Civ6 Combat Formula

[T-hawk]

Those aren't quite equivalent?  The originally suggested 75%..125% of base isn't the same as 24..36.  It's 80%..120% of a base 30 that would work out to 24..36.

Yeah, tiny nitpick.

[fluffyflyingpig]

Those aren't quite equivalent?  The originally suggested 75%..125% of base isn't the same as 24..36.  It's 80%..120% of a base 30 that would work out to 24..36.

Yeah, tiny nitpick.

That will show me for trying to do math early in the morning 

[HansLemurson]

Those aren't quite equivalent?  The originally suggested 75%..125% of base isn't the same as 24..36.  It's 80%..120% of a base 30 that would work out to 24..36.

Yeah, tiny nitpick.

Yeah, I overestimated the dispersion range when I eyeballed it.  Checking my data again, it does seem that all the values were between 82% and 122% of what I predicted.

[williams482]

I figure necromancing this 5+ year old thread is better than making a new one on the same topic, especially since I have relatively little extra to add.

Ljubljana and Thrawn made an interesting discovery about the combat formula in Ljubljana and Woden's PBEM20 thread, starting here. In short, all combats have 12 possible damage outcomes, distributed evenly. This has a pretty significant effect on calculating kill chances if the actual formula can be worked out, and even keeps the probability spaces small enough that figuring kill probabilities for multi-combat actions could plausibly be done in a spreadsheet. 

I did some brief testing of my own, and found that the damage outcomes for even combats in a controlled setting range from 24 to 35, 12 possible options as expected. This is almost consistent with the theoretical formula described upthread: 

Great work.  Restated, using the variables from the xml:

Damage = [ COMBAT_BASE_DAMAGE + Rand(0,COMBAT_MAX_EXTRA_DAMAGE) ] * exp( COMBAT_POWER_SCALING * StrengthDifference)

Damage = [24 + rand(0,12)] * exp(0.04 * StrengthDifference)

Damage cannot be less than COMBAT_MINIMUM_DAMAGE, which defaults to 1



Of course, this is exactly the same as the formula you came up with initially for the default xml parameters.

... except that there is clearly a -1 in there somewhere, or the range would be 24-36 with zero strength differential. I've tried to match up a few different formulae, but I have yet to find a perfect match for the data we have for both neutral and +25 combats. 

So, I have nothing really new to report here. But I figured I'd restart the discussion somewhere a little more central than the PBEM20 subforum.

[T-hawk]

In most computer languages, a random function with parameters (a,b) means a range that is inclusive of a but exclusive of b. So rand (0,12) really gives a number from 0 to 11 (or a floating point up to 11.999999... that gets truncated.) That would account for your observation here.