Combat odds for large stacks

[Shiber]

Originally posted by vulture
What is the bombard defense of a unit on a mountain? Is it just their combat strength with terrain modifier, as normal, or is it something weird. Defensive bombard always seems to do better than I'd expect somehow.

That's a good question.
I have absolutely no idea how defensive bombardment is calculated. I've only seen threads about experiments being made with attack bombardment. I've even seen a very comprehensive study on CFC recently and it didn't have anything on defensive bombardment either.

[Arrian]

If you're talking about the shots our cats will get if Vox attacks our cities, I don't know either, but I strongly suspect that it's the cat's bombard power (4?) versus either the Immortals' attack power (4) or defense power (2). Not sure which. I very much doubt that the terrain matters at all.

My experience with cats on defense has been limited to watching the effect AI cats have on my attacking troops in the ancient/medieval eras. My horsemen almost always get hit. My knights get hit fairly often. My Cav sometimes get hit by cats...

I think it's probably the attack strength that matters. So that would give our cats a 50/50 shot at attacking Immortals.

Total guesswork, though.

-Arrian

[vulture]

Updated odds, get them while they're hot!

Still no catapult data as such, but I've done two cases, one with no catapults, and one assuming all catapults hit. On average we will end up about halfway between the two, but it shows the range of difference the catapults can make.

Stacks on Arashi 2 and Arashi 9 attack Arashi (and attack with everything, which probably isn't realistic, as before - how often are they going to attack with a spearman or 1 hp immortal).

First column, number of Vox survivors (aka no. of Vox victories), second is prob, 3rd cumulative prob, both ignoring catapults. 4th and 5th are prob and cumulative prob with maximum benefit from 3 catapults.

0 || 8.5% 8.5% || 14.4% 14.4%
1 || 20.4% 29.0% || 27.2% 41.6%
2 || 25.4% 54.4% || 26.6% 68.2%
3 || 21.4% 75.7% || 17.7% 85.9%
4 || 13.6% 89.3% || 8.9% 94.8%
5 || 7.0% 96.3% || 3.7% 98.5%
6 || 2.8% 99.1% || 1.2% 99.7%
7 || 0.7% 99.8% || 0.2% 100.0%
8 || 0.1% 100.0% || 0.03% 100.0%
9 || 0.01% 100.0% || 0.0% 100.0%

Averages without catapults (and with catapults):

Vox: dead 6.52 (7.03), promoted 0.40 (0.33), leaders 0.0 (0.0)
GS: dead 2.48 (1.97), promoted 1.86 (2.03), leaders 0.050 (0.060).

On average the presence of leaders increases our leader odds from 5% to around 5.5%, which is nice. Leader odds are probably overstated, since I suspect quite a lot of them come from a spearman attacking an elite pikeman, which is something that just wouldn't happen in a real game, so the 3% from the previous tables is more realistic.

[vulture]

And for the Arashi 2 stack attacking Tempest (columns as before):

0 || 11.5% 11.5% || 19.2% 19.2%
1 || 26.7% 38.2% || 33.3% 52.4%
2 || 28.7% 66.9% || 26.9% 79.4%
3 || 19.8% 86.7% || 14.1% 93.4%
4 || 9.6% 96.3% || 5.2% 98.6%
5 || 3.0% 99.3% || 1.2% 99.8%
6 || 0.6% 99.9% || 0.2% 100.0%
7 || 0.1% 100.0% || 0.03% 100.0%

Averages (with catapults):

Vox: dead 4.99 (5.43), promoted 0.30 (0.24), leaders 0.0 (0.0)
GS: dead 2.01 (1.57), promoted 1.44 (1.59), leaders 0.027 (0.032).

[Shiber]

I searched poly and CFC for hours... still no idea how defensive bombardment works.
Vulture: great job!