SummonersLab, Part 2: Crit Algorithem Improvement

Lord Desert·12/1/2016, 9:52:30 PM·5 votes·940 views

Today we will look at the Crit Algorithm in LoL and make some adjustments with very low and very high amounts of CritChance.

Currently those are the topics and their (hopefully) release date: SummonersLab, The Introduction Here SummonersLab, Part 1: An additional Crit Item Here SummonersLab, Part 2: Crit Algorithm Improvement Here SummonersLab, Part 3: Tower Changes Here SummonersLab, Part 4: Ohmwrecker Here SummonersLab, Part 5: Support Role Improvement(1) Here SummonersLab, Part 6: Wits End Here SummonersLab, Part 7: Smite Buffs Here SummonersLab, Part 8: Plants Here SummonersLab, Part 9: ** Support Role Improvement (2)** _ Here _ SummonersLab, Part 10: ** General Improvements (1)** Here _ SummonersLab, Part 11: ** General Improvements (2)**_ Here Ill put links to the posts here, so you can easily view all of them.

1. The Problems

We all have been there, someone crits you, while they have only 1% or 10% CritChance. Ok, if they crit you once, thats unfortunate, but if they crit you twice or more with such low amounts is not just unfortunate or bad luck, thats flat out unfair/ extremely tillting from the get go of a game. If that wasnt bad enough, you adcs may have felt it, even if you finally reach the 70-80% Crit mark or higher, you dont seem to crit at all?! This may only accure in less then 1% of all games, but you know that when you get to play as adc or vs a 1%Critchance guy, it will happen in 50% of your games! Trust me, i speak from personal experience :P

We want to fix or atleast better this, but first alot of disclaimers:

Im not from riot and the exact formula of Crits is secret(and that is good), but we know that LoL uses a PRD(explaination later), i have tested and verified that. Since we dont know the exact numbers, we can look at other known crit formulas which will be ~99% the same as the one LoL uses. I will base this on those values.
This will not change the way Crits work, it will still be a Chance based on RNG!!!! But the really extrem cases, the so called "outliers", will be removed/ atleast heavily toned down.

Oh boy, this will include alot of math, but fear not, ill break it down so it should not be that bad. watch out for this boxes: > Important Info

Ill put the most important infos in there, so you dont need to follow everystep. Ok, lets start:

2. The Idea

Since we dont want to change the RNG part that much, a good way to "balance" those outliers are Caps. "Caps? ive heard that before!" Yes, the movementspeed calculation for example uses SoftCaps. Above 415ms every extra ms will multiplied by 80% (so every extra ms above 415 will be reduced by 20%) and above 490ms it will be multiplied by 50%. While Crit Chance is hardcapped at 100%.

Lets look a low amounts of CritChance first: So to eliminate those outliers, we simply cap how many crits you can do, in a row, after you crited once. And this is gated by your CritChance.

> Forcing a certain amount of NonCriting AAs after a Crit, and limiting the max amount of crits in a row, all based on your Critchance

Those limitaions are very hard at very low amounts of CritChance, and will ease up the more CritChance you get.

Those Limits should look like this: Basic Cap: <=20% CritChance = 2 NonCrits forced after a Crit >20% - <40% CritChance = 1 NonCrit forced after a Crit >=40% - <50% CritChance = max. 2 Crits in a row (3rd AA will not crit) >=50% - <60% CritChance = max 3 Crits in a row (4th AA ...) >=60% - <80% CritChance = max. 5 Crits in a row >=80% CritChance = No limit, because of how the algorithm works. (view PDR explaination)

Since it might be still a bit unclear, here some examples: You have 10% Crit Chance and now do a Crit, normaly your next AA could crit too, its extremely unlikely, but possible. With the BasicCap, your next AA will not Crit what so ever! It will not crit. Even the AA after this will never crit too! But the AA after that can crit again. What does this mean? The most "luckest" Outcome changes from (Crit, Crit, Crit, Crit) to (Crit, NormalAA, NormalAA, Crit). We simply are forcing normal AAs and thus more time between the Crits.

Now lets say we have 30% CritChance: When we crit now only the next AA will never be a Crit. But now AA after the never criting AA can crit again! So the luckiest case looks like this: (Crit, NormalAA, Crit, NormalAA, Crit)

3. More Math

Now that we limited the maxium possible luck, we now can Limit the misfortune! But since granting guarenteed Crits, while you only have low amounts of critchance, have a very high potential to be abused (In the Early stages Tryndamere were able to abuse this), we should refrain from giving them left and right!

But before that we need a little excurse into PRD.

PRD Explaination PRD (Pseudo Random Distribution) is a way to get pseudo randomness. And it balances the randomness, so that we have way less outliers!

PRD works like this: You have 50% CritChance. But Your 1st AA ONLY has a 25% Chance to Crit. BUT if this AA did NOT crit, then the FOLLOWING AA gets +25% CritChance. So your 2nd AA has a 50% Chance to crit. If this failed again, the 3rd has a 75% Chance to crit. If failed again, the 4th has then a 100% Chance to crit. After a Crit was scored, you will be reset back to your 1st AA! So after a crit you basicly only have a 25% chance to crit, and not 50%, but with every following failed AA you get more and more %Chance to crit.

> 50% Crit is only 25% on the first AA and not 50% on every AA, but you get +25% on every NonCriting AA! After a crit you get reset to the basic 25% again!

In numbers: 50%CritChance is not 50% on every AA, its only 25% on the first, 50% on the 2nd, 75% on the 3rd, and finally 100% on the 4th. If you crit you will be reset to the 1st AA.

As a quick reminder: If you have 50% Crit chance and scored 4 Crits in a row, the chance of this happening was not 1/16 (1/21/21/2*1/2) = 6,25% It was only 1/64 to 1/256 = 1,56% - 0,39%. Basicly the chance of you getting 4 crits in a row is not 6% but only about 1%!!!! So if you see thos crits, you know that someone got really lucky!

Those numbers(50% -> your first AA only has a 25% Chance) are calculated constants! if you want to see the most likely possible numbers, check this out: http://imgur.com/xmLzg5n

Heres the original page, with some futher explaination: Link

Problems with High CritChance

Since you now know how a PRD works, you can see that 80% get reduced to ~50%. So you are basicly guarenteed to get a crit after a NonCritAA. But since you get reset to the 50%, you get far more noncrits then you should! Effectivly lowering your overall CritChance to around 66%!!! This is a problem with the numbers from the start: Warcraft first introduced PRD but made a small mistake at the high values. (you normaly are interested only in those values below 50%, so this mistake was ignored. a bit history for you all) So first we should change that to ~66% at the first AA, making the effectiv %Chance way closer to the intended 80%.

This will fix alot of problems, but you can still get really unlucky and get stuff like this: (Crit, NormalAA, Crit, NormalAA, Crit etc.) at worst only 50%. While you have 80% CritChance! If that would not tilt you from the face of the earth, then i dont know what else could do that. And we all know that 1 Crit can make the differnce of losing or winning a game. To fix this we can use our trusted caps again, but this time we need a bit advanced version. Putting everything together in 1 AdvancedCap:

Advanced Cap: <=20% CritChance = 2 NonCrits forced after a Crit >20% - <40% CritChance = 1 NonCrit forced after a Crit >=40% - <50% CritChance = max. 2 Crits in a row (3rd AA will not crit) >=50% - <60% CritChance = max 3 Crits in a row AND After 3 NonCritAAs in a row, your next 2 AAs are guarenteed Crits >=60% - <80% CritChance = max. 5 Crits in a row AND After 2 NonCritAAs in a row, your next 2 AAs are guarenteed Crits >=80% CritChance = After a NonCritAA, your next 3 AAs are guarenteed Crits

This is rather complicated to understand, but basicly we are removing extrem bad cases, giving a better minium CritChance, in the worst case. ( the 80% could be only 50% in the worst case, we change that to 60%(66%) in the worst case. Doesnt sound like much, but remember we only tweak the RNG a bit, we dont want to temper with it to much, and guarenteed Crits are rather powerfull).

> We increase the worst case CritChance, specialy at high CritChance values.

With this change we finally have a rather good improvement already!

4. Extras

Since we take something that you rightfully got (you can get extremely lucky), without any compensation! We can change that, but remember: Guarenteed Crits with high amounts of CritChance are somewhat fine, but they are extremly bad, if you only have low amounts of CritChance!! So we could give a compensation by for example doubling the starting chance on this attack, but this also can be abused. It will not break anything or be really bad, but it increases your chances of getting an extra crit. And giving possible benefits is a risk i would not take, but this or other compensations can be freely discussed if you want. I personaly would rather advise against it, but thats not set in stone :P

5. TL;DR:

Holy moly, what a massiv wall of text, luckily theres this neat thing called TL;DR :D

This mainly deletes Outliers! You will not feel any difference! BUT theres a flaw with high CritChance that NEEDS to be adressed
implementing a cap with Forced NonCrits + Crits in a row + Guarenteed crits after NonCrits in a row, all depending on the current CritChance.
extrem luck with low %Chance tuned down
extrem misfortune with high %Chance tuned down
to much math, but RNG Outlier removed -> helps the game health
the Cap in detail: <=20% CritChance = 2 NonCrits forced after a Crit >20% - <40% CritChance = 1 NonCrit forced after a Crit >=40% - <50% CritChance = max. 2 Crits in a row (3rd AA will not crit) >=50% - <60% CritChance = max 3 Crits in a row AND After 3 NonCritAAs in a row, your next 2 AAs are guarenteed Crits >=60% - <80% CritChance = max. 5 Crits in a row AND After 2 NonCritAAs in a row, your next 2 AAs are guarenteed Crits >=80% CritChance = After a NonCritAA, your next 3 AAs are guarenteed Crits

Since this took way longer to get nice and bearable for the NonMathJunkies, the Tower Changes Part might be delayed a bit :/