Damage vs Accuracy

[Gordon]

Dropping down to dlvl 75, I ended up in a small rectangular room. Casting my usual mae, mdf and mcg, I saw no traps, no monsters and only one unknown item in the room. I sauntered over to take a look and saw a Mithril ring. At this point there were only 5 unknown rings, 4 of power and Tulkas. A Mithril ring sure sounded like...yes! Nenya! I can't believe I found it without having to fight my way through a horde of Pit Fiends. Now I can get rid of this shabby looking Hard Leather Cap of Thranduil and finally wear this beautiful Golden Crown of Gondor that I've been hauling around to occasionally protect me from confusion and stunning. I can also lose the Ring of Constitution <+6> that I have been wearing forever, it seems. And my Ring of Speed <+12> is pretty much redundant at this point. Not much difference between speed 34 hasted and speed 46 as far as I can see. This opens up a ring slot and hence my question.

I have two candidate rings, a Ring of Accuracy (+21,0) and a Ring of Damage (0,+15). I see that accuracy is dismissed a lot here, but looking in my monster memory at the Great Wyrm of Chaos, for instance, I see that by wielding the Ring of Accuracy, my chance to hit rises from 35% to 47%. When wielding the Ring of Damage, my sword does 348 damage per round against evil creatures. Multiplying this by 0.35 yields effective damage per round of 121.8. Meanwhile, wielding the Ring of Accuracy gives 292 damage per round. Multiplying by 0.47 yields 137.2 effective damage. The Ring of Accuracy has the additional benefit of fewer wasted shots when I use my bow. So how is it not advantageous to choose the Ring of Accuracy over the Ring of Damage?

[Derakon]

Your chance to hit sounds abysmal. Most characters have a chance to hit in the upper 60th percentile at minimum, and a Ring of Accuracy gives only 1-4% improvement in hit chance, not the 12% you're seeing.

Post a character dump? Something strange is going on.

[Gordon]

Perhaps it is due to the fact that @ is 2'10" and weighs only 13lb .

  [Angband 4.0.5 Character Dump]

 Name   Ringo        Age             24          Self  RB  CB  EB   Best
 Race   Hobbit       Height       2'10"   STR! 18/100  -2  -3 +13 18/180
 Class  Mage         Weight    3st 13lb   INT! 18/100  +2  +3  +6 18/210
 Title  Arch-Mage    Turns used:          WIS! 18/100  +1  +0 +10 18/210
 HP     825/825      Game       2164988   DEX! 18/100  +3  +0  +5 18/180
 SP     394/394      Standard    334507   CON! 18/100  +2  -2 +11 18/210
                     Resting      57125

 Level                 50    Armor     [78,+124]    Saving Throw    100%
 Cur Exp          7313706                           Stealth       Superb
 Max Exp          7313706    Melee       4d5,+57    Disarming       100%
 Adv Exp         ********    To-hit       33,+53    Magic Devices    131
                             Blows      4.0/turn    Perception    1 in 1
 Gold             2689831                           Searching        48%
 Burden          174.8 lb    Shoot to-dam    +15    Infravision    40 ft
 Overweight       -5.1 lb    To-hit       38,+44    Speed             24
 Max Depth    3750' (L75)    Shots        1/turn

 You are one of several children of a Hobbit Warrior.  You are a credit
 to the family.  You have hazel eyes, straight auburn hair, and an
 average complexion.


rAcid:......++*.... Nexus:.............
rElec:.+....+...... Nethr:....+........
rFire:.+....++.+... Chaos:........+....
rCold:++.*+.++.+... Disen:......+......
rPois:............. pFear:+.......+....
rLite:+........+... pBlnd:...+.....+...
rDark:....+.+...... pConf:.........+...
Sound:........+.... pStun:.........+...
Shard:............. HLife:...++.......+

Regen:++.++....+... Stea.:.......++..+.
  ESP:...+......... Sear.:..........+..
Invis:+..+.+...+... Infra:............+
FrAct:+..+....+.+.. Tunn.:.............
Feath:...+......++. Speed:+..+...+...+.
S.Dig:+............ Blows:.............
ImpHP:............. Shots:.............
 Fear:............. Might:.+...........
Aggrv:............. Light:+....+...+...


  [Character Equipment]

a) the Long Sword 'Ringil' (4d5) (+21,+24) <+10, +1>
     Dropped by Hoarmurath of Dir at 3500 feet (level 70)
     
     +10 speed.
     Slays demons (powerfully), trolls, undead, evil creatures.
     Branded with cold.
     Provides resistance to frost, light.
     Provides protection from fear.
     Cannot be harmed by acid.
     Blessed by the gods.  Slows your metabolism.  Speeds regeneration.
      Prevents paralysis.  Grants the ability to see invisible things. 
     
     Radius 1 light.
     
     When activated, it creates a frost ball with damage 100.
     Takes 136 turns to recharge at your current speed.
     Your chance of success is 98.6%
     
     Combat info:
     4.0 blows/round.
     Average damage/round: 401.6 vs. creatures not resistant to cold,
     509.2 vs. demons, 348 vs. trolls, 401.6 vs. undead, 348 vs. evil
     creatures, and 294 vs. others.
     
b) the Short Bow of Amrod (x4) (+12,+15) <+2>
     Conjured forth by magic at 2050 feet (level 41)
     
     +2 strength.
     +2 constitution.
     +2 shooting power.
     Provides resistance to lightning, fire, frost.
     Cannot be harmed by acid, fire.
     Speeds regeneration.  
     
c) a Ring of Damage (+0,+15)
     Taken from a chest found at 3500 feet (level 70)
     
d) the Ring of Adamant 'Nenya' (+3,+3) <+2, +5>
     Found lying on the floor at 3750 feet (level 75)
     
     +2 strength.
     +2 intelligence.
     +2 wisdom.
     +2 dexterity.
     +2 constitution.
     +5 speed.
     Provides immunity to frost.
     Provides protection from blindness.
     Cannot be harmed by lightning.
     Sustains intelligence, wisdom, constitution.
     Feather Falling.  Speeds regeneration.  Prevents paralysis. 
     Sustains your life force.  Grants telepathy.  Grants the ability
     to see invisible things.  
     
     When activated, it restores your experience to full.
     Takes 686 to 1020 turns to recharge at your current speed.
     Your chance of success is 93.7%
     
e) the Jewel 'Evenstar' <+2>
     Found lying on the floor in a pit at 2050 feet (level 41)
     
     +2 wisdom.
     Provides resistance to frost, dark, nether.
     Sustains wisdom, constitution.
     Speeds regeneration.  Sustains your life force.  
     
     When activated, it restores your experience to full.
     Takes 510 turns to recharge at your current speed.
     Your chance of success is 97.3%
     
f) the Star of Elendil <+3>
     Conjured forth by magic at 2650 feet (level 53)
     
     Cannot be harmed by fire.
     Grants the ability to see invisible things.  
     Radius 3 light.
     
     When activated, it maps the area around you.
     Takes 173 to 340 turns to recharge at your current speed.
     Your chance of success is 98.0%
     
g) the Mithril Plate Mail of Celeborn (-3) [65,+25] <+3>
     Found lying on the floor in a vault at 3500 feet (level 70)
     
     +3 strength.
     Provides resistance to acid, lightning, fire, frost, dark,
     disenchantment.
     Cannot be harmed by acid.
     
     When activated, it removes all non-unique monsters represented by
     a chosen symbol from the level, dealing you damage in the process.
     Takes 1700 turns to recharge at your current speed.
     Your chance of success is 97.3%
     
h) the Elven Cloak of L&Atilde;&ordm;thien [6,+20] <+4, +3, +2>
     Conjured forth by magic at 2050 feet (level 41)
     
     +4 intelligence.
     +4 wisdom.
     +3 stealth.
     +2 speed.
     Provides resistance to acid, fire, frost.
     Cannot be harmed by acid, fire.
     
     When activated, it restores your experience to full.
     Takes 850 turns to recharge at your current speed.
     Your chance of success is 97.3%
     
i) the Small Metal Shield of Thorin [5,+25] <+3, +4, -1>
     Dropped by Lugdush, the Uruk at 1100 feet (level 22)
     
     +3 strength.
     +4 constitution.
     -1 stealth.
     Provides immunity to acid.
     Provides resistance to sound, chaos.
     Provides protection from fear.
     Cannot be harmed by acid.
     Prevents paralysis.  
     
j) the Golden Crown of Gondor [0,+15] <+3, +2, +1>
     Dropped by a Patriarch at 2950 feet (level 59)
     
     +3 strength.
     +2 wisdom.
     +3 constitution.
     Provides resistance to fire, frost, light.
     Provides protection from blindness, confusion, stunning.
     Cannot be harmed by acid.
     Speeds regeneration.  Grants the ability to see invisible things. 
     
     Radius 1 light.
     
     When activated, it heals 500 hit points.
     Takes 850 turns to recharge at your current speed.
     Your chance of success is 97.3%
     
k) a Set of Alchemist's Gloves of Thievery (+6,+1) [0,+15] <+3, +4>
     Found lying on the floor in a vault at 2300 feet (level 46)
     
     +3 dexterity.
     +4 searching skill.
     Cannot be harmed by acid, fire.
     Feather Falling.  Prevents paralysis.  
     
l) a Pair of Leather Boots of Elvenkind [2,+11] <+3, +7>
     Dropped by Eöl, the Dark Elf at 2700 feet (level 54)
     
     +3 stealth.
     +7 speed.
     Cannot be harmed by acid, fire.
     Feather Falling.

[jevansau]

Looks like the worst case for melee - Hobbits have poor melee and mages are the worst.

I think the advice is - for classes that RELY on melee, damage vastly trumps accuracy.

[Gordon]

So perhaps it is conditional then. I'm normally a mhh sort of guy, but when it comes to dragons, I like to get up close and personal. I have observed that when they can use their teeth and claws, they are a lot less likely to breathe all sorts of nasty stuff at you.

[Philip]

The advice to choose Damage over Accuracy is, as jevansau noted, intended for characters capable of melee combat, and who have a lot of blows. As a mage you get 2/3 the advantage a warrior gets from a ring of damage, and your base accuracy is low enough that improving it has actual benefits. That said, watch out. Your character should never fight a Great Wyrm of Chaos or anything that has a similar AC in melee. These calculations would be better made on the type of monster you do end up fighting in melee as an end-game mage, who tend to have much lower AC, meaning your base accuracy is higher, meaning that increasing accuracy is probably less necessary/helpful.
The advice is also kind of a holdover from back when the effect of increased damage was immediately apparent, while the effect of increased accuracy was invisible.

Traditionally I would recommend using a different ring on a mage, except you have absolutely everything including stats, resists, abilities, speed covered quite nicely so you may as well go ahead and use the Accuracy ring. Just don't let it tempt you into actually using melee against anything even remotely threatening, whether it needs to die fast or is scary in melee.

EDIT: Written before I saw your post. Unless something has recently changed, dragons are in fact equally likely to breathe at you at all times. They are, on the other hand, going to do a lot more damage with their breaths in melee range than they would, say, 10 tiles away, since breath attenuation was implemented some time back. Note that other monsters, including Sauron and Morgoth, will also use spells at the same frequency in and out of melee. The only significant difference being in melee causes (outside of effects on breath damage) is that when their AI rolls not to cast a spell, they will hit you if in melee range and move towards you if not.

[Gordon]

Hmm, this is not what I have observed. When fighting dragons from a distance, they almost always breathe. When fighting at melee range they rarely breathe. It takes a long time to whittle them down with so little damage per round, but @ can take melee damage with 252 AC after mee, since they tend to miss often. So far @ has defeated 15 Great Wyrms with this strategy. Of course, I am using melee mainly to preserve mana here, so I do tend to throw in a few Mana Storms to help with the whittling.

[Gordon]

Another advantage of melee is that it tends to keep neighboring creatures asleep. As a Hobbit @ has enough stealth to be safe from anything that is not permanently awake, such as Zephyr Hounds and Quylthulgs. In fact, @ needs to walk up and bop a Great Wrym on the nose to get its' attention.

[Philip]

It is possible having a lot of AC helps make the melee damage of a Great Wyrm less scary (they are not particularly powerful), but it still stands that they are just as likely to breathe (I am quite certain), and their breaths do full damage, rather than the damage being reduced (of which I am entirely certain). Additionally, by taking dragons down slower, you give them a lot more time (which they can use to breathe) and because you are doing damage slowly, they remain capable of doing a lot of damage with their breaths for longer.

There are a lot of cognitive biases that come into play when playing angband, which has a lot of unintuitive probabilities and emotional baggage (you notice the third consecutive failed teleport a lot more when it makes you die etc.).

I don't know much about how monster awakeness works, and it's possible something changed with the tweaks to pathfinding and such, but last I recall, the only activities that really affected how monsters wake up or not was whether you had damaged them or shone a light in their direction. I doubt that melee is significantly quieter (especially when you factor in the extra time killing the monster takes) than spellcasting, in any case.

As for conserving mana, yeah, that's always nice to do. I recommend relying a bit more on devices to supplement mana, mages get a lot of bonus damage with those in current V. A wand of annihilation with a mage can consistently do around 300 damage a round, at range, with the only mana cost being recharging. Even rods would be likely to outdamage your melee, I think.

[Gordon]

I gave up on wands a long time ago. I had a Wand of Drain Life that I tried on a monster that had 840 HP and it only took it down 1 star per hit which I assume is 84 HP. This in spite of the fact that it claimed to do 150 HP damage and my device skill would raise that by some large percentage. I do have a Wand of Annihilation in my home that claims to do 250 HP damage and my device skill will currently raise that by 71 percent for presumably 427.5 HP damage. I'll give it a try to see if that is correct or not.