Chance to HIt (CTH) formula

[chattius 2,653]

This developed from a discussion with Munera we did with personal messenges:

 

My daughter did some tests while she was bored at hospital. But since she is only approaching 13 she hasn't done a full mathematical proof:

Base hit chance with 2312 attack value versus a level 160 goblin in niob: 57%

with 2312 attack and 62% -enemy chance to evade: 152%

with 2312 attack and 4.4% sure hits: 62%

with 2312 attack, 4.4% sure hits and 62% -enemy chance to evade: 164%

 

if we now do a hit formula:

 

(base_hitchance+sure_hitchance)/(1+(enemy_evade_chance - chance_that_enemy_can't_evade)/100)

 

we will be down to rounding errors it seems, if we assume that the goblin has only a defense value but no evade chance.

 

(57+4.4)/(1+(0-62)/100)=61.4/.38=162%

 

Note that the sure hit chance synergizes with the chance that enemy can't evade. It seems to be applied before the evade comes in.

 

What I need is: People who do some tests with the above formula and who say if it fails for more than 2% at certain cases. I think we have to allow 2% error for rounding up in sigma statistics, hit chance showing, ....

 

P.S.:

In german version it is x% sichere Treffer (sure hits), in english: chance that enemy can not evade ?

[essjayehm 58]

P.S.:

In german version it is x% sichere Treffer (sure hits), in english: chance opponents cannot evade ?

 

Exact wording I edited in red above. I typically abbreviate this COCE

 

Enemy Chance to Evade is Opponent's Chance to Evade. I usually use OCE for this.

[chattius 2,653]

So if we do:

ignore all block and reflect

BHC for naked hitchance with just attack value

COCE for chance opponents cannot evade

BOCE for base chance of opponent to evade

OCE for minus Opponent's Chance to Evade

 

hit chance = (BHC+COCE)/(1+(BOCE-OCE)/100)

 

What we see, as long the enemy has no chance to evade and we go near to 100% OCE we will divide by something real small and the hit chance will be real high, well at least as long as (BHC+COCE) are not 0. So we should add at least add one COCE item to prevent low hit chance versus enemies which have a high defense value. COCE is also needed if the enemy has an evade chance.

 

Edit: I am getting unsure if BOCE may be already used to calculate base hit chance. Somehow it would be weird if an enemy with an evade chance of 90% would only reduce its chance to be hit by 1/(1+.9) which means only half chance to be hit. But since we can't see enemy evade chance it is guessing right now. But if the enemy has no base evade chance, or if it is allready calculated into BHC the formula seems to fit:

 

hit chance = (BHC+COCE)/(1-OCE/100)

Edited September 23, 2010 by chattius

[chattius 2,653]

If nobody comes up with a counter example I will consider the formula as correct.

 

Let's do some transforming in case the enemy has no evasion chance. We start with:

 

hit chance = (BHC+COCE)/(1-OCE/100)

 

Obviously we want a hitchance of 100%.

 

100 = (BHC+COCE)/(1-OCE/100) Bring this up to the counter of the fraction

100 = 100*(BHC+COCE)/(100-OCE)

1 = (BHC+COCE)/(100-OCE) Bring this to the other side

100 - OCE = BHC + COCE

100 - BHC = COCE + OCE

 

Is it really this easy? If you have a base hitchance of 70% :

 

100-70 = 30 = COCE + OCE

 

COCE is scaling , OCE isn't but has normally lower values. But the sum of both of them has to be just the missing hit chance. Heureka, I think this a such an easy formula everyone will understand.

 

And now the funny part:

If the enemy has no evasion chance: if your OCE and COCE sums up to 100% you will always hit. No weapon skill, no +attack value needed.

 

CAUTION:

This is only correct if the enemy has no evasion and if the start formula is correct.

 

post scriptum: Fot Math Freaks: since COCE is scaling it cannot reach 100%. So OCE or BHC has to be above 0.

Edited October 23, 2010 by chattius

[Munera 1]

The thing I can't see in any formula is the role of attack/defense. I'm very curious about it and it's certainly the most important part of the equations.

 

Regarding sure hits (chance that opponents cannot evade attacks) I think it's added to the final chance to hit after all the calculations have been mate. It adds directly to your hit chance, and nothing seems to reduce the bonus it provides. For example, if you have +10% sure hit, it doesn't matter if your hit chance is 62%, 75% or 90%, it will add that 10% whatever happens.

[chattius 2,653]

Attack/Defence would be BHC- base hit chance.

[Munera 1]

And how do they work? ^^ I mean, how would we be able to calculate a chance to hit when there is no sure hit, chance to evade neither opponent's chance to evade, only attack and defence involved?

[chattius 2,653]

Der leichte Beweis bleibt dem geneigten Leser überlassen....

The easy proof is left to the interested reader ....

 

I always hated this line in math books. But I fear without knowing the defense value of an opponent.... PvP would be the only way to find it out. And then we have to make sure that PvP is using same formula as PvM.

 

Or finding how attack value works versus a single enemy with a fixed defense value, .... hmmm

[Munera 1]

Or finding how attack value works versus a single enemy with a fixed defense value, .... hmmm

 

Actually, we could increase our attack value and see how our chance to hit fluctuate, as the previous enemy's stats don't change. Anyway, I think you are right: the only way to make an accurate formula is using PvP

[chattius 2,653]

Anyone knowing if there are enemies which have natural evasion, meaning which is not coming from a (mini-)buff?

 

I asked my kids to do some testing with a few Bosses and using Gogo's hit chance calculator. It looked as if 100 in the sum of COCE and OCE is enough to show a 100 %hit chance. But it could be that evasion from a mini-buff thy had while they were alive is not shown in last kills hit chances. Could it be that (mini-)buffs are removed before the hit chance is shown?

 

So if you have time, try to help if there are beasts which show a lower than 100% hitchance even the some of COCE (scaled value) and OCE is above 100.

[chattius 2,653]

The question I put more than half a year ago is answered.

 

Yes, several niobium bosses have a chance to evade. I did some hit chance tests and plotted the hit chance function at a fixed enemy, fixed attack value, no sure hit and changing 'minus enemy chance to evade'. I got a value of around 50% evade chance at a boss, so at high evasion niobium bosses the balance should be more shifted towards sure hits.