@calculus studens, request parabolic equation for....

LilxPaprika·Mar 18, 2015·4 votes·1,685 views

http://i.imgur.com/fCPpdlN.jpg

This graph is for lichbane to give it a higher early game damage that tapers out into the current spellblade equation when someone reaches about 300 or so ap. starts at 250% base damage scales progressively more with ap as you get more and more ap. and progressively less with base damage the more ap you build. the spellblade damage always increase the more ap you buy of course exponentially/aka accelerates the more you buy until you hit 300 or so ap in which case it reverts to the current spellblade. Such that using both spellblade equation, where your AP value =300, spellblade's damage equals the same in both cases.

the 250% base ad and 300 ap is just to give an idea of where i'm going and can be changed at will to keep the item balanced.

Edit on bottom graph on the right I wrote %75 ap scaling which should read the current 50% ap scaling

31 Comments

PryotraMar 18, 20152 votes

So, forgive me if I am inaccurate, I haven't needed calculus since... well... Cal II.

Let me first see if I understand what you are asking. You want a higher base damage, but you want the ratio itself to scale off of the amount of AP? And you want it to intersect at 300 AP. Honestly, this level of math, while doable, would never be included in the game. I mean, they were afraid that Darius' 1k true damage ult that reset on kills was too mathy, so they initially gave it a grace period. Just imagine their reaction if they were asked to add a calculation on this scale to an item.

If you just want the base damage higher, but don't want a scaling ratio, then you could very easily calculate the ratio as a simple quadratic equation.

I'll try to do the math for either, but seeing as it's really to early for me to even be conscious, I'd appreciate it if you limited the amount of math to 1 general equation.

LilxPaprikaMar 18, 20151 votes

It would begin at a higher base damage than the current one. But to make up for this extra early damage, for the first 300 or so ap you buy, spellblade's overall damage will not increase that much. It will however increase in an accelerated fashion the more ap you buy until you hit 300 ap then return to the current format and scale in a linear fashion (assuming your level 18 and your base damage is static).

I was hoping there was an easy way about doing it.

So same damage at 300 ap, with higher base start

Let's pretend ap is time and this is physics. And one car starts from scratch and needs to build up speed aka accelerates. While other car starts out running at a steady velocity Steady velocity is for every 5 seconds he travels 2.5 feet. The car that starts from a stop starts the race in frontt of the other car by 250-75 = 175 feet ahead..., Find equation such that they both arrive at same place when time hits 300ap Haha, zilean would be proud here I am comparing ability power to time.

LilxPaprikaMar 18, 20151 votes

Nevemind this is more complicated ... Already have headache. The 250% base ad would have to reach 75% at 300 ap. And the way it scales from ap would have to reach 50%? Simultaneously is that even possible. Best to just make it change over only one variable...

How's this:

Make it start at 250% base ad and 0% base ap (+(equation)% to ap scaling for every x ap and minus (46.6666...)% to base ad scaling for every 80 ap) this ceases when you reach 75% ad and 50% ap. The + ap scaling would have to be greater than the damage you are substracting from the base ad. I got 46.6666 from 300/80=3.75 80 being lichbane's base ap.
250%-75%=175%. 175% /3.75 = 46.66666

PryotraMar 18, 20152 votes

ok, So, from what I gather, you want it to ramp up the ratio up to 300 Ap, where the ratio levels off and the damage is about the same?

In that case, it is doable. you just need to split the equation based off of the value of X, where X = AP, y = AD, z is total damage done from lichbane.

Where X < 300:

Z = .5 (X/300) X + (2.5 - 1.75 (X/300)) Y

Where X >= 300:

Z = .5 X + .75 Y

LilxPaprikaMar 18, 20151 votes

Thank you so much! You must be one of heimerdinger's disciple.

Will this look like the graph? Maybe I should try plotting points to see how it works So what are your thoughts? Do you think its beyond the scope of riot to integrate it into the game? What do you think of the change itself? Would you like to see this sort of buff to lichbane?

PryotraMar 18, 20151 votes

It should line up with the graph, more or less. It would depend on the champion tbh. You might have issues as on your graph, the Y Axis is my Z variable, and your X axis is my X axis, and you don't have a 3rd axis to match the AD of the champion using the item.

As far as my thoughts go, while Riot could very easily implement this (Heck, I just gave them the algorithm), I highly doubt that they will. As I said before, they have had past concerns with mathy-ness on FAR simpler things. Also, as another poster mentioned, for ADC's that don't want the AP, this is a HUGE buff to an item that might make them pick it up, especially as it would effectively add damage to lots of their crits.

Even if you evened out the numbers so that AD's wouldn't buy it, you still have the issue of mathy-ness. I personally would like to see the ad moved to a flat 50%, and then maybe buff the AP ratio up. That way, it feels better even with a little AP. Granted, I don't think that this item should be good unless you are building AP, but it should help those supports that sometimes struggle to make the money for the necessary AP.

LilxPaprikaMar 18, 20151 votes

I mean it won't be any difference from trinity force so I don't see the issue. Even as a tank I prefer itemizing against mixed damage than to see my armor get shredded by lastwhsiper.

I guess riot could go in and create another value to scale off of that they would assign a value to each champion based on how much they want them to scale with lichbane. So a value similar to base ad exclusively for the lichbane that could also perhaps be used for future items/game interactions.

PryotraMar 18, 20151 votes

Trinity force is a poor choice to compare it to considering the sheer cost and stats in it. Think more like an AP version of Iceborn without the slow field.

The issue of assigning each individual a value to scale off of an item is two fold: it's not scalable, and it's nonsensical. To date there is only 1 instance of them doing this that I am aware of, and that is heimer's turret health scaling, where each level is unique. At least that is on 1 champion, and not on an item that can potentially be picked up by any 1 person in any champion regardless of fore knowledge. The burden of knowledge for the sheer amount of variables would only grow as more champions are input into the game.

By scalable, I'm actually talking about overall health to the item. Lets say that in some future meta, the Item is OP on many, if not all champions. How do you fix the Item? Go by each champion and nerf the number? Time consuming, tedious, and twice as much to test.

LilxPaprikaMar 19, 20151 votes

Before i go into the discussion of why it would work or not. I'd just like to say that its worth a visit to the PBE. I think we can learn a lot from the result and get a lot of insights out of the conversation that comes out of it.

regarding: assigning each individual a value...

agreed.mainly brainstorming there. theoretically ya you would have to. which is kind of the case with base ad though just less so and base ad plays a much bigger role in that it works with each auto attacks.

Another idea would be to add an If condition, where it won't scale as well if the player has more than such and such combined ad/crit chance. Again brainstorming.

but i still think its fine even if lichbane is stronger early. sure you could build it for funsies on an adc. but people will call you out for trolling. its doable but not optimal.

You are spending a lot of gold to get that damage.. why should lichbane be relegated to a 30 minute point in the game. so what if its ap. At the end of the day be it ad or ap its still just plain old damage. The only real difference is how you go about getting armor or magic penetration and whether or not you prefer to sustain from it.

Triforce still gives more base stats and the phage passive, this is enough to warrant the extra 700g cost even if both trigger about the same amount of damage from their sheen procs.

I think at least lich bane is in between triforce and ibg. Rylais/mallet and IBG are in an area of their own since slow items are designed to offer less stats given the potential usefulness of their slows, so naturally ibg's dmg ought to be toned down. i mean think about it why am i getting less damage on an ap item without a slow field out of the gate compared to IBG. kind of a stretch but It'd be like luden's echo doing less damage than rylais out of the gate.

imo IBG could be around 2600 gold see post here since you paying for 500 mana. It almost more of a mana item than a damage item. So price wise it pretty much sits in between both. lich bane's sheen proc was designed to stand up to trinity force and/or even surpass. From the wikia: "The proc from Lich Bane item.png Lich Bane far surpasses Trinity Force item.png Trinity Force with a Rabadon's Deathcap item.png Rabadon's Deathcap alone on the majority of champions, not to mention other AP items."

Whereas triforces surpasses lichbane in terms of attackspeedcrit/sustain/utility.

what if you were a champion eyeing lichbane thinking you are being deprived of what otherwise could be a really cool item. Id be telling other champs something like. oh ya well i could stand up to you if items synergized with my kit as well as yours.

whats nice about my suggestion is that it gives lichbane two possible playstyles without either compromising the other. Full glass canon champions looking for that assassination potential will be unaffected. And can be used on champions who want to get as many sheen procs off over drawn out fights. Like phoenix udyr with rageblade and lichbane (what phoenix udyr's kit's been begging for) add righteous glory for mobility and now you have true diversity. Hybrid champions have been neglected. This meet their needs.

Example, Ap bruiser evelyn. wota lichbane ap jungle item the rest tanky. or cinderhulk lichbane rylais.

Angry MonsterMar 19, 20152 votes

So i floated through this thread. Lets forget the math for a second. You state the purpose of your math according to you is to improve the early game. Why does liche bane need a better early game?

Its a scaling item. Since it scales it then should be gated early. You need to present a valid argument why it needs to have a better early game. Something not vaild is saying its not worth building first. A lot of things in this game are not worth building first, LW, Void staff, Ageis to name a few.

LilxPaprikaMar 19, 20151 votes

I have. For one its a mana item and mana is Needed/bought particularly early game. A lot of champions would excel with it. Ap bruisers like say gragas with just lichbane and roa for ap the rest tank. Or Warwick with lichbane wits end sunfirecape and perhaps abysal scepter. Or lichbane gunblade On evelyn. These champions will not reach 300 ap and even if they did they would not reach it until late in the game. In the meantime this early game lichbane will still be of use. As opposed to being underwhelming.

Its the perfect solution to make gunblade see more usage on character kits that would otherwise be the perfect candidates for using gunblade. When is the last time you saw shaco build gunblade for example.

This also helps with runes and masteries you won't feel as obliged to get ap quints and invest as much into ap masteries. Hybrid champions could consider other things like Attackspeed, armor quints or CDR quints etc without feeling as if they won't be getting their moneys worth from lichbane.

Rubbery SkrubMar 19, 20151 votes

They shouldn't be getting their money's worth from lich bane because they shouldn't be building it if they aren't going to stack AP, it's meant to be a scaling item.

Angry MonsterMar 19, 20151 votes

I do not think this a good reason. First of if you build sheen on a bruiser that is going ot have less than 300 AP then you should take triforce or frozen fist. This is why it has alternative builds paths. If you want to stack mana and more tank you go frozen. If you want more burst and a closer play to liche you go Tri.

Your stepping into the territory of the other items. Liche is supposed to be the AP scaling auto item. Making it have an early game just does not make sense. Plus you are forgetting that if you just sit on seen you have AD damage procs mixing your damage pool.

I am sry but i think you are on the wrong track here. You may get people saying great idea, cause they always want more power and they do not understand the game. Riot devs can not let that type of attitude effect there thinking.

AetherKingdomMar 18, 20151 votes

It wouldn't be balanced. ADC would buy it for actually ridiculous crits.

LilxPaprikaMar 18, 20151 votes

Trinity force would still be stronger in every instance. The 250% base ad is at 0 ap, lich bane gives it 80, so it'll be more like 220 base ad. Which 20% base ad < 10% crit.

Also:

the 250% base ad and 300 ap is just to give an idea of where i'm going and can be changed at will to keep the item balanced.

Also its magic damage so if your ADC and you have last whisper this isn't a good buy Nor will you life steal off it

AetherKingdomMar 18, 20151 votes

I actually forgot about the base AP lolz. Honestly I'd try and actually solve it but I forgot everything I learned in Calc 1.

LilxPaprikaMar 18, 20151 votes

Same I still have my calc book, but looking at it I get a head ache real fast. I'd need someone to direct me first as to where to start. Last thing I want to do is re learn a whole chapter only to find out I didn't need it.

Desmond LawMar 18, 20151 votes

You can't compare AP/AD with magic and physical damage directly when dealing with conversions like these. There are still champions that have AP scaling spells that deal physical damage and vice versa.

Desmond LawMar 18, 20151 votes

Lich's Spellblade: After casting a spell, you next auto attack deals (75% base AD + 50% AP) bonus magic damage Base AD scaling increases by 15% per 100 AP

This way you can have a high base AD ratio without fear of marksmen abusing it. Hybrids could go to town with this though.

You also have to take into consideration of the spellblade mastery and if your AP is greater than your AD, your auto attacks scale with 40% AP when attacking towers.

LilxPaprikaMar 18, 20151 votes

Base AD scaling increases by 15% per 100 AP

Problem with that is you'd buff the current lichbane for full ap champions and it wouldn't change the base damage that much.

As for towers they'd have to keep it as is 75% as and 50% ap in other words scales differently based on your target structures being handled differently. The end user doesn't need to know so much the values so long as the item performs as desired. If you want to find out more about the intricacies of how lichbane works on towers they could check out the wikia etc

Desmond LawMar 18, 20151 votes

What is the goal you are trying to achieve? A big boost the moment you get the item, or have it be a power house if you can build into it?

LilxPaprikaMar 18, 20151 votes

Im looking to not effect lichbane the way its currently used in the late game. that's why they nerfed it in the first place. The problem is the nerf effected its early / stand alone viability. So ya giving it a boost early that doesn't effect late. Not necessarily a big boost. Viable enough that I won't be laughed at for just going lichbane and banner of command on sona support for example. Or lichbane and rageblade on Warwick. Such that it could be built like all the other sheen items. And be strong on its own. Not even strong just viable.

LilxPaprikaMar 19, 20151 votes

After all that's when mana items are meant to be built early in the game. Its counterintuitive to build a 250 mana item after deathcap. At least this way it will be useful as you complete your deathcap and you'll get your gold worth out of the mana. This will also help give gunblade more legitimacy/belonging as right now its a very niche item that only a few champions call their own. The spellvamp could have a 50% reduced efficiency on spellblade. Comparable to life steal.

Hirok0Mar 19, 20151 votes

The damage you would deal between 0-200 ap would be basically the same, since you lose a whole lot of base dmg % on a 70-90 aa hit while gaining almost the same amount in ap damage. It could literally do less damage as you get ap until after that 200 mark where 1% ap scaling actually means 2 dmg and 1% baseAD means 'almost' 1. Kind of counter's its scaling until late game.

LilxPaprikaMar 19, 20151 votes

{quoted}

The damage you would deal between 0-200 ap would be basically the same, since you lose a whole lot of base dmg % on a 70-90 aa hit while gaining almost the same amount in ap damage. It could literally do less damage as you get ap until after that 200 mark where 1% ap scaling actually means 2 dmg and 1% baseAD means 'almost' 1. Kind of counter's its scaling until late game.

you're right so the equation isn't right then. at least you're not getting back enough to makeup from the lost in base damage.

LilxPaprikaMar 19, 20151 votes

{quoted}

The damage you would deal between 0-200 ap would be basically the same, since you lose a whole lot of base dmg % on a 70-90 aa hit while gaining almost the same amount in ap damage. It could literally do less damage as you get ap until after that 200 mark where 1% ap scaling actually means 2 dmg and 1% baseAD means 'almost' 1. Kind of counter's its scaling until late game.

Ooops, you're right the equation is wrong. Went ahead and plotted some points. Current spellblade: AT 300 AP... Z = .5 X + .75 Y nothing should exceed this. But should always climb towards this. With new formula: Z = .5(X/300) X + (2.5 - 1.75 (X/300)) Y @0 ap = 250 @80 ap, Z=214 @140 ap, Z=201 @200 ap, Z=199.999999

Its doing the opposite of acceleration in fact. I need like the inverse of this . He has it descending towards the current spellblade formula. Whereas it need to do the opposite.

** The equation i'm looking for just so happens to coincide/intersect at 300ap as with lichbane's current formula it doesn’t make it its goal to taper out at 300 ap. Such that at 300 it can cease to be used/ tossed aside/switched out it as it did its job to get us to the current spellblade's value at 300 ap ** while starting from a higher starting point of 250% base ad.

LilxPaprikaMar 19, 20151 votes

[{quoted}](name=Kaosu Desu,realm=NA,application-id=3ErqAdtq,discussion-id=EePk8eO5,comment-id=000500000001,timestamp=2015-03-19T19:21:13.182+0000)

If you want to stack mana and more tank you go frozen. If you want more burst and a closer play to liche you go Tri.

but i want ap damage because i have magic pen. and I want spellvamp. I also want more flat ap to scale with my spells. the list goes on. I'm proposing changing lichbane's identity. I wouldnt so much call it changing it so much as just making it viable early in the game. Since the way its currently being used will remain unaffected.

{quoted}

They shouldn't be getting their money's worth from lich bane because they shouldn't be building it if they aren't going to stack AP, it's meant to be a scaling item.

i think for a 3k gold item you ought to get your moneys worth right off the bat if you so choose to build it first. Lichbane, as with other sheen items is usually your primary damage item. This isn't an atmas impaler, at least that built from avarice blade. Atmas was probably more cost efficient with just a bit of hp. as it stands you shouldnt be building it first item even if you are going to stack ap in the near future. Unless you have stacked ap glyphs even then.

Alright so i went over the numbers again and boy did i overshoot. so 250% ad was a stretch.

lol at 300 ap spellblade does less than 220% base ad.

At 300 ap current lichbane spellbalde does: 237 dmg with 116 base ad at level 18

2.2*116=255.2

so ya i think that at 80 ap it ought to do something closer to 160% ad. 116*1.6=185.6 now that's something you could use to climb towards 237dmg. in the end you'll be getting less damage per ap until you pass 300 ap. but it won't matter since you'll also be doing more damage.

It could also give progressively more damage as you approach 300 ap. instead of being linear. so like the curve i have. Although I think having it be linear would be fine as well.

LilxPaprikaMar 20, 20151 votes

http://i.imgur.com/riNe9ZU.jpg

I was overcomplicating things Lets Just make it linear. We know that at 300 ap the damage with 116 base ad = 237 dmg Now I’m trying to set spellblade’s damage at 80 ap to be equivalent to 1.6% of ad So 1.6*116=185.6

S= spellblade. So what Number times(S)=185.6 185.6/127=1.4614… So lets create letter E, E=1.4614 at 80 ap That’s at 80 ap since that’s the lowest possible Ap that lichbane can scale from. At 300 ap E=1 , Since 1 times spellblade = spellblade. 300Ap is the break off point from when you go back to the current formula and no longer need to buff its damage.I figured 300 was a fair amount since its somewhat difficult to attain if you aren’t looking to stack ap.

Using poportions: We know that to get from 80 to 300 ap, you have to multiply the current lich bane formulate by 1.41614. so that’s + ≈0 .416 increase per 220 ap. (300-80)/.41614 is proportionate to (300-X)/number we’re looking for

So (300X.416)/220 = E So lichbane’s equation could read as follows Where X < 300, spellblade’s damage is multiplied by Z. Z=1+[((300-X) *0.416)/(300-80)] Lichbane could also spellvamps for this number. And won’t surpass 300 ap worth. or can't spellvamp for more than 237 dmg. at a 50% or 2/3rds reduced effectiveness.

@80ap the new lich bane = 1.461*(Old lich bane formula)=185.6 @150ap 1.28236 * (162) = 207.7 DMG @200ap 1.18909 * (187) =222.36 @250ap 1.09454 * (212)= 232.04 @ 300ap 1* (237) = 237 dmg. Trinity force does 232 dmg with base damage of 116. I think this is a pretty good number to work with. The spellblade could spell vamp for this number at all times.

LilxPaprikaMar 20, 20151 votes

**where X = AP, Y = AD, Z is total damage done from lichbane.

Where X < 300:

Z= (.5 * 300 + .75 Y) - 7((300-X)/30)

Where X >= 300:

Z = .5 X + .75 Y

237-185.6=51.4 220/51.4 = 4.28 closest whole numbers i could find that equaled 4.28 was for every 30 ap* (beyond the initial 80 ap)* you get 7 extra damage. 30/7= 4.28