Battle formula

[Shendemiar]

This is a thread about investigating the relation between win % in the ingame calculator, and the actual losses% in the battle.

Post any relevant info or ideas here.

[Shendemiar]

As a part of my investigation finding the relation between Win% and losses% i attacked with a big fleet on weak isle. The results were interesting.

Huge fleet suffered as much damage than several smaller fleets would have done, while it had to bear the risk of being kampfed.

With the odds like 99.7% i still suffered 18% losses, equaling roughly the strength of the defender.

Taking into account 5X200LWS is far more easier to produce than 1X1000LWS, and that they do similiar damage, and the kampf factor, it seems highly advisable not to use the huge fleets in attacks until we have studied more our battlereports.

action=Isle_events&Target=1_35_15

[eproxy]

The closer you get to 100% after a certain point (say 95%) then fleets can become less efficient . Imagine trying to kill 100 people - if you send 100 yourself then the odds are 50/50. If you send 200 then you'll probably win and suffer losses only to the enemy - send 2000 and you suffer a similar number of kills to the enemy but you'd take quite a few friendly fire/attrition losses. Of course that isn't how IK actually works it out - it's a relatively good analagy though.

Added; the actual reason is that the % decrease in losses incurred by the extra units is 'overtaken' by the extra number of units. Ie. 5% of 100 is 5 where as 3% of 200 is 6 (ie. you'd still lose more since %victory chance is not linear).

Added2; If the attacker has superior odds and then wins (this therefore excludes 'kampfs which are a random event anyway) they will take (SQRT*(2*(1-V)) losses. Ie. 97% chance to win results in that person taking 0.316% losses (about 1/3 of the fleet) - 0.99

Attacker Victory Chance (decimalised)	Victor Losses (decimalised)
0.900	0.4472
0.905	0.4359
0.910	0.4243
0.915	0.4123
0.920	0.4000
0.925	0.3873
0.930	0.3742
0.935	0.3606
0.940	0.3464
0.945	0.3317
0.950	0.3162
0.955	0.3000
0.960	0.2828
0.965	0.2646
0.970	0.2449
0.975	0.2236
0.980	0.2000
0.985	0.1732
0.990	0.1414
0.995	0.1000

Attacker Victory Chance (decimalised)	Victor Losses (decimalised)
0.9950	0.10000
0.9951	0.09899
0.9952	0.09798
0.9953	0.09695
0.9954	0.09592
0.9955	0.09487
0.9956	0.09381
0.9957	0.09274
0.9958	0.09165
0.9959	0.09055
0.9960	0.08944
0.9961	0.08832
0.9962	0.08718
0.9963	0.08602
0.9964	0.08485
0.9965	0.08367
0.9966	0.08246
0.9967	0.08124
0.9968	0.08000
0.9969	0.07874
0.9970	0.07746
0.9971	0.07616
0.9972	0.07483
0.9973	0.07348
0.9974	0.07211
0.9975	0.07071
0.9976	0.06928
0.9977	0.06782
0.9978	0.06633
0.9979	0.06481
0.9980	0.06325
0.9981	0.06164
0.9982	0.06000
0.9983	0.05831
0.9984	0.05657
0.9985	0.05477
0.9986	0.05292
0.9987	0.05099
0.9988	0.04899
0.9989	0.04690
0.9990	0.04472
0.9991	0.04243
0.9992	0.04000
0.9993	0.03742
0.9994	0.03464
0.9995	0.03162
0.9996	0.02828
0.9997	0.02449
0.9998	0.02000
0.9999	0.01414
1.0000	0.00000

Oh and don't be fooled by the in-game calculator, even when it says 100% victory chance it's just rounding up (from say 0.9997). Like with the exponential function e, no matter the exponent you'll never actually reach 0 (using a real number at least).

The trick is to have the correct sized fleet for every circumstance (not always the biggest).

[inyati]

eproxy said:

<snip>
The trick is to have the correct sized fleet for every circumstance (not always the biggest).

And what about makeup?
Would 100LWS+100SWS actualy be more effective than 200LWS?
Or would that be 100LWS+80SWS be the best ratio?

Now I'm really sad I dont have fleets to test this out, but would anyone be interested in attacking using the same amount of lws+sws to check out how that works? I'm sure good easy targets against the orc could be used as experiments.

[eproxy]

The Gold saved by using any amount of SWS instead of LWS is not offset by the lower efficiency of them (related to the number of units they fit inside themselves) and therefore the higher losses you'd take. Ie. just use Large Warships for proper battles.

[Shendemiar]

Great work eproxy, (Exalts)

How do you calculate the odds prior the attack more precisely than the ingame calculator?

What i've preliminarily found out, is that with same odds, the losses may be different from time to time, but that need solid testing to be claimed the truth.

[eproxy]

Unfortunately I can't work out the odds more precisely than the in-game calculator - no matter how hard I try I just can't figure out the formula for it (I always seem to get a massive mental block). I remember somebody once mentioning that you multiply the offence/defence levels together or something. Eitherway the fact that there is an asymptote at either end should help me out (but it never does). I still can't work it out with access to essentially an unlimited amount of results either ^^

I don't know why the losses would be different although I do know that the actual application of my forumla doesn't always go to plan. I've had actual losses vary by about 5% from what I 'should' have had (perhaps due to the 'inaccuracy' of the in-game calc? unless I made an error when I worked it out). Luckily though, on average, it is usually no more than 5 or so LWS out.

[mmupatton]

Wow. An exalt is on the way, definitely.

I have trouble following the math here, which bothers me quite a bit. I consider myself good at math! Anyway - is there a specific combination of ships and men that would generally yield a better result than others?

[Arminius]

Can we (from the database) work out what the chances are for a kampf? Also, can we test the formula on all those attack reports?

[AeroS]

I always send clearing fleets with just LW's and spears that have a 45% chance of success. If I lose, then the army that is left is very small and I get a 99% chance of success with my colo fleet. If I win.... well thats just great.
When I send fleets of this size, I cant get Kampfed because I already know that the fleet will be a complete loss already.

[eproxy]

If your a 'defensive' player (ie. keep the barracks running 24/7) then your best set-up is do as AeroS states - use purely LWS full of Spears and the minimum number of catapults (usually 25 does).

As far as ships go the LWS is alot more efficient than the SWS (and for the same relative price). As for catapults they're highly ineffective compared to their price. The main debate is whether to use Archers or Spearfighters.

For those of you who like to keep the barracks running 24/7 then spears are always the way to go (they're better all rounders and make better use of the barracks build time). If your barracks does have some spare time each day then it may be wise to utilise that 'spare' time by training some Archers in place of some of those Spears. I'm not sure of the stats using the XXL 'trick' but being honest I'd probably still make 24/7 Spears and some LWS on all my isles anyway.

Take this example: If you have 100 LWS and put away enough time to build say 500 Archers you could have made 670 spears instead. Also, considering that Spears make better attackers than Archers do defenders then spears are again the way to go.

Added; Being 'kampfed is essentially just losing when you did in fact have the majority chance to win (ie. 80% chance to win means 'kampf chance 20%). In this case you automatically lose everything and the 'winner' (who should have lost) will lose a standard 95% of their units.

[Shendemiar]

arminius said:

Can we (from the database) work out what the chances are for a kampf? Also, can we test the formula on all those attack reports?

Yes i have had some initial research with our results and they seem to follow the logic given here in most cases. But mmore research is needed.

[mmupatton]

I see a lot of calculators around the 'net emulating the in-game calculator. Does anyone know how the percentage (chance of success) is calculated?

[Shendemiar]

mmupatton said:

I see a lot of calculators around the 'net emulating the in-game calculator. Does anyone know how the percentage (chance of success) is calculated?

I would consider that secondary, since you can always derieve the odds from ingame, but the relation of the odds vs actual damage isnt very clear... Thats the subject to study.

[eproxy]

Unfortunately I can't get more accurate than the above formula - for what it's worth I looked up the different estimates for a couple of attacks I sent.

I'm presuming the current version of the Corleth tool uses the above formula?

This battle was only just won (55.8% victchance)
ikcalc+form 0.940212741
actual 0.937565472
germsite 0.928556463
corlethtool 0.94

Funnily enough looking at the fact the ingame calc rounds to 1 dp that % could actually be as high as 55.85% - which would give 0.9396... losses, ie. pretty close to the actual losses. The actual loss % could also be as high as 0.9376... although they never actually overlap.

This battle involved a 99.6% chance to win.
ikcalc+form 0.089442719
actual 0.1445
germsite 0.0825
corlethtool 0.089

Note: this is the germsite.

For the more equal battles (victchance closer to 50%) both the german site and calculation seems to work within acceptable limits. Once you start to outnumber the enemy more the cacluations on both sites tend to underestimate the losses.