RoS vs RoD: math edition

[Sky]

 Name   Maethedir    Age            127          Self  RB  CB  EB   Best
 Race   High-Elf     Height        6'5"   STR! 18/100  +1  +3  +6 18/200
 Class  Warrior      Weight    12st 1lb   INT! 18/100  +3  -2 +20 18/***
 Title  Lord         Turns used:          WIS! 18/100  -1  -2 +15 18/***
 HP     1108/1108    Game        655019   DEX! 18/100  +3  +2  +7 18/***
 SP     0/0          Standard    111701   CON! 18/100  +1  +2 +10 18/***
                     Resting      22791

 Level                 47    Armor     [28,+131]    Saving Throw    100%
 Cur Exp          6608248                           Stealth       Superb
 Max Exp          6608248    Melee       5d6,+49    Disarm - phys.  100%
 Adv Exp          7000000    To-hit       97,+61    Disarm - magic   73%
                             Blows      5.2/turn    Magic Devices     83
 Gold              944332                           Searching        76%
 Burden          174.4 lb    Shoot to-dam    +13    Infravision    40 ft
 Overweight       -5.5 lb    To-hit       97,+52    Speed      44 (4.3x)
 Max Depth    4450' (L89)    Shots        1/turn

a) the Two-Handed Great Flail 'Lemed' (5d6) (+19,+18) <+2, +3, +4>
     Dropped by Lungorthin, the Balrog of White Fire at 4150 feet
     (level 83)
     
     +2 intelligence.
     +3 wisdom.
     +4 dexterity.
     +2 constitution.
     +3 tunneling.
     Slays undead (powerfully), dragons (powerfully), demons
     (powerfully), giants, trolls, orcs, animals, evil creatures.
     Branded with acid.
     Provides immunity to lightning.
     Provides resistance to acid, fire, cold, poison, shards.
     Cannot be harmed by acid, fire.
     Grants telepathy.  Grants the ability to see invisible things. 
     Prevents paralysis.  
     
     When activated, it heals 500 hit points.
     Takes 477 to 585 turns to recharge at your current speed.
     Your chance of success is 95.0%
     
     Combat info:
     5.2 blows/round.
     With +1 STR and +0 DEX you would get 5.5 blows
     Average damage/round: 606.4 vs. creatures not resistant to acid,
     825.2 vs. undead, 825.2 vs. dragons, 825.2 vs. demons, 606.4 vs.
     giants, 606.4 vs. trolls, 606.4 vs. orcs, 496.5 vs. animals, 496.5
     vs. evil creatures, and 387.1 vs. others.

 Name   Maethedir    Age            127          Self  RB  CB  EB   Best
 Race   High-Elf     Height        6'5"   STR! 18/100  +1  +3  +6 18/200
 Class  Warrior      Weight    12st 1lb   INT! 18/100  +3  -2 +20 18/***
 Title  Lord         Turns used:          WIS! 18/100  -1  -2 +15 18/***
 HP     1108/1108    Game        655022   DEX! 18/100  +3  +2  +7 18/***
 SP     0/0          Standard    111702   CON! 18/100  +1  +2 +10 18/***
                     Resting      22791

 Level                 47    Armor     [28,+131]    Saving Throw    100%
 Cur Exp          6608248                           Stealth       Superb
 Max Exp          6608248    Melee       5d6,+63    Disarm - phys.  100%
 Adv Exp          7000000    To-hit       97,+61    Disarm - magic   73%
                             Blows      5.2/turn    Magic Devices     83
 Gold              944332                           Searching        76%
 Burden          174.4 lb    Shoot to-dam    +13    Infravision    40 ft
 Overweight       -5.5 lb    To-hit       97,+52    Speed      27 (3.6x)
 Max Depth    4450' (L89)    Shots        1/turn

 

a) the Two-Handed Great Flail 'Lemed' (5d6) (+19,+18) <+2, +3, +4>
     Dropped by Lungorthin, the Balrog of White Fire at 4150 feet
     (level 83)
     
     +2 intelligence.
     +3 wisdom.
     +4 dexterity.
     +2 constitution.
     +3 tunneling.
     Slays undead (powerfully), dragons (powerfully), demons
     (powerfully), giants, trolls, orcs, animals, evil creatures.
     Branded with acid.
     Provides immunity to lightning.
     Provides resistance to acid, fire, cold, poison, shards.
     Cannot be harmed by acid, fire.
     Grants telepathy.  Grants the ability to see invisible things. 
     Prevents paralysis.  
     
     When activated, it heals 500 hit points.
     Takes 434 to 533 turns to recharge at your current speed.
     Your chance of success is 95.0%
     
     Combat info:
     5.2 blows/round.
     With +1 STR and +0 DEX you would get 5.5 blows
     Average damage/round: 680.1 vs. creatures not resistant to acid,
     898.9 vs. undead, 898.9 vs. dragons, 898.9 vs. demons, 680.1 vs.
     giants, 680.1 vs. trolls, 680.1 vs. orcs, 570.1 vs. animals, 570.1
     vs. evil creatures, and 460.7 vs. others.

the one on the top has 2x RoS +17
the one on the bottom has 1x RoS +17 and 1x RoD +14

one has a multiplier of 3.6, the other has 4.3

double ring of speed DPS x multiplier: 2141
RoS + RoD DPS x multiplier: 2052


granted that +17 speed is unusual, most runs you'll get +12 at most, and finding TWO +17 speed rings is even rarer (it used to be more common..), but when you have this much speed boost the final damage output is actually higher with RoS rather than RoD.
(character is already hasted)

[Pete Mack]

Damage, all the way. Permanent speed above 30 has *seriously* diminishing returns. Permanent speed 27 is pretty much ideal.

[Derakon]

I'm having trouble finding fault with Sky's math here; this does seem to be a case where the RoS is worth more than the RoD. In this case, Sky's character is trading being 19.4% faster (4.3x normal speed vs. 3.6x) vs. getting 19.0% more damage per attack action (460.7 damage per attack vs. 387.1). So they're not even sacrificing any damage, really. It certainly helps that the faster character's speed bonus is right at the front of the area of diminishing returns and that they have a significant speed bonus to throw around, of course. But it does put the lie to the statement that you're always better focusing on damage instead of speed once you get to +30.

Diminishing returns doesn't mean zero returns; it takes a long time before speed is completely worthless, and even if it came in at a slight damage disadvantage (which it doesn't in this case) the tactical value of getting turns more frequently is not to be ignored. For example, it reduces the odds that having two enemies in LOS will result in them both using their biggest attack before you get a chance to react.

[Pete Mack]

Derakon--that is true unhasted. But once he uses !speed, the difference will genuinely be marginal.

[Nick]

On the other hand, he doesn't have to use !speed.

[archolewa]

On the other hand, he doesn't have to use !speed.

This is I think big, because it eliminates a potential source of human error: forgetting to keep your speed above 30 against Morgoth. Its all too easy in that fight to miss the fact that your speed ran out and then get double moved by Morgoth. And seeing as how by the endgame, the players biggest threat is usually their own stupidity...

[DavidMedley]

All the figures already include !speed

[Nick]

All the figures already include !speed

Right, so Pete and I are both wrong

[Grotug]

Umm... nice weapon?

[eastwind]

I'm confused by the "x multiplier" part.

If the weapon inspect says (different example for easy math):
5.0 blows/round.
Average damage/round: 300 vs others.

Isn't that 300/round not 1500/round? If it was 300 per blow wouldn't it say per blow instead of per round?

[Derakon]

The multiplier is for how fast the player is moving; it converts from damage per attack action to damage per some set amount of in-game time (specifically 10 game turns). Think of it as the Angband equivalent of "damage per second".

[eastwind]

So how long is a 'round'? Isn't that a constant amount of time?

As a player I have understood, just reading the inspect output, that the player's speed is already boiled into the reported average damage per round.

You hit the key to attack, you get however many 'you hit the icky thing' messages depending on how many attacks you get per round, and that's one round. The monster then gets however many attacks per round it gets. Average damage per round as reported by 'inspect' is taking into account all those attacks, the probability of each one hitting, and the average damage per attack that hits.

Now that's from reading the output and applying logic. If the output should say 'damage/blow' instead of 'damage/round' then your math is right and the text is wrong.

If 'round' is not a fixed amount of time, then what is it, and why is damage being reported in terms of rounds?

If it meant average damage/attack, why would 'inspect' say 'round' and not 'attack'?

[Sideways]

A round means one round of attacks - in this case, one flurry of 5 blows - which will (in melee) always take exactly one player turn. So if you have 5 blows/round, 300 damage/round, that's 60 damage per blow (and 300 damage per player turn because one round of attacks equals one turn).

Speed, though, means you get a turn more often. So if you only did 150 damage/round, but had 2x the speed, that would mean you get the same total effective damage output over time; you need to attack twice as often, but you are twice as fast so that's something you can actually do. Of course, you don't need to spend all those turns attacking - you can spend them positioning, quaffing healing, teleporting, etc.; so in that situation speed always wins.

As for whether a "round" is a fixed amount of game time regardless of your speed... that's a question that actually doesn't have one good and clear answer because of how time works in the game. Technically, a round of attacks consumes no time at all; what it consumes is a fixed amount of energy, and you then need to spend some speed-dependent amount of time recovering that energy.

[eastwind]

Speed, though, means you get a turn more often.

Ah, that was, I think, the part I was missing. Thanks, that's much clearer.

[DavidMedley]

Hmm I had assumed that the "damage/round" reported on weapon inspection takes speed into account, but now I see that's not the case. So I guess it's just a round of all of your blows.