Pryotra's Mathcrafters Club! League Mathcrafting inside! Request at will! Feel free to join in!

Pryotra·Jul 16, 2014·7 votes·576 views

I was inspired by a recent post asking about the value of a certain item passive, and thought, "You know what would be cool? A place were lazy or busy people could ask others with time on their hands to do the hard math to help them with league!" Hence, this thread!

#IT'S MATH TIME!

http://imgur.com/gjjEnhV

The idea here is to help one other with math, or request Math Problems related to league balance. This is NOT a place to get people to do your math homework. Trust me, we will know the difference. If you are good with math, FEEL FREE TO HELP! Just to make it easier on everyone, lets get some base rules to help each other get more MATH solved!!!

#RULES Requesters:

Be polite - No one needs to help you find out just how many minions you need to last hit in order to afford a Trinity Force. Keep in mind that you are the one asking for a favor, and if people don't feel like you appreciate it, they do not have to answer you.
Be patient - Just because you have to leave for school/work in 5 minutes doesn't mean anyone is on, or can even type fast enough to show you the way to find out just how many times Baron can spawn per match. When you post here, just realize it might be a little bit before someone is on to see it and answer it.
Keep it League related - I've already said this, but let me reiterate. This place is to find out math relating to league and balance. Not a place for someone to do your Cal III homework. If you word questions trying to get around this rule, people will know, and most likely will not help. That said, If you are just curious about just how much AP it is possible to get on Fiora, then ask away!

Examples: Good -

Hey, at how much health does buying armor become more effective, or vice versa? Thanks!

Bad -

Hey Buttholes, I need you to answer this Question quick, as I gotta be places. Anyways, If I have 20 Teemos, and they each bought 5 Rabadons each, how many Rabadons would have been bought?

Mathmaticians:

Show your work - This might sound weird, but alot of people really benefit off of seeing the steps. While I'm very impressed that you can know exactly how much AP that Galio will get after a rabadon's and a Guardian Angel off the top of your head, but just posting the number might not help the guy who is asking all the way. Which means he asks more questions. Which means more MATH. Maybe that's not a bad thing though...
Be Gracious - Congrats! You discovered the cheapest way to max out Yasuo's crit chance possible! While it's great that you accomplished this, there is no point in being rude about it. Simply show them how you got there, don't spend a paragraph gloating. If you want to pat yourself on the back, there is ALWAYS instagram.

Examples Good -

Good question! We can start by finding the value of those two stats, then comparing effective health values to find your answer!

Insert math here

Now, lets cross refence those values so that you can find generally where that change happens!

Mathing intensifies

Bad -

The answer is 100, dummy! I can't believe you had to even ASK, I did it in my head. It took longer for me to type this than it did to figure it out!

Alrighty, let's get this party STARTED! Start asking question that myself and others can MATH our way through! Have fun guys!

14 Comments

12talesJul 16, 20142 votes

Ooh, math. Fun.

I'll ask one that's been puzzling me for a while - Muramana Kassadin.

For a Kassadin with Maximum mana M, Starting mana m, and X Muramana procs/second - how much damage will Muramana deal, expressed as a function of time? Assume that Kassadin is spamming his (rank 5) 7.2s cooldown W on an enemy champion whenever possible, but is otherwise not expending any mana.

PryotraJul 16, 20141 votes

Wow, good Question there. His W will be an interesting one considering that it regens mana.

That said, I think you have an item build in mind. Muramana doesn't contain CDR, but if his W is at 7.2 seconds on cd, you would have to have some cdr. Also, this build has another problem: attack speed. You see, Manamune's toggle will require 3% of your mana per attack. If you somehow have maxed AS, then you will likely drain mana more than restore it, whereas if he doesn't have any, then he will hardly scratch his mana between W's.

So, in order for me to answer your question, I'll need a few more peices of info:

His AS for the build you have in mind.
His total cdr
Any other mana regen items. This will factor into the math, unless you want me to exclude it.
Anything else that you might want me to include that seems relevent. For example, are you using Rageblade, which has ramping AS? Things like that I could factor in, should you want me to.

I look forward to doing this math problem, it really seems fun!

12talesJul 16, 20141 votes

Alright then - the build I have in mind has 44% Attack Speed from runes, masteries and itemization. So, that would put his attack speed as .64(1+(.037Level)+.44). If you'd like a constant instead, you can just assume that he's level 18, which would give him 1.35 Attacks/Second.
20%
Muramana is the only mana regen item. It's fine if you don't want to factor it in, though - sounds like it'd be a lot of work.
Nothing like that. Remember that his W procs Muramana twice sequentially, since it's both an auto attack and a single target spell (I tested this in game - the second Muramana proc is calculated after the first one's consumed mana).

PryotraJul 16, 20142 votes

Alright, so assuming level 18, with 1.35 AS and 20% CDR, without any other Mana/mana regen items, The math is as follows. I will be calculating the average DPS per cycle, meaning the dps averaged over the 7.2 seconds. I will ignore mana regen, so know that the damage will be very slightly higher than the end calculation.

So, first let's find how many attacks he will get off in that time frame.

1.35 X 7.2 = 9.72

Seeing as .72 attacks cannot happen in this game, he will get 9 attacks in this time frame, with the first being the empowered W hit. Considering that Muramana costs mana per hit, and bases it's damage upon the amount of mana consumed, let's find out his total mana pool. From there, we can find his AD. I will assume you bought no other Mana or AD items. Once we have that, his W will be added to find the Base Attack Value, or BAV. that we can use that to help in finding his later attacks total damage. Note that his W has an AP ratio, and will be extra damage that I will not calculate in. If you want to figure out how much extra damage, simply add AP X 0.1 to every attack, then average them together for the average DPS.

Formula for the Mana: 230 + (70 X level) + 1000 = Max Manapool 230 + (70 X 18) + 1000 = 2490 mana

Formula for AD: 52.3 + (3.9 X level) + ( 2490 X 0.02) + 25 = AD 52.3 + (3.9 X 18) + (2490 X 0.02) + 25 = 197.3 AD

Formula for BAV: 197.3 + 20 = 217.3 BAV

So, now that we have a set amount of damage that Kassadin will do each auto attack, we can now factor in item 3042 's toggle and W. We will start with the first attack, as that will be a huge number in comparison to the rest. I'm not entirely certain in what order the mana costs apply, so If I calculate them in the wrong order the Mana for all consequent attacks will need adjustment. For now, lets assume that the mana regeneration applies last. Also, you will need to add AP X 0.6 to the end of this particular hit to account for AP.

Formula for W empowered hit: BAV + First Muramana proc + Second Muramana proc + 140 = damage for first hit.

First Muramana Proc Damage: (0.03 X 2490) X 2 = 149.4 Remaining Mana: 2490 - 74.7= 2415.3

Second Muramana Proc Damage: (0.03 X 2415.3) X 2 = 144.918 Remaining Mana: 2415.3 - 72.459 = 2342.841

W empowered hit: 217.3 + 149.4 + 144.918 + 140 = 651.618 damage Mana replenished: 2490 Total Damage done: 651.618 Attacks left: 8

So, we now have the tough calculation for damage done, we can Simplify our damage for the remaining hits. All we need to calculate now is the muramana procs for the 8 remaining hits, add them together with the BAV's to find each hits damage, add up all the damage, then average it. Sounds like alot, but really it isn't, and we already have done most of the work.

First Muramana Proc Damage: (0.03 X 2490) X 2 = 149.4 Remaining Mana: 2490 - 74.7= 2415.3

Second Muramana Proc Damage: (0.03 X 2415.3) X 2 = 144.918 Remaining Mana: 2415.3 - 72.459 = 2342.841

Third Muramana Proc Damage: (0.03 X 2342.841) X 2 = 140.57046 Remaining Mana: 2342.841 - 70.28523 = 2272.55577

Forth Muramana Proc Damage: (0.03 X 2272.55577) X 2 = 136.3533462 Remaining Mana: 2272.55577 - 68.1766731 = 2204.3790969

Fifth Muramana Proc Damage: (0.03 X 2204.3790969) X 2 = 132.262745814 Remaining Mana: 2204.3790969 - 66.131372907 = 2138.24772399

Sixth Muramana Proc Damage: (0.03 X 2138.24772399) X 2 = 128.294863439 Remaining Mana: 2138.24772399 - 64.1474317197 = 2074.10029227

Seventh Muramana Proc Damage: (0.03 X 2074.10029227) X 2 = 124.446017536 Remaining Mana: 2074.10029227 - 62.2230087681 = 2011.8772835

Eighth Muramana Proc Damage: (0.03 X 2011.8772835) X 2 = 120.71263701 Remaining Mana: 2011.8772835 - 60.356318505 = 1951.52096499

It seems that I have hit the character limit. Oh dear. I will reply to myself with the rest. Sorry for that. =/

PryotraJul 16, 20141 votes

Ok, Sorry for that here is the rest:

Alright, now that I have all the procs done. The rest is easy.

Damage Formula: Empowered hit + (8 X BAV) + 1st through 8th proc= Total damage done in 9 attacks. 651.618 + (8 X 217.3) + 149.4 + 144.918 + 140.57046 + 136.3533462 + 132.262745814 + 128.294863439 + 124.446017536 +120.71263701 = 3466.97607 total damage

3466.97607 / 7.2 = 481.524454167 DPS

So, your average DPS would be about 482, not factoring in AP. After this full rotation, you should still be able to fully regen your mana with a single W. I hope this helped you. Time for FOOD.

Quantum WeebJul 16, 20141 votes

Praise be to math!

It's actually kind of sad and funny what outrageous claims people make without quickly checking if it would be reasonable.

"Nidalee 2 shot me at level 10 with just a Doran's ring!"

Not unless you're Sona with a negative magic resist she didn't.

PryotraJul 16, 20141 votes

Math shall show the way!

Yeah, I figured that this thread might be a good general way to help people so that it doesn't become as prevalent here.

Well, that, AND I like math. So really, it's win - win.

Noam BraumskyJul 16, 20141 votes

Should you max your Q or W on a Twisted Fate? It seems pretty hard to calculate, but with the extra mana, damage, slow, stun, etc. which one is better?

Cirno StrongestJul 16, 20141 votes

Should you max your Q or W on a Twisted Fate? It seems pretty hard to calculate, but with the extra mana, damage, slow, stun, etc. which one is better?

I don't play TF so if you do and what I'm saying doesn't hold up in practice don't crucify me.

Just based on damage alone maxing q is better hands down as his q gains an additional 200 base damage as opposed to the additional 80 damage on his blue card. TF's strength isn't so much his ability to do large amounts of damage however; it's his ability to roam and gank other lanes with his ultimate and gold card. Maxing his w will double the stun duration from the level 1 stun. Considering a level 6/9 gank, maxing w over q will give you a 0.5s/0.75s increased duration on your stun at the cost of 85/127.5 damage. As map pressure is TF's strong point I would go w over q unless I needed q for the waveclear.

PryotraJul 16, 20141 votes

Well, that depends.

AP TF: If you can manage the ramping costs with levels, Maxing Q will give you the better poke due to it's Range. So long as you get a point early for the utility in w, maxing Q will give you better damage at longer range. Hands down, no contest. If you do have mana issues, just use the low cost W to last hit a bit, then come back.

To give you a bit of context, I will compare two lvl9 TF, with 0 AP and no items each, one maxing W and the other Q

Maxing W Highest damage with blue card. Blue card damage calculation : 20 + (20 X level of W) + AD + (AP X 0.5) At level 9: 20 + 100 + 76.11 + 0 = 196.11

Maxing Q Wild Card damage Calculation : 10 + (50 X Level in Q) + (AP X 0.65) At level 9: 10 + 250 + 0 = 260

Side By Side Considering that Q has a better AP ratio than W, AP will ALWAYS do more damage with a maxed Q over a maxed W, even before AP. That is before factoring things like range or cost. While maxing Q is indeed more mana hungry, if you can manage it then it is the better choice. Last hitting with blue card at level 1 should easily help your costs significantly.

AD TF: Will be back to finish this math. Need to go eat.

Noam BraumskyJul 16, 20141 votes

Thanks.

GoumindongJul 16, 20141 votes

The reason you max Q on TF is because Q does damage to entire creep waves. This lets TF push farm effectively at all points in the game. The lowered CD on W may get you better DPS in a fight, but that is irrelevant if you are not able to leverage your strong mid game roam. Leveraging your strong mid game roam means clearing waves so you can roam.

GundayMondayJul 17, 20141 votes

Great idea. I'd like to contribute if I can. Brain is getting lazy at my current job and this is good practice for keeping the math chops well practiced.

PryotraJul 17, 20141 votes

Great idea. I'd like to contribute if I can. Brain is getting lazy at my current job and this is good practice for keeping the math chops well practiced.

Welcome to the Mathcrafter's club! Feel free to Math as you see fit!

Have fun!