Forum: empire-en

Board: [589] Strategy & Tactics Discussion

Topic: [343618] Crunching the numbers.

[-343618] unr341 (US1) [None] :: Nov. 14, 2017, 5:09 a.m.

hey ppl! thx in advance 4 ur time n attention.

im trying to figure out the attacking/defending ratio (ie salvaging or losing troops).
im attaching some screencaps n adding afterwards some math, any help would be much appreciated.
this is the battle i used 4 trying 2 figure this out...

this is the commander i used:



the castellan i went against:



the battle overview:



the battle details:



ok, on 2 the math.. i went full "melee force" thru the front, so the battle took place directly in Cyard..

MELEE DEFENSE: 417 units ( all units, including ranged n armed citizen )
1188 + 1350 + 530 + 8450 + 19170 = 30.688
+17% ( def bonus ) 5.216 = 35.904

MELEE ATTACK: 688 units
25724 + 5664 + 2125 + 17500 + 1390 + 1490 + 875 + 15438 + 21.170 = 91.376
+107% ( 80% melee + 27% Cyard ) 97.772 = 189.148

35.904 vs 189.148

LOST UNITS: 90
2774 + 1992 + 175 + 149 + 139 + 2380 + 250 + 708 + 3379 = 11.946
+107% ( 80melee + 27Cyard ) 12.782 = 24.728

( generating ratio using attack power against attack power lost )
189.148 / 24.728 = 7.64914267227

( generating ratio using total units against lost units )
688 / 90 = 7.64444444444

is all of this correct? or am i missing something?

if i make 100(%) / 7.64914267227 = 13.0733605431 <-- loses in % relative 2 full body, using force ratio
if i make 100(%) / 7.64444444444 = 13.0813953488 <-- loses in % relative 2 full body, using units ratio

using those results (loses in %) against the the full force i get:

189.148 / 13.0733605431 = 14468.2003817
189.148 / 13.0813953488 = 14459.3137778

n yet i lost, 12.782... n 24.728 with added bonuses

it doesnt match up
is my math wrong?... does this ratio exist?
am i chasing my tail here?

greetings.

[4864326] Raggle Fock (US1) [None] :: Nov. 14, 2017, 12:37 p.m.

your assuming there is a linear relationship between troop losses and relative power. i'm not sure thats the case.

[4864344] Wiglema (NL1) [NL1] :: Nov. 14, 2017, 1:52 p.m.

First of all, please don't use the same symbol "." as both a decimal point and a thousands divider, because that's very confusing.

Second, the last bit of math is not correct. If you want to properly chase your tail, it should be:

189,148 * 13.0733605431% / 100% = 24728.0
189,148 * 13.0813953488% / 100% = 24743.2

The difference between the outcomes is due to rounding effects in the 90 soldiers loss. Mathematically there would have been 89.94 lost soldiers, but in practice that means 90 soldiers were lost. So, basically, your numbers do match up.

Third, you did add the +17% melee defense bonus, but you forgot to take into account the -30% courtyard defense due to the broken wall. Anyway, in your calculations you did not use the total defense strength, so this is a harmless mistake. [Edit: should be -30% for the attacker, not the defender, but that won't make a difference for the ratios either, so still harmless.]

Fourth, just in case you want to use similar calculations to predict your losses, it's not going to work, because the loss ratio does not scale linearly with the attack/defense ratio.
The only thing that is linear, is the loss ratio in troops compared to the loss ratio in attack power, apart from small errors due to rounding. This is exactly what your calculations show (after correcting the math).

[4865495] Peter John (US1) [US1] :: Nov. 14, 2017, 10:50 p.m.

@Wiglema (NL1) The -30% cy apply as penalty to the attackers.

And there is a "luck/random" factor too (not much tho).

[4865528] Wiglema (NL1) [NL1] :: Nov. 15, 2017, 12:07 a.m.

Hi Peter John,

You're quite right, I had missed that the -30% is for the attacker. I'm not used to seeing that in my own attacks, haha.
For the above calculations it doesn't really matter; some numbers will change, but the lost troops ratio and the lost power ratio will still be the same.

Same for the (small) random factor. It will not change the mentioned ratios. It matters for the attack/defense ratio, but the calculations are not about that.

[4865567] Peter John (US1) [US1] :: Nov. 15, 2017, 4:04 a.m.

not sure what's the point comparing the lost troops ratio vs lost power ratio, of course it will be the same (well, not really, due to the rounding, as you said). but the relation between the attacking troops and attack power is in a linear direct proportion. If 1 M Att. has power 100, then 2 M att. (of the same type) will have power of 200. So I don't understand what's fuzz about it. They are essentially the same thing, just different metric.

I guess I don't quite understand exactly what the OP is after. But I'm guessing ultimately he try to predict the losses. If this is the case, I suggest he collect the data vs NPC, where the def. formation won't change, so he then can experiment with different attack formation vs the same defense, to test whether his power att/def ratio calculation is correct or not.

Once he feel comfortable on his formula, collect as many as data point and run it to an interpolation software to get the converting formula from att/def power ratio to losses.

[4866325] unr341 (US1) [None] :: Nov. 16, 2017, 12:55 p.m.

sry 4 the late response
@Winglema

1. sry bout the decimal point n thousand divider confusion, just formatted like it 2 help on the eyes, thx 4 ur understanding.

2. also, thx 4 correcting me on the math, im always up 4 learning, n i got it really wrong when trying 2 verify the results with that last bit, such a silly mistake.. (im not a math wiz but i try 2 do it anyways) now thanks 2 u ive learned from my mistake, glad 2 know they DO match n i was at fault there

3. ofc ur rite again, bout the -30%, bc i wasnt aware that taking only 1 flank would rest 30%, only knew of the bonus at CY bc of the stats on equip n what few other players mentioned me bout, now im more aware of the whole taking flanks importance when adding bonuses at courtyard

4. gonna work on this next

@Peter John
i calculated both bc i didnt know how to face the problem solving, regarding 2 as how was calculated who lost what, how much n why, so didnt know if facing at it analazing units coalition results, or atk forces coalition results, bc of having the added bonuses n what not (thought maybe i was making a mistake when adding  n calculating bonuses, hence losing more troops than xpected), made it more of a challenge 4 me since im not that good at math, hence my silly mistake at the end of the formula.