Aim vs. Rapid Shot vs. neither

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lukep
Sher'Tul Godslayer
Posts: 1712
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Aim vs. Rapid Shot vs. neither

#1 Post by lukep »

EDIT: http://anydice.com/ can do proper shots to kill, using:

Code: Select all

function: shots A from B{
C: (10 - (A>B) - (A+A>B) - (A+A+A>B) - (A+A+A+A>B) - (A+A+A+A+A>B) - (A+A+A+A+A+A>B) - (A+A+A+A+A+A+A>B) - (A+A+A+A+A+A+A+A>B) - (A+A+A+A+A+A+A+A+A>B) - (A+A+A+A+A+A+A+A+A+A>B))
result:C
}

X: (100 * (99 + 1d41)) * (100 + 50 * (1d100<10))/10000

output [shots X from 1200]
I decided to test the relative differences in damage output between Aim, Rapid Shot, and using neither of them. Note that I did not include ammo consumption, accuracy, APR, or talent use in this comparison.

Damage per hit = (char sheet display) * (1.2 for damage range) * (100% + 1/2 crit rate) + damage on hit total

Damage per turn = DPH * (1/shot time)

baseline: lvl 50 archer, 60 STR, DEX, CUN, lvl 1 bow mastery, level 6.5 talents, non-ego Dragonbone longbow, non-ego 56 base power dragonbone arrows.

baseline
Normal: 82 * 1.2 * 1.09 +0 = 107.3 damage per hit * 1/0.8 = 134.1 damage per turn (100% of normal)
Aim: 93 * 1.2 * 1.32 + 0 = 147.3 damage per hit * 1/1.0666 = 138.1 damage per turn (103% of normal)
Rapid: 82 * 1.2 * 1 + 0 = 98.4 damage per hit * 1/0.4848 = 203.0 damage per turn (151% of normal)

-baseline, with +40 damage on hit elemental arrows:
Normal: 82 * 1.2 * 1.09 +40 = 147.3 damage per hit * 1/0.8 = 184.1 damage per turn (100% of normal)
Aim: 93 * 1.2 * 1.32 + 40 = 187.3 damage per hit * 1/1.0666 = 175.3 damage per turn (95% of normal)
Rapid: 82 * 1.2 * 1 + 40 = 138.4 damage per hit * 1/0.4848 = 285.5 damage per turn (155% of normal)

-baseline, with lvl 10 bow mastery:
Normal: 129 * 1.2 * 1.09 +0 = 168.7 damage per hit * 1/0.8 = 210.9 damage per turn (100% of normal)
Aim: 140 * 1.2 * 1.32 + 0 = 221.8 damage per hit * 1/1.0666 = 207.9 damage per turn (99% of normal)
Rapid: 129 * 1.2 * 1 + 0 = 154.8 damage per hit * 1/0.4848 = 319.3 damage per turn (152% of normal)

Aim is still useful at conserving ammo, using talents more efficiently, and against heavily armoured and high DEF enemies, but Rapid Shot is clearly superior at killing enemies when you are not facing those restrictions. Thoughts/comments?
Last edited by lukep on Sun Dec 30, 2012 7:53 pm, edited 4 times in total.
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bricks
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Re: Aim vs. Rapid Shot vs. neither

#2 Post by bricks »

A few thoughts:

One, sustains aren't that fun, especially when you need to micro-manage them. I understand why they are needed in this case, but they feel like a really strained attempt at making a fundamentally boring class interesting.

Two, you mentioned a lot of factors that aren't considered in this comparison, but I think you missed the biggest one - kill power. If Aim lets me kill an enemy in fewer turns, then it is much more valuable.

Three, speed-altering abilities are awkward to use. Skills like Aim or Rapid Fire makes more sense in a real-time or action-point time system. The movement restriction is barely noticeable, unless something totally unexpected jumps you. I've never found kiting to be a viable strategy in ToME (or most roguelikes, for that matter).

And four - it wouldn't surprise me if Rapid Fire really is the best choice at max level, when you are loaded down with great gear and lots of talent choices. Aim is great in those dungeon-style zones, which mostly show up earlier in the game.

I don't really know what should be done. Skills that interacted more with the new reloading mechanic would probably be good replacements. Also, a skill that actually allowed you to kite would be nice. Maybe not a sustain; more like range-1 Disengage + a regular shot on a short cooldown (although that sounds really familiar, maybe I'm forgetting a talent that already does that?).
Sorry about all the parentheses (sometimes I like to clarify things).

phantomglider
Archmage
Posts: 372
Joined: Fri Jan 20, 2012 12:13 am

Re: Aim vs. Rapid Shot vs. neither

#3 Post by phantomglider »

bricks wrote: Also, a skill that actually allowed you to kite would be nice. Maybe not a sustain; more like range-1 Disengage + a regular shot on a short cooldown (although that sounds really familiar, maybe I'm forgetting a talent that already does that?).
Marauder's Hack 'n' Back is basically this, but as a melee attack.
<Ferret> The Spellblaze was like a nuclear disaster apparently: ammo became the "real" currency.

donkatsu
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Re: Aim vs. Rapid Shot vs. neither

#4 Post by donkatsu »

The entire point of the original post was that Aim has less "kill power" than Rapid Shot, under the stated restrictions. As in, you will kill things in fewer turns with Rapid Shot according to the given data. Not quite sure what you're getting at here.

If by kiting you mean attacking, running away for a few turns, then attacking again, then kiting is often an excellent strategy in ToME. Surely you don't just stay in one spot until everything around you is dead? For me, that has only ever been a consistently viable strategy as an Archmage.

Anyway, I did some more calculations thinking that the addition of factoring in Steady Shot would greatly skew the balance in favor of Aim, but that appears not to be the case. The assumption is that Steady Shot is on a 2 turn cooldown (due to whatever that bow ego is called), and it is at level 6.5, doing 235% damage.

235% every 2 turns = +135% / 2 weapon damage per turn
Steady DPT = DPT + 1.35 * (DPH - damage on hit) / 2

baseline
Normal: 134.1 + 1.35 * (107.3 - 0) / 2 = 206.5 (100% of normal)
Aim: 138.1 + 1.35 * (147.3 - 0) / 2= 237.5 (115% of normal)
Rapid: 203.0 + 1.35 * (98.4 - 0) / 2= 269.4 (130% of normal)

-baseline, with +40 damage on hit elemental arrows:
Normal: 184.1 + 1.35 * (147.3 - 40) / 2 = 256.5 (100% of normal)
Aim: 175.3 + 1.35 * (187.3 - 40) / 2 = 274.7 (107% of normal)
Rapid: 285.5 + 1.35 * (138.4 - 40) / 2 = 351.9 (137% of normal)

-baseline, with lvl 10 bow mastery:
Normal: 210.9 + 1.35 * (168.7 - 0) / 2 = 324.8 (100% of normal)
Aim: 207.9 + 1.35 * (221.8 - 0) / 2 = 357.6 (110% of normal)
Rapid: 319.3 + 1.35 * (154.8 - 0) / 2 = 423.8 (130% of normal)

bricks
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Re: Aim vs. Rapid Shot vs. neither

#5 Post by bricks »

My point is that you aren't shooting a target with an infinite amount of health. If Rapid Fire makes me shoot faster but take more game turns to kill something, I'm not sure why I'd use it. Whether or not Aim is preferable over Rapid Fire is not an easy question in light of constantly shifting damage-to-enemy health ratios, and more of a math problem than an interesting tactical choice.

Regarding kiting - what I'm talking about is the same philosophy that bows/slings had for increased attack speed. Attacking faster doesn't allow you to kite, it just means you get more hits in.
Sorry about all the parentheses (sometimes I like to clarify things).

donkatsu
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Re: Aim vs. Rapid Shot vs. neither

#6 Post by donkatsu »

lukep wrote: Normal: 82 * 1.2 * 1.09 +0 = 107.3 damage per hit * 1/0.8 = 134.1 damage per turn (100% of normal)
Aim: 93 * 1.2 * 1.32 + 0 = 147.3 damage per hit * 1/1.0666 = 138.1 damage per turn (103% of normal)
Rapid: 82 * 1.2 * 1 + 0 = 98.4 damage per hit * 1/0.4848 = 203.0 damage per turn (151% of normal)
Emphasis added. Rapid Fire does more damage per game turn, therefore it takes fewer game turns to kill something. Again, I'm not sure what's confusing you so much. The amount of health the target has is irrelevant to whether Aim or Rapid Fire is better, unless you factor in overkill (and thus, wasted damage) which actually favors Rapid Fire. The bottom line is, given the assumptions outlined by lukep, Rapid Fire makes you shoot faster AND kill things in fewer game turns, as clearly shown in his calculations.

As for kiting, I was responding to your claim that kiting is not a viable tactic. It is, but as you point out, attack speed is irrelevant to kiting. So use a movement infusion or a controlled phase door rune.

phantomglider
Archmage
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Re: Aim vs. Rapid Shot vs. neither

#7 Post by phantomglider »

I think the problem with this argument is that there are two meanings to "turn" here - there's the times when the game is stopped and you get the opportunity to choose an action, and there's the game's internal measurement of turns as measured by things like poisons ticking, abilities cooling down, and enemies acting. The two are not the same thing, as can be seen by turning on a movement infusion and watching a one-game-turn movement speed buff last through multiple movement actions. Rapid Shot makes killing things take more real-world actions, but fewer in-game turns.
<Ferret> The Spellblaze was like a nuclear disaster apparently: ammo became the "real" currency.

bricks
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Re: Aim vs. Rapid Shot vs. neither

#8 Post by bricks »

I'm sorry, donkatsu, you are correct. No idea what I was thinking.
Sorry about all the parentheses (sometimes I like to clarify things).

ohioastro
Wyrmic
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Re: Aim vs. Rapid Shot vs. neither

#9 Post by ohioastro »

I have two skills. One makes me shoot faster and have a higher chance of missing.
The other makes me shoot slower and hit harder. This post shows that If I neglect
the "higher chance of missing" part and the extra resource consumption I'm stacking the deck.
If I take extra turns to reload, or if I miss more, then the notional advantage vanishes.
If I don't hit as hard I also can have problems with threshold damage barriers.

It's nice that there is a theoretical window where things can work, but I'm not confident that these assumptions are accurate.

lukep
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Re: Aim vs. Rapid Shot vs. neither

#10 Post by lukep »

To those that are (rightly) questioning how applicable my methodology was, I present "player", the level 50 cornac archer. I cheat-leveled to 50, teleported to the bottom of Dreadfell, and generated 20 purples for each equipment slot, choosing the best (subjective, biased towards more damage) of each set. Here are the results:

relevant stats (unchanging): +14% physical damage, 228% crit multiplier, 29 capacity quiver, 6 reloads per turn, 30 damage on hit

Damage per hit = (char sheet display) * (1.2 for damage range average) * (1.00 + 1.28 * crit rate) * physical damage mult + damage on hit total

Normal: 168 * 1.2 * 1.24 * 1.14 + 30 = 315 damage per hit * 1/0.8 = 394 damage per turn
Aim: 179 * 1.2 * 1.99 * 1.14 + 30 = 517 damage per hit * 1/1.0667 = 485 damage per turn
Rapid Shot: 163 * 1.2 * 1 * 1.14 + 30 = 259.8 damage per hit * 1/0.4848 = 536 damage per turn

Anything with 38 or less armour and 44 or less DEF still is always hit for full damage by rapid shot.

Now, against some enemies (note, I won't be showing my work anymore, if you are curious, just ask).
Shots to kill = average damage per shot / HP, rounded up.

Orc Berserker: 1250 HP, 23/55% armour, 17 DEF, 10% crit reduction
Normal: 286 damage per hit, 5 shots to kill, 4 turns to kill
Aim: 485 damage per hit, 3 shots to kill, 3.2 turns to kill
Rapid: 260 damage per hit, 5 shots to kill, 2.424 turns to kill.

Patchwork Troll: 2500 HP, 60/30% armour, 17 DEF, 0% crit reduction
Normal: 287 damage per hit, 9 shots to kill, 7.2 turns to kill
Aim: 516 damage per hit, 5 shots to kill, 5.33 turns to kill
Rapid: 223 damage per hit, 12 shots to kill, 5.81 turns to kill

Orc High Cryomancer: 1200 HP, 0/30% armour, 9 DEF, 0% crit reduction
Normal: 316 damage per hit, 4 shots to kill, 3.2 turns to kill
Aim: 516 damage per hit, 3 shots to kill, 3.2 turns to kill
Rapid: 253 damage per hit, 5 shots to kill, 2.424 turns to kill

This is a much more thorough analysis, though I still left off talent use and other build options.

EDIT to add commentary: This turned out much more even than I was initially thinking. Aim scales better than Rapid Shot with equipment that boosts some stats (dex, crit rate, crit multiplier), and slightly worse with others (STR/physical power, damage on hit). I believe that a build that focused on defensive options rather than kill power would take a bigger hit to Aim damage per turn than to Rapid Shot damage, due to lowered crit rate and smaller bonuses from Aim from lower DEX.

Character Dump (not validated, obviously) (also, disregard the high HP and +all damage, they do not affect the results).

Code: Select all

  [ToME4 @ www.te4.org Character Dump]

Sex              : Male         STR:  84
Race             : Cornac       DEX:  79
Class            : Archer       MAG:  10
Level            : 50           WIL:  19
Exp              : 0%           CUN:  20
Gold             : 1444.74      CON:  71

Accuracy(Main Hand):  70        Life             :     100244/100244Encumbrance      : 95/191
Damage  (Main Hand): 168        Stamina          :     270/270  Difficulty       : Normal
Permadeath       : Adventure
APR     (Main Hand):  38        
Crit    (Main Hand):  19%       
Speed   (Main Hand): 0.80       
Range (Main Hand):  11          
                                
                                

Fatigue          : 18%          Spellpower       : 10
Armor            : 21           Spell Crit       : 4%
Armor Hardiness  : 30%          Spell Speed      : 1
Defense          : 28.075       
Ranged Defense   : 28.075       
All damage       : 100000%
Physical damage  : 100014%

Physical Save    : 42.75
Spell Save       : 11.15
Mental Save      : 18.65

All Resists:  15%
Arcane Resist(cap):  -5%( 70%)
Fire Resist(cap):  30%( 70%)
Cold Resist(cap):  34%( 70%)
Lightning Resist(cap):  32%( 70%)
Acid Resist(cap):  26%( 70%)
Confusion Resistance:  38%
Disarm Resistance:  46%
Pinning Resistance:  10%

Number of NPC killed: 65
Most killed NPC: dread (14)

  [Talents Chart]

 - Technique / Archery - bows         (mastery 1.30)
    Bow Mastery (class)               10/10
    Piercing Arrow (class)            0/5
    Dual Arrows (class)               0/5
    Volley of Arrows (class)          0/5
 - Technique / Archery - slings       (mastery 1.30)
    Sling Mastery (class)             0/10
    Eye Shot (class)                  0/5
    Inertial Shot (class)             0/5
    Multishot (class)                 0/5
 - Technique / Archery training       (mastery 1.30)
    Steady Shot (class)               5/5
    Aim (class)                       5/5
    Rapid Shot (class)                5/5
    Relaxed Shot (class)              0/5
 - Technique / Archery prowess        (mastery 1.30)
    Flare (class)                     1/5
    Crippling Shot (class)            0/5
    Pinning Shot (class)              0/5
    Scatter Shot (class)              0/5
 - Technique / Field control          (mastery 1.00)
    Disengage (generic)               0/5
    Track (generic)                   0/5
    Heave (generic)                   0/5
    Slow Motion (generic)             0/5
 - Technique / Combat veteran         (mastery 0.90)
    Quick Recovery (class)            0/5
    Fast Metabolism (class)           0/5
    Spell Shield (class)              0/5
    Unending Frenzy (class)           0/5
 - Technique / Combat training        (mastery 1.30)
    Thick Skin (generic)              5/5
    Armour Training (generic)         10/10
    Combat Accuracy (generic)         10/10
    Weapons Mastery (generic)         0/10
    Knife Mastery (generic)           0/10
 - Cunning / Survival                 (mastery 1.00)
    Trap Handling (generic)           0/5
    Heightened Senses (generic)       0/5
    Piercing Sight (generic)          0/5
    Evasion (generic)                 0/5

  [Inscriptions (2/3)]

Infusion: Wild
Infusion: Regeneration

  [Current Effects]


  [Character Equipment]

 In main hand
a) thaloren dragonbone longbow of true flight
   Type: weapon / longbow
It must be held with both hands.

Physical crit. chance: +6.0%
Attack speed: 80%
Firing range: +11
Travel speed: +200%
When wielded/worn:
Changes damage: +14% physical
Talents cooldown: Volley of Arrows (-2 turns) Steady Shot (-1 turn) Pinning Shot (-1 turn)

 In off hand
 On fingers
b) gladiator's voratun ring of warding
   Type: jewelry / ring

When wielded/worn:
Physical power: +9
Changes stats: +6 Str / +6 Con
Changes resistances: +9% fire / +11% cold / +11% lightning / +7% acid

c) gladiator's voratun ring of warding
   Type: jewelry / ring

When wielded/worn:
Physical power: +9
Changes stats: +7 Str / +5 Con
Changes resistances: +9% fire / +11% cold / +9% lightning / +6% acid

 Around neck
d) warmaker's voratun amulet of murder
   Type: jewelry / amulet

When wielded/worn:
Accuracy: +8
Armour penetration: +5
Physical crit. chance: +4.0%
Changes stats: +6 Str / +6 Dex / +4 Wil
Changes resistances: -23% arcane
Critical mult.: +14.00%
Spell save: -8

 Light source
e) nightwalker's alchemist's lamp of illusion
   Type: lite / lite

When wielded/worn:
Physical crit. chance: +3.0%
Physical power: +5
Defense: +4
Changes stats: +3 Wil
Physical save: +9
Spell save: +9
Mental save: +5
Light radius: +3

 Main armor
f) marauder's drakeskin leather armour of Toknor (5 def, 8 armour)
   Type: armor / light

When wielded/worn:
Physical crit. chance: +3.0%
Physical power: +5
Armour: +8
Defense: +5
Fatigue: +8%
Changes stats: +3 Str / +3 Dex
Critical mult.: +13.00%
Physical save: +5
Disarm immunity: +15%

 Cloak
g) murderer's elven-silk cloak of warlust (3 def, 0 armour)
   Type: armor / cloak

When wielded/worn:
Accuracy: +5
Armour penetration: +7
Physical crit. chance: +2.0%
Physical power: +3
Defense: +3
Changes stats: +3 Cun / +4 Dex
Disarm immunity: +6%
Confusion immunity: +13%

 On head
h) champion's voratun helm of trickery (0 def, 5 armour)
   Type: armor / head

When wielded/worn:
Armour penetration: +5
Armour: +5
Fatigue: +5%
Changes stats: +2 Str / +3 Dex / +2 Wil / +3 Cun
Confusion immunity: +15%
Light radius: +1

 Around waist
i) monstrous drakeskin leather belt of recklessness
   Type: armor / belt

When wielded/worn:
Physical power: +10
Critical mult.: +21.00%
Disarm immunity: +10%
Confusion immunity: +10%
Size category: +1

 On hands
j) archer's voratun gauntlets of mighty criticals (0 def, 3 armour)
   Type: armor / hands

When wielded/worn:
Accuracy: +8
Armour: +3
Changes stats: +2 Cun / +3 Dex
Critical mult.: +30.00%

 On feet
k) blood-soaked pair of drakeskin leather boots of invasion (0 def, 5 armour)
   Type: armor / feet

When wielded/worn:
Armour penetration: +3
Physical crit. chance: +1.0%
Physical power: +6
Armour: +5
Fatigue: +5%
Changes resistances penetration: +5% physical
Disarm immunity: +15%
Pinning immunity: +10%

 Tool
l) overpowered ash totem of cure illness [power 3]  (34 cooldown)
   Type: charm / totem

It can be used to removes up to 3 diseases from the target, placing all other charms into a 34 cooldown.
   Dropped by Sandworm Queen
 Quiver
m) battle-ranger's quiver of dragonbone arrows of the elements (29/29, 53.5-74.9 power, 18 apr)
   Type: ammo / arrow

Base power: 53.5 - 74.9
Uses stats: 70% Dex, 50% Str
Damage type: Physical
Armour Penetration: +18
Physical crit. chance: +3.0%
Capacity: 29
Damage when this weapon hits(ranged): +9 acid / +7 lightning / +7 ice / +7 fire
When wielded/worn:
Ammo reloads per turns: +2
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Melee Talent Creator
Annotated Talent Code (incomplete)

jenx
Sher'Tul Godslayer
Posts: 2263
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Re: Aim vs. Rapid Shot vs. neither

#11 Post by jenx »

is this analysis still valid in b42?
MADNESS rocks

lukep
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Location: Canada

Re: Aim vs. Rapid Shot vs. neither

#12 Post by lukep »

jenx wrote:is this analysis still valid in b42?
Pretty much. Neither Aim nor Rapid Shot have changed (IIRC), but egos may have, and there is still the issue of talent use (and that I didn't do proper statistical work, just averages).
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Annotated Talent Code (incomplete)

Hunter
Uruivellas
Posts: 638
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Re: Aim vs. Rapid Shot vs. neither

#13 Post by Hunter »

Maybe this is s stupid question, but wouldn't omitting ammo usage issues (as you said you did) seriously skew the analysis when dealing with the most powerful enemies? It's one thing if we're dealing with the trolls and cryomancers that go down in less than a half-dozen shots (and there aren't any other enemies around.) If I run out of ammo when fighting a rare Eternal Bone Giant with a dozen emperor wights and master skeleton archers around, I'm going to be concerned about ammo, even if I have a high-capacity quiver. Kiting/fleeing, of course, are always going to be options, but they'll still be options either way. I get what the analysis is saying, and it seems to be an excellent point...when dealing with enemies within a certain range. One-shot kills, of course, don't need Rapid Shot, especially if Aim kills them in one shot and Rapid Shot doesn't. Dealing with really powerful enemies, especially ones with crowds might favor Aim as well, especially considering that you don't necessarily want to volley and eat up huge amounts of ammo while barely harming the most powerful opponent.

lukep
Sher'Tul Godslayer
Posts: 1712
Joined: Mon Mar 14, 2011 10:32 am
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Re: Aim vs. Rapid Shot vs. neither

#14 Post by lukep »

Omitting ammo didn't seem to be a big issue. With the setup above, the player could deal 7500 damage from full using Rapid Shot, and about 15000 using Aim. This is usually enough to kill an enemy, or at least to last you until you need to retreat (it takes about 5 turns to fully reload, during which you can do some other stuff)

Still, take it all with a grain of salt. There is still the huge omission of talent use, as Aim can use Steady Shot every 2-3 times, and Rapid Shot can use it every 4-7.
Some of my tools for helping make talents:
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Hunter
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Re: Aim vs. Rapid Shot vs. neither

#15 Post by Hunter »

Okay, gotcha. That's a lot of damage. I tend to get frustrated with archers (though I had a grand time with magebows until I started hitting the stronger dungeons and the incompleteness of the class tended to bog me down) so I've yet to reach the 15000 damage threshold. I tend to die in Dreadfell at the very latest.

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