roll you need to hit it will be far less than 20.

 

[Kordeth]

@eamon: Nifft just saved me a lot of typing! The cases you describe are addressed in my analysis, but they are imaginary/academic: any creature requiring a 20 to hit is that way because its level is far above yours, so will not participate in any encounter you have until you are of a suitable level, at which time the roll you need to hit it will be far less than 20.

Slightly off-topic, but this seems to be something a lot of people with gripes about 4E miss, whether it's saying that powers like Come and Get it can be used on PCs to force them to move against their will or that enemies could exploit a disarm maneuver to steal a PCs weapon and effectively cripple him for the duration of a fight.

Well, yes, all these things, including creatures you can only hit on a 20 showing up to take your lunch money, are possible. But as I mentioned in another thread, there is one simple, guiding principle that underscores all of 4E DMing: Don't be a jerk to your players. Challenge them, frighten them, make them work for their victory, but if there's something you can see in the rules that will take away their fun, don't do it.

 

[eamon]

If you have a less than even chance of hitting a creature, careful attack can be better than twin strike, given a high enough careful attack bonus. This situation can occur. Fighting against an overlevel enemy isn't uncommon - for 6 players a 3rd level young black dragon is a low-end "hard" difficulty encounter (being 875XP, and the hard range being 900-1200XP), but it has 22AC, which a 1st level ranger can certainly hit - but not easily.

Certainly careful attack can be better, if the bonus is high enough. The problem is partially that any bonus high enough to make it see common use (+6 - +8?) is so high that it's begging to be abused by creative combos. Conversely, a bonus of +2 is completely pointless. I think a bonus of +4 is a reasonable compromise, though it's still a sucky power then, since in the situations where twin strike loses to careful attack with a +4 bonus you're only hitting on a 17 or higher... ...and though, especially if the circumstances are against you, this can happen, it's rare, and further, you're almost certainly better off spending your action doing something to improve the circumstances rather than almost certainly missing.

Perhaps the defense bonus fix would be reasonable - especially in combination with a higher bonus - a +4 to hit and a +1 to all defenses is probably still not broken.

As a bit of an aside, I find the stories that it used to be +4 and was then changed to +2 prerelease to be somewhat worrisome - I mean, how hard is it to see that careful attack is simply a situational power, even at +4, and a pretty terribly choice at +2?

 

[Kordeth]

If you have a less than even chance of hitting a creature, careful attack can be better than twin strike, given a high enough careful attack bonus.

Yes. This is entirely the point. The two powers are so inextricably similar that no matter what you do, you can crunch the numbers and see that one will always be better than the other. The problem isn't that Careful Strike sucks, it's that as written, Careful Strike is a "player trap." It looks like a good power choice until you dig into the probability, at which point you realize it's a waste of a power. If you make Careful Attack better than Twin Strike, you have the exact same problem except that now Twin Strike is the sucker's bet. At the absolute best you might find the perfect number at which Twin Strike and Careful Attack are perfectly balanced, but that's extremely unlikely given the relative coarseness of D&D's math.

As has been stated numerous times, the only way to really fix the problem is to make one of the powers removed in some way from the "hit and inflict damage better" model.

Perhaps the defense bonus fix would be reasonable - especially in combination with a higher bonus - a +4 to hit and a +1 to all defenses is probably still not broken.

Depends--in your version, do you still lose the ability bonus to damage? If so, that might be on the upper-end of balanced, if not, it's probably way too good.

As a bit of an aside, I find the stories that it used to be +4 and was then changed to +2 prerelease to be somewhat worrisome - I mean, how hard is it to see that careful attack is simply a situational power, even at +4, and a pretty terribly choice at +2?

As stated before, the reason Careful Attack is so bad is not (entirely) because it's flat-out worse than Twin Strike, it's because Sure Strike looks like a good choice on paper. It's deceptive--heck, the first time I played an archer ranger, I didn't do the math and assumed that Sure Strike + Hunter's Quarry (to make up for the lost Dex bonus) was the winning combo. Granted, it didn't help that the character was a pregen who didn't have Twin Strike, but still--if a lot of playtesters are using Careful Attack excessively because it looks good, it's easy to think, as a designer, "hmm, everybody's using this power all the time, it's probably too good) and nerf it without realizing it's not as good as people think.

 

[eamon]

Yes. This is entirely the point. The two powers are so inextricably similar that no matter what you do, you can crunch the numbers and see that one will always be better than the other. The problem isn't that Careful Strike sucks, it's that as written, Careful Strike is a "player trap." It looks like a good power choice until you dig into the probability, at which point you realize it's a waste of a power. If you make Careful Attack better than Twin Strike, you have the exact same problem except that now Twin Strike is the sucker's bet. At the absolute best you might find the perfect number at which Twin Strike and Careful Attack are perfectly balanced, but that's extremely unlikely given the relative coarseness of D&D's math.

See, this is just false - if the bonus is high enough, then careful attack will be good in those situations where it's hard to hit the opponent, and twin strike will be good in those where it is easy. This balance is possible, and occurs with all careful attack variants that have a bonus of somewhere in the range of +3 to +10, and depending on the bonus the crossover point shifts. Nevertheless, it's probably unwise to put the bonus too high since it begs abuse.

Depends--in your version, do you still lose the ability bonus to damage? If so, that might be on the upper-end of balanced, if not, it's probably way too good.

In my version, you still lose the ability bonus to damage. I find the varieties of careful attack which simply hit more frequently not particularly inspiring, but if that's the errata use, a +2 suffices.

As stated before, the reason Careful Attack is so bad is not (entirely) because it's flat-out worse than Twin Strike, it's because Sure Strike looks like a good choice on paper. It's deceptive--heck, the first time I played an archer ranger, I didn't do the math and assumed that Sure Strike + Hunter's Quarry (to make up for the lost Dex bonus) was the winning combo. Granted, it didn't help that the character was a pregen who didn't have Twin Strike, but still--if a lot of playtesters are using Careful Attack excessively because it looks good, it's easy to think, as a designer, "hmm, everybody's using this power all the time, it's probably too good) and nerf it without realizing it's not as good as people think.

Yeah, I can completely agree with you here. It's really nasty, and should be errata'd somehow. It's disturbing that the designers nerfed the power despite the fact that it's not particularly good at +4, since it indicates they're not even doing superficial numerical sanity checking.

 

[Keenath]

Just poking at the math a bit, I noticed that Sure Strike is *always* inferior to Reaping Strike if you have a positive strength modifier.

If you look at it one way, Reaping Strike essentially says, "You deal STR damage. If you hit, you deal [w] damage." Sure Strike says, "You get +2 to hit. If you hit, you deal [w] damage." They're *really* easy to compare.

SS has a 10% better chance of dealing [w]. Thus, you simply ask: Is [w]/10 better than your STR modifier? If so, then Sure Strike is the superior attack for you. This can't happen if you start with even a 12 in STR. (In this case, you just replace [w] with the average weapon damage -- 5.5 for a greatsword, 4.5 for a longsword, etc. Crits may be ignored, as both attacks crit at the same rate and deal the same damage on a crit.)

Changing the bonus of SS just alters that percentage. Make it +4? Okay, then is [w]/5 better than your STR modifier? If you started with +1 STR, it's break even. If you started with a higher score, Reaping is always better.

Rangers are a little more complicated with their Twin Strike and Hunter's Quarry, but the fighter is easy -- Sure Strike is a sucker bet.

 

[PSchirf]

Either Or?

Some are saying that Twin-Strike isn't overpowered, but given it's versatility, it looks that way to me. And I don't see the versatility being analyzed in the number crunching above. The issue, for me, is that the player can choose to use it against a single target or multiple targets, with ranged or melee weapons. Flatly restricting the power to one or two of these options nerfs the other options too much.

I'm considering breaking Twin-Strike up into four options, two melee (one target or two target versions) and two ranged (one target and two target versions), and limiting the ranger to one of the options (changeable when power swapping is permitted). Comments?

To improve Careful Attack, I like the idea of making it grant a +1 AC bonus until the start of the Rangers next turn... i.e. being more careful.

The fighter's Sure Strike... I don't yet see an option that I like. I'm leaning toward making the +2 to hit last until the start of the Fighter's next turn, thereby making OAs (or AP attacks) at +2 if Sure Strike was used as the previous attack.