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Old March 7, 2012, 00:57   #11
Magnate
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Quote:
Originally Posted by jevansau View Post
I've noticed that past a point of prowess/finesse, the damage display becomes meaningless still (although no crashes which is great). For example at +943/+884, damage is showing as 10644.4 for normal creatures. Testing showed it is clearly not doing anything like this amount of damage.

If someone would like to tell me the method of working out damage, I'll come up with an algorithm for displaying the damage.
Hmmm. Part of the problem is that you aren't supposed to end up with anything like that amount of +fin/prow - could you post a dump?

Don't forget that that's damage per *round*, not per blow. But 2000 damage per blow is still ridiculous.

The damage is simply:

1. XdY diceroll
2. Multiplied by "mult" (which is derived from your prowess score and your weapon's preference for prowess, which we call heft, plus any slay or brand mult)
3. Check for crit chance (which is fin^2 plus prow^2 all / 5000 and capped at 99%).
4. If the check fails, stop - that's the total damage.
5. Add 1dY if successful, multiply chance by 0.95 and go back to 3

It's the x0.95 that messes things up - there's a nice mathematical equation to calculate the crit damage if chance is constant, but it isn't.
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Old March 7, 2012, 21:17   #12
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Thanks for that - I actually got impatient yesterday and grabbed a clone of the source, and did some testing with a spreadsheet.
Formula for extra critical dice is:
dice = c + (.95c)c + (.95c)^2c +(.95c)^3c ...
where c is the critical chance. Because of the .99 cap, a total of 14 terms gives a very close approximation.
Tops out at about 5.2 dice average at 99%.

Dump attached.
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Old March 7, 2012, 21:34   #13
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That is one beastly weapon you have there. 5d10 damage and an acid brand! I kinda feel like the Disruption affix should make the weapon be heavily prowess-oriented -- having a 35-pound weapon that's 70/30 balance/heft seems wrong.

You're getting 335 finesse from race/class/level, 348 from equipment, and 260 from DEX. The original intent was that you get about a third from race/class/level, a third from equipment, and a third from DEX, so things are slightly out of whack here, but it wouldn't seem like they're excessively so.

Your crit chance should be ((.7 * 943)^2 + (.3 * 743)^2) / 5000 + 1 = 98%. So we didn't actually hit the crit cap. It would take 14 successful crits before your chance of getting an extra crit would be below 50%. If we brought your non-DEX finesse mods down to 260 to match DEX (and didn't change the prowess mods) then you'd be at ((.7 * 780) + (.3 * 743)^2) / 5000 + 1 = 70%. That's still pretty high; it'd take 7 successful crits before the chance for another drops below 50%.

So it sounds like weapon and class mods may need a bit of a nerf, but more importantly that .95x multiplier needs to be brought down. At .8x the two cases outlined above become 4 and 2 iterations, respectively, before the chance for further crits drops below half.
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Old March 7, 2012, 21:52   #14
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I did see one with 6d10 and a 6.64 slay multiplier for undead. Too heavy though and 10/90.

The calculation I gave seems about right when I look at number of turns to kill compared to health of monster.
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Old March 7, 2012, 23:19   #15
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Alternate solution: increase the divisor further (to 7500 or 10000, say) and cap max crit chance at 50% (or whatever), then do away with the .95x multiplier altogether. That would, per Magnate's post, also make it easier to calculate expected damage from crits.
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Old March 7, 2012, 23:22   #16
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Quote:
Originally Posted by Derakon View Post
That is one beastly weapon you have there. 5d10 damage and an acid brand! I kinda feel like the Disruption affix should make the weapon be heavily prowess-oriented -- having a 35-pound weapon that's 70/30 balance/heft seems wrong.
Agreed. Since affixes predate balance and heft, we can't yet modify them, but it shouldn't take long to make that happen. I've opened ticket #1627 for this.
Quote:
So it sounds like weapon and class mods may need a bit of a nerf, but more importantly that .95x multiplier needs to be brought down. At .8x the two cases outlined above become 4 and 2 iterations, respectively, before the chance for further crits drops below half.
The alternative is to increase the 5000 divisor still further, and reduce crit chance across the board. Probably a combination of the two. I don't particularly like the decay in chance, but it's necessary if crit chances are going to get that high. And maybe they should, but only for prowess chars. I'm definitely leaning away from the symmetry in the chance calc. I'm thinking something like (fin + (prow/10)^2) / x, where x needs retuning.

Personally I'm fine with race/class and equipment contributing more than stats in the ratio 3:3:2.
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Old March 8, 2012, 00:01   #17
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Some kind of nonlinear crit chance would be nice, so you don't never get crits early on, but also don't always get crits in the late game. For example:
Code:
y = x - (x ^ 2) / 1000
This has a more-or-less linear gain for X in the range 0-250, then smoothly flattens out to max at X = 500 with a value of 250 for Y. Of course, it then starts decreasing, but if we just declare the cap to be the value when X = 500 then that's no problem.

So the remaining question is how heavily to weight finesse and prowess in the calculation. The current system favors finesse fighters using finesse weapons (precisely striking a weak point) and prowess fighters using prowess weapons (pancaking the opponent's skull) while disfavoring compromise fighters. Personally I like that but others may feel differently.

EDIT: so, for example, if we leave the current "applied finesse squared plus applied prowess squared" system in place, then a possible formula for crit chance could be given as
Code:
factor = (finesse * balance) ^ 2 + (prowess * heft) ^ 2
if factor > 400000:
    chance = 50
else:
    chance = (factor - (factor * factor) / 800000) / 4000
This gives a curve that peaks at 400k with a value of 50. "factor" for jevansau's character up there was 485k, for reference. A young character might have, say, 2 blows at a 1.5x multiplier, giving factor = (100^2 + 50^2) = 12500 for a crit chance of 3. Later on at 5 blows with a 2x multiplier, factor = (400^2 + 100^2) = 162500 for a crit chance of 32. Seems like it ought to scale well.

EDIT 2: one issue here being that factor gets squared again. 400k squared is much bigger than 2^32. Unfortunate! We could replace the squaring in generating factor by just the sum of products (i.e. finesse * balance + prowess * heft), but that just mirrors the normal damage roll, so it basically says "if you already do lots of damage, then you have a better chance of dealaing even more damage." I prefer the current system where normal combat favors compromise fighters and crit calculations favor fighters that are all-finesse or all-prowess.

So one possibility is to divide factor prior to plugging it into the chance calculation:
Code:
// Yields a value between 0 and 100 for factors from 0 to 400k
factor = ((finesse * balance) ^ 2 + (prowess * heft) ^ 2) / 40000
if factor > 100:
    chance = 50
else:
    chance = (factor - (factor ^ 2)) / 200
No more overflow worries!

Last edited by Derakon; March 8, 2012 at 00:57.
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Old March 8, 2012, 02:30   #18
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One quick thing - the last formula is wrong - should be:
chance = (factor - (factor ^ 2) / 200 )
Otherwise chance will be negative.

Otherwise seems like a good method.
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Old March 8, 2012, 05:56   #19
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Oops, good call. Thanks for the correction.
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Old March 8, 2012, 08:35   #20
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Quote:
Originally Posted by Derakon View Post
Oops, good call. Thanks for the correction.
In the first equation of the second set did you mean to divide by 40000 at the end of calculating factor, or by 4000?

But in principle it works for me. If chance maxes out at 50% then we don't need to decay it, and calculating the expected damage becomes a lot easier.
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