PF: Crit Probabilities of X d20s and feat consideration Zen Archer

[Dimcair]

Writing up a Zen Archer right now and wondering about feats.

I am especially interested whether I should take Pinpoint targeting at 10th OR Improved Critical but other comments are very well appreciated.
(therefore you are welcome to comment on this even if you, like me, have no idea about the math going on^^)
As I see it at 10th level with 5 attacks (spending an extra Ki) + perfect strike I will roll 7d20. While I need to chose 1 of the first 3 perfect strike rolls the pure chance of still getting at least 1 natural 20 with 7d20 is something like this:

(19/20)^3 * (1/20) * 7 = 0.30008
~ 30%

Is this right? It can't be, it is way too high. After all every roll is more or less a 1 in 20 chance in itself?
Please help me out, I haven't skilled math sufficiently =(. I don't think I properly adjusted the formula.



The Char most likely will start around 8th level.


Zen Archer Qigong Monk 8 (human)

Str 14
Dex 14
Con 14
Int 8
Wis 22
Cha 7


F=Feat, normal
B=Feat, bonus
H=Feat, human

Traits: Exile and reactionary = +4 Initiative Or Reactionary and resilient = +2 Initiative +1 Fort saves.
01H: Lightening Reflexes
01F: Toughness OR Improved Initiative ?
01B: Precise Shot
02B: Pointblank Shot
03F: Deadly Aim
5F: Defensive Combat Training
6B: Improved Precise Shot
7F: Vital Strike
9F: Clustered Shots
10B: Improved Critical
11F: Hammer the Gap OR take it at 17th and take something better?
13F: Stunning fist
14B: Dodge, Shot on the run, Deflect Arrows? / Pin point targeting
15F: Improved Vital Strike
17F: Mantis Style?
18B: Combat Reflexes? Lol
19F: Touch of serenety???

Maybe sub something for monkey style somewhere?

Skills:
Acrobatics max
Stealth max
Perception max
Climb, Sense motive shared +maybe some heal?

[Drelua]

In my opinion, just don't bother with Pinpoint Targeting. It's a standard action instead of a full-round, but the main time you'd be attacking as a standard is when you moved, and you can't use it in that case. It's going to be extremely rare that a monster has so much of a difference between its touch and normal AC that you'll be more likely to hit with one touch attack than a flurry of normal attacks, so the only time I can see this being useful is when you have to draw your bow and then take a shot, and I don't think it's worth it for that much of a corner case, especially when you could draw as part of a move to reposition yourself. Plus, by level 10 you could afford a few brilliant energy arrows if you really wanted to make touch attacks, or you could get scorching ray as an SLA with the qinggong archetype.

Of course, I don't have much direct experience with the feat, but the one time I did see it in action was pretty pathetic. The DM told me 'this guy uses pinpoint targeting,' so I said 'okay, I use deflect arrows:smallamused:.' I ended up taking a two or three rounds of full attacks from four of those guys and not getting hit once.

[meschlum]

You do indeed roll 7 dice, and a 20 on any of them means you have a critical threat.

The likelihood of NOT rolling a threat is what you're after: it's (19/20)^7 ~ 69.8%. The rest of the time, you've rolled one or more twenties, so you have a critical threat coming. That's 30.2%.

Given that you have a threat, the outcomes depend on whether it's from your 'Perfect' attack or not.

For a normal attack, your odds of hitting are p (from 5% (need a 20) to 95 (automiss on a 1)). So you really have p/20 of scoring a critical, which means you get (1 - p/20)^4 of scoring no criticals with four normal attacks (and 1 - (1 - p/20)^4 of scoring at least one critical).

For your perfect attack, you need one 20 and one die that confirms the threat.

That's 1 - (19/20)^3 of getting a 20, and given that you have a 20, the other two dice could be anything. You'll fail to confirm (1-p)^2 of the time, so you do confirm with probability 2p - p^2.

So your perfect attack fails to get a critical 1 - (1 - (19/20))^3*p*(2-p) of the time (threat * probability of confirming).


Multiply the probabilities of getting no criticals from your normal and 'perfect' attacks, and you have your odds of scoring no criticals.

Take one minus the chance of scoring no criticals, and you get your odds of scoring at least one.


Of course, this all assumes you use the same base attack bonus on all your attacks - or the likelihood of scoring a critical goes down, as p is decreased from one attack to the next.


As a first order approximation, you can just use 30% * p, on the principle that you're going to threaten only one critical from your flurry, and it'll probably be for one of your normal attacks.

A slightly better guestimate is that there is a 4/7 chance that your (assumed single) threat will be from your 'normal' attacks and 3/7 that it will be for your 'perfect' one, which has a better chance of confirming, so you get 30% * (p + 3 p * (1 - p) / 7)), which is a bit more (and gets to its highest level when p = 1/2).

Good luck!


Math aside, the odds of rare events happening are can be counter-intuitive. That said, 30% is reasonable: you'd expect to get one threat when rolling 20 dice, so when you roll 7 (about one third of 20), you have close to a one in three chance of getting a 20 (30% instead of 33% from 1/3, or 35% from 7/20).

[Dimcair]

Thanks meschlum, I rest assured, also thanks for the calculations on the chances of confirming the threat!


Drelua, you are right. Somehow I didn't realize that. I thought about surprise rounds or situations in which the AC of the monster is too high for me to reach it. But a surprise round might be better spend in just proper positioning/buffing than with a single attack. That gives me an additional featslot to think about. Appreciate it.


Since the math problem is off my back I would be happy to hear some more critique and improvement suggestions =).

[Drelua]

Okay, let me take a look at your feats. First off, I wouldn't really bother with Lightning Reflexes. As a monk, you'll probably not be failing many reflex saves, plus reflex is probably the least important save. At level 9 you'll be taking half damage even if you fail, and the effects of of Fortitude or Will saves tend to be worse. It looks like you've mostly made the right choices with your Monk bonus feats, there's really nothing great for the later levels, although you might want to ask your DM to let your Reflexive Shot ability and Flurry qualify you for Improved Snap Shot (http://www.d20pfsrd.com/feats/combat-feats/improved-snap-shot-combat) instead of Snap Shot and Rapid Shot, and if he says yes take Combat Reflexes a bit earlier. Threatening out to 15 feet makes you pretty dangerous to reach.

I wouldn't bother with Hammer the Gap since that bonus isn't getting very big and it relies on you attacking the same guy. Vital Strike probably isn't worth it either, since it only multiplies the damage die, so it's only another d8 and I think it only works on a standard action. I played a Zen Archer once, though he died at level 2, and they seemed to have the opposite problem from most archers; more feats than you know what to do with. You might consider taking Crane Style, although you should ask your DM if he'll be enforcing the errata that nerfs Crane Wing into the ground. If he is, you'd probably be better off going with Monkey Style instead. Since Mantis Style requires Stunning Fist, that wouldn't really work.

Oh, and I'm just wondering about your traits, where's exile from? It's probably a trait bonus, which means it wouldn't Stack with Reactionary. Other than that, you should be good. There's a couple magic items you might be interested in, the Ki Mathttp://www.d20pfsrd.com/magic-items/wondrous-items/wondrous-items/h-l/ki-mat and the Ring of Ki Mastery (http://www.d20pfsrd.com/magic-items/rings/ring-of-ki-mastery). They'll both make your ki powers last a lot longer. You might also want to get a Conductive (http://www.d20pfsrd.com/magic-items/magic-weapons/magic-weapon-special-abilities/conductive) bow to get better use out of your Scorching Ray.

Anyway, I hope all that helps!

[Spore]

I am not into probability like I was some years ago but my general math "sense" tells me that DOUBLING a crit chance on every roll is preferrable. Your attack bonus while flurrying should be high enough to even hit people in much armor (unless the AC values reach 40+ regularly in your games like on a CR 15 dragon).

One option would certainly contain taking Pinpoint at 10 and Improved Critical on 11 since the first one ignores prerequisites and Pinpoint Targetting is nice vs. high AC enemies.

[Dimcair]

Okay, let me take a look at your feats. First off, I wouldn't really bother with Lightning Reflexes.


ask your DM to let your Reflexive Shot ability and Flurry qualify you for Improved Snap Shot (http://www.d20pfsrd.com/feats/combat-feats/improved-snap-shot-combat) instead of Snap Shot and Rapid Shot, and if he says yes take Combat Reflexes a bit earlier. Threatening out to 15 feet makes you pretty dangerous to reach.

Vital Strike probably isn't worth it either, since it only multiplies the damage die, so it's only another d8 and I think it only works on a standard action.

Scorching Ray



Thanks!
Lightning Reflexes was taken as I lose evasion and improved evasion as a Zen Archer. I thought it might be worth it.

I will ask my DM about the Improved Snap Shot Issue. I've read about this before and it would be very sad if I can't qualify.

Vital strike can be valuable since I can use my Unarmed Strike dice for damage on 1 attack. That is 1d10 at level 8. Vital strike would mean I could do 2d10 instead. At least it is an option for when I need to move or if I only have a standard action. Together with pinpoint targeting it makes a quite save 2d10+strength damage but I might overvalue it. At 15th (Should I ever get there) with Improved Vital strike I would roll 6d6 + modifiers.

About Scorching Ray: I haven't switched High Jump out yet, should I switch it out for Scorching Ray? What is the selling point of scorching ray? Just the damage on a touch attack? Or is it that it can be done as a swift action? oO


Thanks sporeegg for pointing out something obvious I should have seen =D. The only downside would be that I have limited bonus feats to choose from but I suppose there are some I can take anyway.

[Drelua]

Right, I forgot Zen Archers lose evasion. It might be worth getting a ring of evasion, but it's still probably not worth worrying too much about your reflex save.

About scorching ray, have you traded out slow fall yet? The main draw of scorching ray is that it's so easy to get, you just have to trade out an ability that's way less useful than a ring that only costs 2,200 gold. That and barkskin are the main abilities you'd want at low levels because while high jump is pretty cool, it's not all that useful; your acrobatics modifier is already probably good enough, especially with the bonus you get on jump checks for a high speed. Gaseous form's another good one if you want to trade out wholeness of body, since 2 ki points to heal damage equal to your level is a bit steep, though that's mitigated by the ring of ki mastery.

I still don't really think vital strike is worth it since it's only a couple extra dice and Ki Arrows lasts until your next turn, so you could be making a full attack with your unarmed strike damage. I think the idea behind vital strike was that you'd be rolling the same number of dice with a full attack if all your attacks hit, but losing all your modifiers to damage really isn't worth it, especially when you could be making more than one attack at your highest bonus thanks to flurry. You're effectively two-weapon fighting, which means you can get twice as many attacks as the feat was designed around. It's really not worth worrying too much about standard action attacks when you have a range of about 100 feet and you can have your bow in your hand most of the time, it's pretty rare that an archer can't manage a full attack.

One thing worth noting is that depending on your reading of Flurry and Deadly Aim, you might have different bonuses and penalties when you're flurrying. At level 8, for example, your BAB is 6, so you'd take -2 to hit for 4 damage, but when you flurry your BAB is effectively 8, so I believe you'd take -3 to hit for 6 damage, though some people disagree with me on that.

[Dimcair]

Right, I forgot Zen Archers lose evasion. It might be worth getting a ring of evasion, but it's still probably not worth worrying too much about your reflex save.

About scorching ray, have you traded out slow fall yet? The main draw of scorching ray is that it's so easy to get, you just have to trade out an ability that's way less useful than a ring that only costs 2,200 gold. That and barkskin are the main abilities you'd want at low levels because while high jump is pretty cool, it's not all that useful; your acrobatics modifier is already probably good enough, especially with the bonus you get on jump checks for a high speed. Gaseous form's another good one if you want to trade out wholeness of body, since 2 ki points to heal damage equal to your level is a bit steep, though that's mitigated by the ring of ki mastery.

I still don't really think vital strike is worth it since it's only a couple extra dice and Ki Arrows lasts until your next turn, so you could be making a full attack with your unarmed strike damage. I think the idea behind vital strike was that you'd be rolling the same number of dice with a full attack if all your attacks hit, but losing all your modifiers to damage really isn't worth it, especially when you could be making more than one attack at your highest bonus thanks to flurry. You're effectively two-weapon fighting, which means you can get twice as many attacks as the feat was designed around. It's really not worth worrying too much about standard action attacks when you have a range of about 100 feet and you can have your bow in your hand most of the time, it's pretty rare that an archer can't manage a full attack.

One thing worth noting is that depending on your reading of Flurry and Deadly Aim, you might have different bonuses and penalties when you're flurrying. At level 8, for example, your BAB is 6, so you'd take -2 to hit for 4 damage, but when you flurry your BAB is effectively 8, so I believe you'd take -3 to hit for 6 damage, though some people disagree with me on that.

Ah there are ring of evasions. Who knows, maybe I will get my hands on one. (Altough my DM doesn't allow magic marts^^).
If I would switch it out, I would prolly go for a fortitude save? Since my Wis should be high enough.

Slow fall is traded for bark skin.

High Jump was kept since I thought it could get me out of nasty situations with the running start. But Scorching ray seems too yummy.

Wholeness of body I was going to switch out at level 8 for restoration (http://www.d20pfsrd.com/magic/all-spells/r/restoration). But if that is useful will depend on the evilness of my DM I guess. It can get rid of some no safe debuffs. Gaseous form is a strong other option I considered.

I see your point with vital strike. It seems a waste to spend 1 Ki on just 1 improved attack (that might fail if I dont have pinpoint targeting). It might be kind of dependent on monks robe, which lets you treat your unarmed attacks damage dice as if you were a monk 5 levels higher.

Do you see any other options though of milking a standard action when I can't full attack? Btw I think you got something wrong or we are misunderstanding each other, vital strike doesn't lose you your damage modifiers. I also get your point that it should be easy to get full attack as a ranged character, still I would like something to fall back to =D. And I have to spend SOME feats there if I can't get imprv. snap shot allowed.

I agree with you on deadly aim. -3 +6 is how I calculated it as well.

Cheers

[Drelua]

Slow Fall for Barkskin is a solid choice, maybe better than Scorching Ray, I'm not sure. Restoration is another good option, though unfortunately I believe you have to swap the abilities out at the level you get them, so you wouldn't be able to trade Wholeness of Body at 7th level for Restoration at 8th.

Sorry, didn't mean to say that you lose your damage modifiers with Vital Strike, just that they only get counted once, so you're probably losing out on a fair bit of damage compared to a full attack and not gaining too much even compared to a standard. If you really want something to do as a standard action other than just a single attack, you could look for a good offensive ki power, maybe Dragon's Breath later on or Hydraulic Torrent.

[Dimcair]

Slow Fall for Barkskin is a solid choice, maybe better than Scorching Ray, I'm not sure.

Restoration is another good option, though unfortunately I believe you have to swap the abilities out at the level you get them, so you wouldn't be able to trade Wholeness of Body at 7th level for Restoration at 8th.



I mean I can still switch High Jump for Scorching Ray, that also gives me something to do in a standard attack. I think activating it would be a standard action, even if it is not clearly stated.

For switching out powers later, I can't find anything conclusive that forbids it.