stochastic energy and fractional blows

[Napsterbater]

3d4 = avg dam of 7.5
1d4x1d3 = avg dam of 5

the critical is far stronger on average

and just in case I misinterpreted

4x1d3 = avg dam of 8 (slightly better than the crit)

You can't measure average damage across multiple blows, because each blow has a variable chance of hitting that depends on monster AC and your abilities.

[Marble Dice]

It's true that accuracy modifies the average damage per attack, and that hit% depends on monster AC, player melee ability, and +hit, but that doesn't mean you can't calculate an average. If you do an average of 16 damage per hit, but only have a 92% chance of hitting a specific enemy at a certain level, then your average damage per attack is 0.92 * 16 = 14.72. Thus, if you have 4 blows, on average you will do 58.88 damage per round.

I think what ekolis was getting at though, is what's the functional difference between many weaker blows versus fewer but more powerful attacks?

For one, fewer more powerful attacks tend to be more "bursty" by nature, whereas many weaker attacks are more consistent. It's the same difference between 3d4 and 1d10+2. They have the same average damage, but the 1d10+2 is more variable, frequently getting very low or very high values.

Secondly (as ekolis points out), many weaker blows are heavily affected by damage reduction. If an enemy's armor takes off 10 damage per hit, then four 25-damage attacks will do less than one 100-damage attack.

In Angband, the main issues that drive the melee weapon imbalance are that a single +dam is more of a boost on a light weapon (with multi blows), and that slay modifiers are a much bigger boost on a heavy weapon (with high base damage).

I think if I wanted to rebuild Angband combat from the ground up, so it made sense and was most balanced, I would:

1) Give every melee weapon a "weapon speed" property, which determines how much base energy is required per swing, and re-balance weapon damage around the formula: base damage/speed.

2) Give every class a static "preferred weapon weight" and a "weapon speed bonus."

To determine the amount of time per blow, you'd modify the weapon's base speed by the class's weapon speed bonus. Dex could also help the weapon speed. Then, for every X lbs over the preferred weapon weight, you would apply a weapon speed penalty. This way you could have a class that gets very fast blows, but only with lighter weapons. Str could also give a bonus to preferred weapon weight.

Finally, I'd make melee slay modifiers affect total damage per hit, not just the base weapon damage, and also I'd divide all the +dam by the weapon speed. This way, +dam gives a static amount of damage per time, regardless of if you're hitting very fast or very slow.

It'd be a lot of re-balancing but such systems work pretty well; it's basically what MMOs do.

[Atarlost]

I don't think doing what MMOs do is a selling point at all. Single player balance and multiplayer balance are not the same beast and Angband places much higher demands on its combat system because there aren't any fancy graphics or socialization to distract players from the monotony.

[pampl]

Secondly (as ekolis points out), many weaker blows are heavily affected by damage reduction. If an enemy's armor takes off 10 damage per hit, then four 25-damage attacks will do less than one 100-damage attack.

Semi-relevant nitpick: that's only true for absolute damage reduction. Angband uses percentile damage reduction for the player, so there's almost no difference between many weak attacks and a few strong attacks. Damage is rounded down before being applied, so weak hits are effected slightly more heavily by damage reduction, but I don't think there are any cases pathological enough for it to be a big deal (eg 100 attacks at 1 damage each versus 1 attack for 100 damage). EDIT: Now that I think about it, the difference is at most 1 point of damage per attack, so at most 4 points of damage per monster turn

I have no preference whether Angband favors heavy weapons or light weapons - if it takes dozens of hits to kill an old man in a rainbow bathrobe then it doesn't matter whether my weapon is called a dagger or a giant battleaxe with smaller battleaxes welded onto it, I'm gonna imagine it as a wet noodle - but if anyone's looking for a roguelike that has a neat and psuedo-realistic implimentation of weapon size vs. power then IMO you should check out Dungeon Crawl.

[zaimoni]

Damage is rounded down before being applied, so weak hits are effected slightly more heavily by damage reduction, but I don't think there are any cases pathological enough for it to be a big deal (eg 100 attacks at 1 damage each versus 1 attack for 100 damage). EDIT: Now that I think about it, the difference is at most 1 point of damage per attack, so at most 4 points of damage per monster turn

Actually (per melee1.c) it's the damage reduction that's rounded down (as a side effect of integer division); net effect is that damage is rounded up. The edit comment is correct.

As for worst pathological case...I haven't done a detailed numerical search, but one that jumps out at me is that 50AC reduces 5 hp to 4hp; 49 AC doesn't reduce.

So...compare 4 5hp hit attacks to 1 20 hp hit attack at 49AC: 0 damage reduction vs. 3 damage reduction . Which one is more lethal depends absurdly on one's current hp.

[Pete Mack]

So...compare 4 5hp hit attacks to 1 20 hp hit attack at 49AC: 0 damage reduction vs. 3 damage reduction . Which one is more lethal depends absurdly on one's current hp.

Yup. That's the standard defense for H-T warriors after getting jumped by Hummerhorns. Equip the highest AC you can, and just keep trying to activate that staff of teleportation. It may take 200 turns, but you will survive.

[Atarlost]

Semi-relevant nitpick: that's only true for absolute damage reduction. Angband uses percentile damage reduction for the player, so there's almost no difference between many weak attacks and a few strong attacks. Damage is rounded down before being applied, so weak hits are effected slightly more heavily by damage reduction, but I don't think there are any cases pathological enough for it to be a big deal (eg 100 attacks at 1 damage each versus 1 attack for 100 damage). EDIT: Now that I think about it, the difference is at most 1 point of damage per attack, so at most 4 points of damage per monster turn

I think damage boosts and armor need to be comparable. Either both should be percentage based or both should be fixed per attack. 1 armor should cancel 1 to hit. That would mean splitting evade from armor.

[Hariolor]

You can't measure average damage across multiple blows, because each blow has a variable chance of hitting that depends on monster AC and your abilities.

One - yes you can, you just have to know your chance to hit, then multiply that by the avg damage of the weapon.

Two - I was only citing the damage per weapon. 3d4/blow vs 1d4 blows at 1d3 apiece. Assuming all blows hit, swinging a 3d4 weapon once is preferable to swinging a 1d3 weapon 1d4 times.

For one, fewer more powerful attacks tend to be more "bursty" by nature, whereas many weaker attacks are more consistent. It's the same difference between 3d4 and 1d10+2. They have the same average damage, but the 1d10+2 is more variable, frequently getting very low or very high values.

Yeah, adding a large number of small dice creates a more distinct bell curve to the damage - it evens the distribution around the mean. This doesn't mean the average (or total) damage dealt will be more or less over time, but it feels more reliable from a psychological perspective.