Stabbing bonus calculation?

[Mackerel]

I see the table here : http://crawl.chaosforge.org/index.php?title=Stabbing

It seems to reference both an additive bonus for short blades, followed by a multiplicative bonus that applies to all weapons. The wiki states that the additive bonus, short blades only, is capped at 30. The calculation for figuring out if you qualify for the max additive bonus is given: (dex * (1 + stabbing skill)). But the formula for calculating the additive bonus is not specified.

How is the short blade additive damage bonus calculated? I'm tempted to think that it is simply a tenth of the cap calculation (dex * (1 + stabbing)) for daggers, and a twentieth of that calculation for other short blades; but I'm not confident in making that assumption. What's the actual formula?

[Mackerel]

Anyone?

[Paroid]

That wiki page seems to be very out of date, here's what I've gleaned by reading the stabbing code:

Stabbing comes in 4 levels
Modifier Applies when Monster is:
1 Sleeping, Paralyzed
2 Netted,Petrifying,Petrified
4 Unable to see your Invisible self,Confused,Fleeing,Ally
6 Distracted (Fighting someone other than you)

Stabbing level 1 will happen every time you attack under those conditions, otherwise the chance to do stab damage is stabbing skill + dex + 1 out of 100. It is out of 90 if you are invis and the monster can’t see you.

If you make the check, you will do extra damage.

First, if you are wielding a short blade, add some additional damage:
(Dex * (Stabbing + 1))/10, double this value if your short blade is a dagger
Then the step down value is applied to this added damage by 10 every 10 with a cap of +30 damage.
To be more clear, hitting the +30 damage cap requires a total of 70 points from the calculation. This basically means that a dagger will hit max damage at half the stabbing skill when compared to other short blades.

Some examples of when you hit the +30 damage cap:
Dex 20, Stabbing 18 with a dagger
Dex 30, Stabbing 23 with a quick blade

Second, calculate a multiplier based on the stabbing conditions and multiply all damage done by this multiplier.
For Short Blades:
( 10 + stabbing / ( stabbing situational modifier) ) / 10
For Long Blades, Club, Spear, Trident, Demon Trident:
( 10 + stabbing / ( stabbing situational modifier + 2) ) / 10
For Everything else:
( 12 + stabbing / stabbing situational modifier ) / 12

Say you have maxed your stabbing skill at 27, here are the damage multipliers based on the weapon type you use:
Weapon Modifier = 1 Modifier = 2 Modifier = 4 Modifier = 6
Short Blades x3.7 x2.3 x1.6 x1.4
Good Stabbers x1.9 x1.6 x1.4 x1.3
Bad Stabbers x3.25 x2.08 x1.5 x1.33

Notice that at these high levels of stabbing, the so called "Bad Stabbing" weapons, like say an executioner's axe are actually much better than the "Good Stabbers" like spears.

Also, you have a "Bad Stabbing" weapon and your expected damage output from it exceeds the dagger expected damage +30, you should probably use that weapon if you enjoy random damage. For example, Unarmed Combat 27 with Blade Hands active will probably beat out a +9 dagger some of the time, but probably not all of the time, since +30 bonus damage is fixed and the average damage of the unarmed attack is probably lower than 30.

If your attack is a successful stab, the enemy's AC is reduced by a random value up to your skill in Stabbing divided by the stabbing situational modifier. This reduction is applied before the enemy's AC is rolled, which means it is somewhat unreliable.

One more thing, the total amount of damage done with the stab is considered to be the damage of your attack, so daggers of holy wrath are actually very good for stabbing since all that damage can get multiplied again as bonus damage.

[Mackerel]

This is very helpful. Thanks.

The complexity of the calculations under various conditions is certainly intriguing. At various stabbing skill levels, it could be better to use a dagger, or a sabre, or a heavy axe.

If I've understood this correctly, here's how I should compare an unenchanted dagger (base damage 4) against an unenchanted sabre (base damage 7):

EXAMPLE 1.
With dex=16 and StabbingSkill=4:
ShortBladeAdditionalDamage = (Dex * (StabbingSkill + 1))/10
ShortBladeAdditionalDamage = (16 * (4 + 1))/10 = 8

This bonus doubles for daggers: thus damage for the dagger = base (4) + bonus (16) = 20
The undoubled bonus for the sabre = base (7) + bonus (8) = 15

Next there is a multiplier, which for short blades at StabbingSkill 4 against a sleeping enemy works out to 1.4:
OverallDamageDagger: 1.4 x 20 = 28
OverallDamageSabre: 1.4 x 15 = 21

At this StabbingSkill level, the dagger is the superior weapon.

EXAMPLE 2.
With dex=20 and StabbingSkill=9:
ShortBladeAdditionalDamage = (Dex * (StabbingSkill + 1))/10
ShortBladeAdditionalDamage = (20 * (9 + 1))/10 = 20

UndoubledBonus (sabre) = base (7) + bonus (20) = 27
DoubledBonus (dagger) = base (4) + bonus (40 -- oops, no, capped at 30) = 34

Multiplier: short blades, StabbingSkill 9, works out to 1.9:
OverallDamageDagger: 1.9 x 34 = 64
OverallDamageSabre: 1.9 x 27 = 51


At this StabbingSkill level, the dagger is the superior weapon.

EXAMPLE 3.
With dex=20 and Stabbing Skill=13
ShortBladeAdditionalDamage = (Dex * (StabbingSkill + 1))/10
ShortBladeAdditionalDamage = (20 * (13 + 1))/10 = 28

UndoubledBonus (sabre) = base (7) + bonus (28) = 35
DoubledBonus (dagger) = base (4) + bonus (56 -- oops, no, capped at 30) = 34

Multiplier: short blades, StabbingSkill 13, works out to 2.3:
OverallDamageDagger: 2.3 x 34 = 78
OverallDamageSabre: 2.3 x 35 = 80

The damage from the sabre has now overtaken the damage from the dagger. Thus for StabbingSkill=13 and higher, the sabre is now the superior weapon.

EXAMPLE 4. Enchanting weapons to +5 damage
With dex=20 and Stabbing Skill=19
ShortBladeAdditionalDamage = (Dex * (StabbingSkill + 1))/10
ShortBladeAdditionalDamage = (20 * (19 + 1))/10 = 40

UndoubledBonus (sabre) = base (7) + enchantment (5) + bonus (40 -- oops, no, capped at 30) = 42
DoubledBonus (dagger) = base (4) + enchantment (5) + bonus (80 -- oops, no, capped at 30) = 39

Multiplier: short blades, StabbingSkill 13, works out to 2.9:
OverallDamageDagger: 2.9 x 39 = 113
OverallDamageSabre: 2.9 x 42 = 121

CONCLUSION (if my math has been correct): in the early game, an unenchanted dagger does more stabbing damage than an unenchanted sabre. Assuming a dex in the high teens or better, the sabre becomes better at stabbing by midgame, when you reach stabbing skill 13 or so. Yet as Paroid has demonstrated, in the later game, with StabbingSkill maxed at 27, a high damage weapon, not a short blade, becomes the best weapon for stabbing. Still, a highly enchanted sabre might turn out to be better than an unenchanted dagger, for some skill levels.

[Paroid]

EXAMPLE 4. Enchanting weapons to +5 damage
With dex=20 and Stabbing Skill=19
ShortBladeAdditionalDamage = (Dex * (StabbingSkill + 1))/10
ShortBladeAdditionalDamage = (20 * (19 + 1))/10 = 40

UndoubledBonus (sabre) = base (7) + enchantment (5) + bonus (40 -- oops, no, capped at 30) = 42
DoubledBonus (dagger) = base (4) + enchantment (5) + bonus (80 -- oops, no, capped at 30) = 39

Multiplier: short blades, StabbingSkill 13, works out to 2.9:
OverallDamageDagger: 2.9 x 39 = 113
OverallDamageSabre: 2.9 x 42 = 121

I didn't really clarify the math in my example to explain this:

Then the step down value is applied to this added damage by 10 every 10 with a cap of +30 damage.

What I meant by that was the game applies the step_down function to the bonus damage, capping it at 30. The stepping increment of this function is set to 10, and it starts at 10. It's a little hard to explain what this function does, but the game uses it everywhere where having a high number would be beneficial to the player.

Basically, the function divides your bonus above the stepping value by half. If your bonus is still too awesome (above the next stepping value) it does it again.

So, when say it steps down the bonus damage by 10 every 10 and caps it at thirty, that actually means you need +70 raw bonus damage to achieve the +30 bonus damage cap.

The first 10 bonus damage is unstepped. Above 10, it divides by half. Above 20, it divides by half again.

So 70 go through the stepping function as 10 + 20/2 + 40/4, for a total of 30.

UndoubledBonus (sabre) = base (7) + enchantment (5) + bonus (40 -- oops, no, capped at 30) = 42
DoubledBonus (dagger) = base (4) + enchantment (5) + bonus (80 -- oops, no, capped at 30) = 39

Also, I feel the need to explain a little about damage randomization here. When a weapon description in game says 4 damage or 7 damage, that's really the base max damage of the weapon. When you have an enchantment bonus on a weapon, that bonus is actually randomly rolled and added to the base max damage. After all the modifiers have been applied, the max damage is randomized again to get your final actually attack damage. Which is then reduced by the randomly rolled value of the opponents AC.

Now, I need to explain that your max damage is boosted before the roll based on stats, weapon skill and fighting skill. This boost is a random multiplier based on your stats and skills. Weapon skill and fighting skill at 27 will on average multiply your damage output by 1.5 each. If you had great Chei boosts and had 39 strength and 39 dexterity on average your damage output will be multiplied by 1.5. Do note that the damage enchantment bonus of your weapon is not multiplied by any of these things, so as your character gets more awesome, the relative value of this bonus goes down.

The rule of thumb I use is, on average, a weapon does 1/2 it's listed base damage. On average, a damage enchantment bonus adds 1/4 of the enchantment to the damage output. On average, slaying damage bonuses add 1/2 their listed amount to your damage output.

Now, as a stealthy stabbity character, you probably don't have 27 fighting, 27 weapon skill, 39 strength and 39 dexterity. Also, after every multiplication your damage output is truncated to an integer, so you might not get any damage boost at all from fighting, weapon or stats.

Once you realize that damage is based on the randomized value of 3 different random rolls, you get a certain appreciation for the fact that the stabbing bonus is a nice solid constant value for every stab, and the damage multiplier for stabbing is similarly constant.