What are the actually effects of +str on damage?

[nago]

I never bother to understand how much str affects melee damage. Or if it affects ranged damage at all.
However, my last char makes me wonder this question, as I have some +str artefact I could swap with something else.

  Code:

 Dungeon Crawl Stone Soup version 0.25-a0-578-gc91f01c (webtiles) character file.

nago the Tycoon (Gnoll Assassin)                   Turns: 77066, Time: 02:14:59

Health: 215/215    AC: 42    Str: 34    XL:     27
Magic:  48/48      EV: 24    Int: 20    God:    Gozag
Gold:   14905      SH: 16    Dex: 14    Spells: 19/60 levels left

rFire    + + .     SeeInvis +   a - +9 sword of Zonguldrok {reap}
rCold    + . .     Gourm    .   Z - +0 kite shield {reflect}
rNeg     . . .     Faith    .   Y - +10 plate armour {MR+}
rPois    .         Spirit   .   k - +1 hat
rElec    +         Reflect  +   J - +1 cloak of Starlight {rElec rC+ EV+4 Stlth--}
rCorr    .         Harm     .   x - +2 pair of gloves of the Comet {rElec Str+6 SInv}
MR       ++++.                  z - +0 pair of boots {Stlth+}
Stlth    ++........             E - amulet "Ywky" {Acrobat rF+ Dex-4 Slay+5 SInv}
HPRegen  0.45/turn              p - ring "Lycwone" {rF+ Str+7 Int+2}
MPRegen  0.31/turn              S - +5 ring of protection {=R}

@: deflect missiles
A: distributed training, fangs 1, horns 1, high mp 1, magic resistance 1, sturdy
frame 1, strong nose
}: 5/15 runes: decaying, slimy, silver, abyssal, gossamer
a: Potion Petition, Call Merchant, Bribe Branch, Renounce Religion


You are on level 1 of the Lair of Beasts.
You worship Gozag.
Gozag is extremely pleased with you.
You are not hungry.

You have visited 10 branches of the dungeon, and seen 50 of its levels.
You have visited the Abyss 2 times.
You have also visited: Trove, Ossuary, Bailey, Gauntlet and Ice Cave.

You have collected 32225 gold pieces.
You have spent 5292 gold pieces at shops.
You have paid 12028 gold pieces to Gozag.

Inventory:

Hand Weapons
 a - the +9 sword of Zonguldrok (weapon) {reap}
   (You found it on level 2 of the Lair of Beasts)   
   
   If a monster killed with it leaves a corpse in good enough shape, the corpse
   will be animated as a zombie friendly to the killer.
 W - a +5 trishula of holy wrath
   (You took it off Mennas on level 5 of the Vaults)
Missiles
 e - 8 curare-tipped darts
 q - 1141 stones
 u - 3 throwing nets {=f, !d}
 v - 42 javelins {=f}
 K - 19 boomerangs (quivered)
 O - 5 boomerangs of dispersal {=f}
Armour
 k - a +1 hat (worn)
   (You found it on level 1 of the Lair of Beasts)
 x - the +2 pair of gloves of the Comet (worn) {rElec Str+6 SInv}
   (You bought it in a shop on level 1 of the Lair of Beasts)   
   
   It affects your strength (+6).
   It insulates you from electricity.
   It lets you see invisible.
   
   If you remove this armour, your AC will decrease by 4 (42 -> 38).
 z - a +0 pair of boots of stealth (worn)
   (You bought it in a shop on level 1 of the Lair of Beasts)
 J - the +1 cloak of Starlight (worn) {rElec rC+ EV+4 Stlth--}
   (You found it on level 2 of the Lair of Beasts)   
   
   It affects your evasion (+4).
   It protects you from cold.
   It insulates you from electricity.
   It makes you much less stealthy.
   
   If you remove this armour, your AC will decrease by 3 (42 -> 39).
 Y - a +10 plate armour of magic resistance (worn)
   (You bought it in a shop on level 1 of the Lair of Beasts)
 Z - a +0 kite shield of reflection (worn)
   (You took it off Donald on level 3 of the Swamp)
Jewellery
 l - an uncursed ring of protection from magic {MR+,}
   (You found it on level 1 of the Depths)
 o - the ring of Roackoug {rN+ Str+5}
   (You found it on level 2 of the Elven Halls)   
   
   [ring of positive energy]
   
   It affects your strength (+5).
   It protects you from negative energy.
 p - the ring "Lycwone" (left hand) {rF+ Str+7 Int+2}
   (You found it in a Gauntlet)   
   
   [ring of protection from fire]
   
   It affects your strength (+7).
   It affects your intelligence (+2).
   It protects you from fire.
 E - the amulet "Ywky" (around neck) {Acrobat rF+ Dex-4 Slay+5 SInv}
   (You acquired it on level 2 of the Lair of Beasts)   
   
   [amulet of the acrobat]
   
   It helps you evade while moving and waiting.
   It affects your dexterity (-4).
   It affects your accuracy and damage with ranged weapons and melee attacks
   (+5).
   It protects you from fire.
   It lets you see invisible.
 S - a +5 ring of protection (right hand) {=R}
   (You found it on level 1 of the Vaults)
Wands
 c - a wand of acid (18)
   (You found it on level 6 of the Lair of Beasts)
 y - a wand of iceblast (52)
   (You found it on level 6 of the Dungeon)
 A - a wand of polymorph (13)
   (You found it on level 4 of the Dungeon)
 D - a wand of digging (6)
   (You found it on level 7 of the Dungeon)
 N - a wand of enslavement (12)
   (You found it on level 5 of the Lair of Beasts)
 U - a wand of paralysis (8)
   (You found it on level 8 of the Dungeon)
 X - a wand of clouds (9)
   (You found it on level 13 of the Dungeon)
Scrolls
 f - 11 scrolls of fog {!r}
 i - 22 scrolls of identify
 s - 3 scrolls of summoning
 t - 23 scrolls of teleportation
 B - 15 scrolls of blinking {!r}
 F - 10 scrolls of fear
 M - 6 scrolls of magic mapping {!r}
 R - 29 scrolls of remove curse
Potions
 h - 13 potions of heal wounds
 j - 6 potions of magic
 m - 11 potions of might
 n - 7 potions of brilliance
 r - 8 potions of resistance
 w - 3 potions of mutation {!q}
 C - 6 potions of curing
 G - 9 potions of invisibility
 H - 12 potions of haste
 Q - 2 potions of cancellation
 T - 6 potions of berserk rage {!q}
Miscellaneous
 b - a box of beasts
 g - a fan of gales
   (You found it on level 5 of the Lair of Beasts)
 I - 2 sacks of spiders
 L - a lamp of fire
   (You found it on level 5 of the Vaults)
 P - a phial of floods
   (You found it on level 3 of the Elven Halls)
 V - a lightning rod (4/4)
   (You found it on level 3 of the Elven Halls)
Comestibles
 d - 23 rations


   Skills:
 + Level 17.6 Fighting
 + Level 17.6 Short Blades
 + Level 17.1 Long Blades
 + Level 17.1 Axes
 + Level 17.1 Maces & Flails
 + Level 17.1 Polearms
 + Level 17.1 Staves
 + Level 17.1 Slings
 + Level 17.1 Bows
 + Level 17.1 Crossbows
 + Level 17.6 Throwing
 + Level 17.1 Armour
 + Level 17.3 Dodging
 + Level 18.3 Stealth
 + Level 17.1 Shields
 + Level 17.1 Unarmed Combat
 + Level 17.1 Spellcasting
 + Level 14.7 Conjurations
 + Level 14.7 Hexes
 + Level 14.7 Charms
 + Level 14.7 Summonings
 + Level 14.7 Necromancy
 + Level 14.7 Translocations
 + Level 14.7 Transmutations
 + Level 14.7 Fire Magic
 + Level 14.7 Ice Magic
 + Level 14.7 Air Magic
 + Level 14.7 Earth Magic
 + Level 14.7 Poison Magic
 + Level 18.4 Invocations
 + Level 17.1 Evocations

Namely I could swap

  Code:

ring "Lycwone" {rF+ Str+7 Int+2}

with another ring of protection, losing that +7 str

How much could that change the dps? Is possible to have a "rule of thumb" without resorting on fsim?

And the very hard question:

  Code:

+2 pair of gloves of the Comet {rElec Str+6 SInv}

I can swap them with the fencer gloves'.
Yeah, more riposte.

Anyone is crazy enough to calculate what is going to get higher damage between the two gloves, and why?

[grinrain]

Riposte only works on a miss, which I have thought was a dodge. With high AC and a shield, you do not dodge all that often, though free hits are nice. Do you need the SInv? I am a complete novice here, but with your AC/Sh vs your EV, would keep the gloves of the Comet.

[stormdragon]

1. Strength reduces penalties from wearing body armour; see {aevp}. Has a small impact on melee and launcher base damage, roughly +25% of initial damage per 10 points of str above 10.
2. applies a slightly harsher penalty for str<10

The "roughly" there is actually very close; each point of STR you gain (above 10) increases your base damage by on average 1/39 of your base damage. This increase gets multiplied by your weapon skill and fighting skill bonuses, which are, respectively, on average, 1/50 per level and 1/60 per level. And as I recently found out, these bonuses are applied separately so that compounding happens. This is all we need in order to calculate the main-attack damage increase from STR for your character:

14 [double sword base damage] * (1 + 17.1 / 50) [long blades damage bonus] * (1 + 17.6 / 60) [fighting damage bonus] / 39 [bonus per point of STR] ≈ 0.623 damage per extra point of STR. Multiply by 7 for that ring and you get 4.36 extra damage, which is more damage than +4 slaying (again, considering main attack only). Pretty sweet. Personally I would use that over a ring of protection, but that's just how I prefer to build.

Riposte is hard to compare to anything because unlike every other source of damage (or really attack speed, since it boils down to getting extra hits), it depends on the enemy speed and accuracy, and on your SH and EV (though it definitely does NOT depend on your AC). You can sort of estimate it by trying to figure a ratio of riposte to non-riposte attacks from your observations; perhaps it's 1:10, in which case the riposte chance (and hence the fencer's gloves) represents about 10% extra post-AC damage. That's estimating really roughly though.

[duvessa]

Multiply by 7 for that ring and you get 4.36 extra damage, which is more damage than +4 slaying (again, considering main attack only).

This character has aux attacks, though...

[stormdragon]

Multiply by 7 for that ring and you get 4.36 extra damage, which is more damage than +4 slaying (again, considering main attack only).

This character has aux attacks, though...

Why do you mention this? I am just providing the comparison of STR to main-attack slaying because the benefit is easy to imagine, since this is what slaying is for most characters. If nago was actually comparing STR to slaying on this character, I could go into more detail; but that is not what's going on here, it's STR vs AC on this character.

[bjourne]

14 [double sword base damage] * (1 + 17.1 / 50) [long blades damage bonus] * (1 + 17.6 / 60) [fighting damage bonus] / 39 [bonus per point of STR] ≈ 0.623 damage per extra point of STR. Multiply by 7 for that ring and you get 4.36 extra damage, which is more damage than +4 slaying (again, considering main attack only). Pretty sweet. Personally I would use that over a ring of protection, but that's just how I prefer to build.

So 1 point of slay is roughly worth 2 points of strength?

[PseudoLoneWolf]

14 [double sword base damage] * (1 + 17.1 / 50) [long blades damage bonus] * (1 + 17.6 / 60) [fighting damage bonus] / 39 [bonus per point of STR] ≈ 0.623 damage per extra point of STR. Multiply by 7 for that ring and you get 4.36 extra damage, which is more damage than +4 slaying (again, considering main attack only). Pretty sweet. Personally I would use that over a ring of protection, but that's just how I prefer to build.

So 1 point of slay is roughly worth 2 points of strength?

Assuming that equation remains true throughout all ranges of strength and there aren't any diminishing returns (which I am unsure of), seems to me that 2 STR == 1.246 Slaying, making Slaying almost twice as effective but with an edge of +1 damage being given to STR once every 10 points or so.

That seems to stand up to a basic sanity check but I admit I am pretty unfamiliar with any of the damage formulas in crawl so this would be something that someone else can confirm better than I.

[Siegurt]

So 1 point of slay is roughly worth 2 points of strength?

Assuming that equation remains true throughout all ranges of strength and there aren't any diminishing returns (which I am unsure of), seems to me that 2 STR == 1.246 Slaying, making Slaying almost twice as effective but with an edge of +1 damage being given to STR once every 10 points or so.

That seems to stand up to a basic sanity check but I admit I am pretty unfamiliar with any of the damage formulas in crawl so this would be something that someone else can confirm better than I.

It's slightly more complicated than that, strength increases the base damage of the weapon by a percentage (randomly per attack of course) whereas slaying just applies a random amount of damage *per hit* so bigger weapons get larger bonuses from strength, and can reasonably be expressed as a percentage bonus (at least on average) whereas slaying is a (randomly rolled) *amount* of damage, regardless of how powerful the weapon is, so percentage-wise applies a larger bonus to smaller weapons.

To make things weirder, strength and slaying have a non-simple relationship to aux attacks as well (Strength, along with dex, increase the odds of *performing* an aux attack when available, up to a point, and again strength gives a bonus to the base attack of the aux, but it's a smaller percentage of a smaller number, and *slaying* effects them, but not other things that are slaying-like (for example weapon enchantment has no effect on aux attacks))

[bel]

Not directly related, but reading the above posts made me think about the following:

I've been playing a lot of Slay the Spire recently, where damage is almost completely deterministic. It does not make the game less interesting in any way. I think the RPG-style games' damage formulae have been needlessly complex. It's not even a matter of determinism: Brogue's damage formulae are very clean. Sil's damage formulae are also pretty easy to understand.

To take a different example, for instance, in the Persona series, the damage is again needless complex. Not only does it make the game somewhat frustrating, it also leads to hard-to-find bugs. For instance, in Persona 5, there's a bug where equipment that gives stat boosts accidentally gives twice as much boost as shown (so a +5 str weapon actually gives +10 str). No game dev noticed it, and when there was a remake released recently (Persona 5 Royal), the same bug still exists.

[Sprucery]

To take a different example, for instance, in the Persona series, the damage is again needless complex. Not only does it make the game somewhat frustrating, it also leads to hard-to-find bugs. For instance, in Persona 5, there's a bug where equipment that gives stat boosts accidentally gives twice as much boost as shown (so a +5 str weapon actually gives +10 str). No game dev noticed it, and when there was a remake released recently (Persona 5 Royal), the same bug still exists.

You don't even have to go that far, we had the double damage bug in DCSS a few years back...

[Shard1697]

I really wonder when I would ever level dex instead of str, post the rework where weapon stat scaling was changed so only str increases damage.

[tealizard]

About sil and brogue damage formulas, I agree that they are easier to analyze mathematically because they involve less complicated dice formulas, but the formulas are inferior to crawl in terms of combat dynamics. Both brogue and sil generally have more predictable, static combat in part because of the way damage is computed.

[bel]

I can agree that Sil has generally more static combat (that's why it has critical hits, to mitigate this issue somewhat), but I don't agree about Brogue.

Anyway, one can disagree about specific forumulae, but my overall point is that DCSS's combat formulae are needlessly complex, because it's based on old RPG-style mechanics with lots of stats and complicated relationships based on those stats. Instead, one can

(a) use fewer parameters (for example, Brogue only has Str)
(b) less complicated dependence on the parameters (like Slay the Spire has Str and Dex, but their effect on attack and defence is very simple).

One can think of other ways to simplify the formulae, while keeping whatever ultimate goal one has in mind. For instance, if one goal is to increase combat variance, one can design formulae based on that goal.

[tealizard]

I think complexity of the formulas, or more generally of the procedures that generate the numbers, is a red herring. The bigger problem is that basic statistics about them are not available to the player and that the design of the formulas is somewhat haphazard -- they seem to work more by coincidence or after the fact tuning than by design.

[bel]

If you reduce the complexity of the formulae, calculating statistics is automatically made easier.

So, suppose we are interested in the minimum, maximum and average damage dealt, and we're interested in how str affects these statistics (like the title of this thread).

In Slay the Spire, the effect of Str on damage is very simple: it increases all damage by +str exactly. (In a multi-hit attack, every attack is affected by Str individually, so again, the statistics are easy to calculate).

Similarly, in Sil, it's easy to calculate the effect of Str on the relevant statistics. Weapons with dice rolls just have (d + Str)-sided dice instead of d-sided dice. So, for a single die, the minimum is the same, and the maximum increases by +Str, and the average is (min + max) / 2. For, multiple dice, it's a bit more complicated, but still very simple: one can just multiply each number by the number of dice.

[tealizard]

I suppose this is true as far as it goes, but the issue isn't so much calculating the statistics as presenting them to players in a convenient and digestible way.

[bel]

Both approaches are possible. Brogue, for instance, shows the relevant statistics: "this monster will hit you typically for 35% damage, and can kill you in 2 hits". In StS and Sil, the formulae are simple enough that they just show the numbers explicitly, and the player can calculate the statistics themselves.

More generally, one can think of the problem like the following: suppose we have a curve of damage vs str. To communicate the curve to the player, one can take two approaches:

(a) Explicitly show the curve: this is the approach I was talking above. If the curve is simple enough, one can do this.
(b) Show where you are on the curve (maybe one can also show the tangent at the current point on the curve, to show how much str increases your damage). This is the "statistics" based approach.

The second approach allows for more complicated curves, but also provides less information about other points on the curve. So, it's possible that the curve is such that the effect of str on damage has some sort of breakpoint in the near future, but the player isn't aware of it at the current point.

-----------------------------------------------------

In general, I don't think complicated curves are necessary to attain whatever goals are desirable.

For instance, in StS, variance in combat is achieved by a very simple mechanism: the monster has two or more moves; each of them has deterministic damage, but the move chosen is random. This is similar to monsters in DCSS having spell lists, and the exact spell chosen is random.

[tealizard]

In some sense, the "best" curves would be exponentials and describing the relationship between their parameters and their statistics is somewhat complicated. It is possible though and the machinery for doing so would provide the bridge between convenience in design and intuition for the player.

Dice formulas are seductive in that they seem easy to understand, but they really aren't. You either have sil-like formulas with multiple dice added and subtracted that aren't really doing what you want if you know what you're doing or you have crazy crawl-like formulas with sums, differences, and products (!) of many dice and dice with numbers of sides determined by complicated parameters or other dice rolls (e.g. 1d(1dX) (!!)) where realistically they probably didn't know what they were doing and stumbled upon something by chance. The difficulty of analyzing relatively simple sil-style multiple dice sum/difference formulas with minimum roll zero is also underrated -- it is certainly not the case that simply showing players what the rolls are gives them a great deal of insight into the process's statistics on its own, except in the most naive sense that it is theoretically possible to work them out.

[luckless]

You can sort of estimate it by trying to figure a ratio of riposte to non-riposte attacks from your observations; perhaps it's 1:10, in which case the riposte chance (and hence the fencer's gloves) represents about 10% extra post-AC damage. That's estimating really roughly though.

fwiw: that's actually a pretty good rule of thumb for 1v1. Unless you totally neglect EV, enemies are usually missing you between 30 and 70% of the time (where ~50% is pretty standard). You get a riposte attempt on 1/3 of those misses, and at mindelay a typical enemy gets 0.7 attacks for each of yours. So you end up with these numbers:

  Code:

  miss       ripostes/     ripostes/
chance    enemy attack   your attack
------    ------------   -----------
   30%             0.1          0.07
   40%         ~0.1333       ~0.0933
   50%         ~0.1667       ~0.1167
   60%             0.2          0.14
   70%         ~0.2333       ~0.1633

Anyone is crazy enough to calculate what is going to get higher damage between the two gloves, and why?

okay, months later and the character's totally done, but I can't resist procrastinating here.

Str gloves: Str 27 multiplies your pre-slaying/AC damage by (39 + 27 - 9)/39. Str 34 multiplies it by (39 + 34 - 9)/34. That's about a 12% increase.
Fencer's gloves: With the gnoll's middling EV and decent SH, riposte isn't going to be triggering that much. Let's be generous and say your typical non-popcorn enemy is going to miss your gnoll 30% of the time—so, 7% of your 1v1 attacks will be ripostes. Fencer's gloves double that to 14%, yielding about a 6.5% total (post-slaying/AC) increase.

So, if we assume for simplicity that the difference between pre- and post-slaying/AC is a wash, the Str gloves are about twice as good 1v1—more than that if you're against a target with more than 15 AC.

Of course, the real answer was to go with the fencer's gloves and trade the sword for an axe. Ripostes can cleave!

[nago]

Up, for a not-totally theorically question.

My VsIE found this:

  Code:

the ring of Moderation {Ice *Contam Str+10 Dex+8 Slay-6}

I'm in Lair and no rf+ source yet, so for now I'm using a plain ring of ice as this one isn't (cheaply) swappable.
My question is: how would evaluate the str bonus\slay malus?

I would roughly consider that, with a 1h and decent fighting\weapon skill, they kinda negate each other. However, the +str bonus would significantly increase bite aux attack chance-
In other word, a decent\good ring if rf+ source is available

[Sorcerous]

Up, for a not-totally theorically question.

My VsIE found this:

  Code:

the ring of Moderation {Ice *Contam Str+10 Dex+8 Slay-6}

I'm in Lair and no rf+ source yet, so for now I'm using a plain ring of ice as this one isn't (cheaply) swappable.
My question is: how would evaluate the str bonus\slay malus?

I would roughly consider that, with a 1h and decent fighting\weapon skill, they kinda negate each other. However, the +str bonus would significantly increase bite aux attack chance-
In other word, a decent\good ring if rf+ source is available

Your "rough" guess is correct imo. The damage bonus or penalty depends on the base damage of your weapon, but at worst it will be very slightly lower on average. The loss of accuracy does not seem significant. IIRC auxiliary bites use combined Str and Dex when it comes to bite chance, so that benefit from wearing the ring is high.

[Magipi]

I would have thrown that ring away without thinking. Now I thought about it, and I still don't understand how is this even a candidate. If it was swappable, it would be marginally better than a ring of ice. Not being swappable is a huge minus. Even if you find a rF ring, that will mean that both ring are stuck on you, and there is no way to actually get rF+. Even thinking about it makes me afraid.

[nago]

Well going with without rf+ in most of the game is fine, and most probably I would have swapped it in zot or once I had found a better ring - and that dex +8 was a nice thing too.

However I yasd the char: remember kids, never play while being inattentive