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Your graphing resource.

Creator: : Searz
January 25, 2011 3:31pm
184 posts page 19 of 19 Forums » Theory Crafting » Your graphing resource.
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Table of contents


Introduction

Legend

Physical runes

Magical runes

Abyssal Scepter vs Void Staff

Last Whisper vs The Black Cleaver

Infinity Edge vs Madred's Bloodrazor

Carry item showdown(WIP)

Dodge vs armor runes

Rabadon's Deathcap vs Void Staff

Champion and/or build specific item comparisons

Making your own graphs!





Introduction


So I finally got all the new graphs done and uploaded.
These kinds of graphs are in my opinion the best way of showing how different things compare to each other in terms of damage.
I'm pretty much taking theory crafting to a new level :]

"Why would this be the best way of showing how damage compares?" You may wonder. That's because it's easy to read graphs and you'll quickly be able to see the area you're interested in without having to look at sheets of data or something like that.
If you don't know how to read graphs: it's pretty easy. Just look at the horizontal axis (line) at the bottom and pick the amount you're interested in. Then look at where the function (the curved lines in the middle of the graph) is and where that is on the vertical axis.
Remember to look at the axis labels. They don't always represent the same thing.

Keep in mind that I only can compare damage to damage (or durability to durability, not damage to durability). I can't compare other bonuses and item costs in the graphs. I will try to make the item cost differences go away in some comparisons by adding the approximate amount of AD/AP you could buy for the leftover gold on the builds. I will write it in the heading when I do.

I will draw conclusions from the graphs, but feel free to make your own.

Keep in mind that enemy champions armor ranges from 15 to 50 early on. Only minions and some monsters have less than that. Also keep in mind that if the line ends before 0armor/MR it means that it deals the same damage all the way down to 0.
Enemy MR is usually about 30 without MR items. Most enemies will end up with about 80-200MR when their build is complete. Lategame armor usually ranges from 70-250.
  • Note that I'm not using ANY masteries on in any of these graphs, but the magic damage masteries. On those I'm using Archaic Knowledge (which also means AP from Archmage's Savvy ).

  • Unless otherwise stated; I will use MrP Marks and AP Quints in all the magical graphs.

  • I'm using a base AD of 100 for both simplicity and the fact that most carries have aproximately that amount. Unless otherwise stated of course. For the level one comparison I'm using a base damage of 50.

  • Unless otherwise stated I will be using ArP Marks in the physical graphs. They're pretty damn standard by now (and this will only confirm that they should be).

  • I've also came up with average base (0.66 attacks/second) and per level (~2.8%) AS values from looking at all the carries.






Legend


DPS = Damage Per Second
CrC = Crit Chance
CrD = Crit Damage
ArP = Armor Penetration
MrP = Magic Penetration
AD = Attack Damage
AS = Attack Speed
AP = Ability Power
MR = Magic Resist
/lvl = Per level. A bonus that is divided over all your levels with a part given each level.





Physical runes

Physical Marks at level one


AD Marks are pretty clear winners here.
AS is a close second, but that's only in DPS. AS is a worse stat than damage when firing shots
ArP beats CrC when your enemies have more than 8armor (pretty much against everything then).
CrD and AD/lvl(too bad to even include) are obviously almost useless at level1.


Physical Marks and Quints at level one


Pretty similar result here. ArP isn't much better than CrC here though.
AD Quints are stronger than the AD Marks because both CrC and ArP Quints give exactly +100% compared to Marks. AD Quints give +137%. That's the reason for the 2 extra graphs.
ArP Marks+AD Quints is a great combo for maximizing damage early on.
CrC Marks+AD Quints is also a good combo, but is generally overshined by ArP Marks+AD Quints. I'd only recommend it if you had abilities that worked with CrC.
CrD and AD/lvl(too bad to even include) are obviously almost useless at level1.


Physical Marks on carry build with LW

( Last Whisper, Infinity Edge, Phantom Dancer, The Bloodthirster and Banshee's Veil)
CrC wins with AS and CrD tightly behind. From this you can pretty much draw the conclusion that CrD will beat CrC above about 60%CrC.
ArP Marks are worse in this comparison because Last Whisper makes all other kinds of armor penetrating/reducing stats less effective. They're still not bad though.
AD Marks are clear losers here. AD doesn't scale as well as the other stats. The earlygame power still makes them viable though.


Physical Marks and Quints on carry build with LW

( Last Whisper, Infinity Edge, Phantom Dancer, The Bloodthirster and Banshee's Veil)
CrC wins with AS and CrD tightly behind, exactly like with the Marks.
AD Quints+ArP Marks is just behind all the others (except for AD Quints+Marks).
AD Quints+CrC Marks are close behind CrD. That makes AD Quints pretty wonderful considering their awesome early damage.
AD only is just like last time in last place. Though keep in mind that it's the AD Marks that are dragging down the AD Quints.


Physical Marks on carry build with TBC

( The Black Cleaver, Infinity Edge, Phantom Dancer, The Bloodthirster and Banshee's Veil)
ArP Marks are clear winners here.
CrC is second with AS and CrD close behind.
AD Marks are last.


Physical Marks and Quints on carry build with TBC

( The Black Cleaver, Infinity Edge, Phantom Dancer, The Bloodthirster and Banshee's Veil)
ArP is by far best here.
AD Quints+ArP Marks is second.
Just like before it's CrC>AS>CrD>AD Quints+CrC Marks after the above. All very close to eachother.
AD is last just like always. Again, keep in mind that it's the AD Marks that are dragging down the AD Quints.


CrC vs CrD runes


I made this graph for an exact comparison of CrC and CrD runes. You may have noticed that the Y axis has no numbers, but they nor the amount of AD or anything else matters in this comparson because these stats are both multiplicative.
The "without IE" example was added because Infinity Edge gives bonus value to CrC, but since CrD runes only beat CrC runes at over 40% CrC it doesn't matter since by then you WILL have IE.
CrC runes are better than CrD below about 62.5%CrC.

Offensive Marks and Quints on a physical ability ( Acid Hunter)(this is a little specific for my Urgot build)

( Manamune, Banshee's Veil, Aegis of the Legion, Last Whisper and Frozen Heart)
ArP runes win. AD Quints+ArP Marks are not too far off in second place. AD Marks are simply not good without crit.



Conclusion:

ArP Marks are the most versatile Marks available. Not only do they give the largest amount of damage in most cases, they totally dominate when used on physical abilities.

CrD IZ BAD. CrD passes CrC runes above about 62.5%CrC AND they're useless early on. Really, really bad.

AD runes dominate early on and are not too shabby in lategame on crit builds, but falls far behind ArP runes without crit items. AD Marks are not viable at all without crit items.

ArP Marks+AD Quints is a very good combo on crit builds. It gives you a lot more early damage, but you'll lose a little lategame damage.

UNCONFIRMED: I'm drawing the conclusion that CrC Quints will beat AD Quints at over about 300 AD with Infinity Edge and 55%CrC.





Magical runes


I'm using Kassadin in most comparisons because his ratios are exactly in the middle of what most champions have. Neither good, nor bad.
To compare a ratio you need to divide the ratio by the flat damage on the spell divided by 100. In Kassadin's case ( Null Sphere): 0.7/2.8=0.25
Higher than that and it's a good ratio, lower and it's a bad ratio. Despite popular belief Nunu's Absolute Zero actually has a low ratio (2.5/1125=0.22).
A ratio affects how effective AP is compared to MrP for damage.


AP vs AP/lvl vs MrP Quints on Kassadin


AP Quints are clear winners here. No surprise.
MrP Quints come second. Their damage gets higher (compared to the others) the more base damage you have on your spell.
AP/lvl is closing in on AP as you level up (duh). AP/lvl Quints will pass AP Quints at level 12.


AP vs AP/lvl vs MrP Quints in lategame on Kassadin


AP/lvl Quints win here, obviously.
MrP and AP quints are pretty equal without Void Staff, but with it AP wins because %penetration makes all other penetration and reduction less effective.


AP vs AP/lvl vs MrP Glyphs on Kassadin


AP Glyphs win early on, while AP/lvl creeps up and beats AP at level 6.
MrP Glyphs are pretty good in this one. MrP Quints+Glyphs is ok, but here the superiority of AP Quints shows.


AP vs AP/lvl vs MrP Glyphs in lategame on Kassadin


AP/lvl Glyphs are clear winners here, obviously.
MrP Glyphs are ok and shares the second place with MrP Glyphs+Quints.
AP Glyphs are last.


AP vs AP/lvl vs MrP Marks on Kassadin


MrP curbstomping.


AP vs AP/lvl vs MrP Marks in lategame on Kassadin


MrP dominating.



Conclusion:

AP Quints incredibly good early on and on abilties you haven't ranked up to max rank yet. AP/lvl and MrP Quints just can't compare in my opinion.
AP Quints also scale with some skills that doesn't deal magic damage, like heals and shields and such (Vlad's Transfusion) and are thus an obvious choice on those champions.

MrP Glyphs are generally pretty lacking. It may be worth picking up 2 of them to reach 30MrP with the MrP Marks and Sorcerer's Shoes, but you'll deal less damage to anyone at higher than 30MR.

Now, I know MrP has always been the obvious choice in Marks, but I still wanted to know how they compare so I decided to graph it. Now afterwards I'm pretty sure I'll never buy AP or AP/lvl Marks :)





Abyssal Scepter vs Void Staff


Since both items give the same amount of AP I can ignore that part and just compare the MR peneration and reduction.

As you can see Void Staff wins pretty big, BUT Abyssal Scepter also gives 57MR. That's a pretty hefty amount and definitely makes up for the loss in damage in my opinion.
They're both great items, I can't quite see one as better than the other, simply get what you need most.






Last Whisper vs The Black Cleaver



As you might've noticed there has been some debate on this subject. With these graphs I'll hopefully shine some light on the subject.


Damage per hit - LW vs TBC on carry build

( Infinity Edge, Phantom Dancer, The Bloodthirster and Banshee's Veil)
Here LW seems to have an advantage. Now let's look at DPS.


Damage per second - LW vs TBC on carry build

( Infinity Edge, Phantom Dancer, The Bloodthirster and Banshee's Veil)
As you can see TBC is a clear winner in this test because TBC gives a decent amount of attack speed.


Conclusion:


TBC gives attack speed for aproximately 840gold, while only costing 575gold more. Because of that the DPS will be noticably better and that more than makes up for the extra cost of TBC in my opinion.
TBC also reduces the armor of the target so that they take more damage from all physical damage, not just your own.

For TBC: Better sustained DPS

For LW: Better physical poke and physical abilities without on hit


Just to give a few examples of champions that I think should be buying each item:
LW: Ashe, Caitlyn, Sivir, Ezreal.

TBC: Corki, Tristana, Vayne, Miss Fortune.





Infinity Edge vs Madred's Bloodrazor


I'm using +50% attack speed with 100 AD which is pretty standard for a carry in midgame. (those 50% include the AS you get from leveling too!)


IE vs Bloodrazor


As a first item they're pretty equal on auto attacks, but physical abilities are far superior with IE.
As the game rolls on you get extra value from both items. More magic damage from Bloodrazor as enemy HP goes up and more physical damage with IE as your crit chance go up.

I tried graphing how much extra damage you get from CrC (compared to enemy HP with Bloodrazor), but since I couldn't limit it to the right values it just looked bad and I didn't want that :3
I feel like it won't bring all that to the comparison anyways, so I just skipped it.






Carry item showdown(WORK IN PROGRESS)




The Black Cleaver

Last Whisper





Dodge vs armor runes

  • These graphs measure damage TAKEN, so unlike the other graphs LOWER IS BETTER here.


  • Keep in mind that dodge ONLY affects auto attacks, not physical spells.


Dodge vs armor Seals:


Dodge Seals win against no ArP and against LW.
Against TBC they're pretty equal.


Dodge vs armor Quints:


Dodge Quints can't hold a candle to armor Quints. The only case dodge Quints can compare to armor in is against Last Whisper.


Dodge Seals+armor Quints vs armor Seals+Quints vs dodge Seals+Quints:



This is just to show that dodge Seals+armor Quints is a pretty good combo on champions who stack a lot of armor.


Conclusion:


Dodge Quints are bad. They just can't compare to the awesomeness of armor Quints.

Dodge Seals are good for lategame auto attack damage mitigation on champions you stack a lot of armor on. They also work good with armor Quints.

Junglers are best off with armor runes, at least while they're jungling.





Rabadon's Deathcap vs Void Staff

(with Sorcerer's Shoes in all functions)


Look at where they cross over. At about 73 MR you'll deal more damage with one 80AP item and Void Staff+57AP. With two 80AP items they cross over at about 82MR.

Deathcap just isn't what it used to be after the nerf (15*1.3=20 less AP). Now you don't get many stats out of it unless you're building an AP item before it. Now it's rarely the best idea to rush it, imo.
I'm certainly not suggesting to rush a Void Staff, I'm just saying that Deathcap is usually a not a good item to rush right now.






Champion and/or build specific item comparisons



Last Whisper vs a fully stacked The Bloodthirster on a physical ability( Acid Hunter)

( Manamune, Banshee's Veil, Aegis of the Legion, Last Whisper and Frozen Heart)

Last Whisper is a clear winner here.

Wit's End+ Madred's Bloodrazor vs Infinity Edge+ Phantom Dancer

(with Bio-Arcane Barrage active and just the AS from Caustic Spittle)

It's a hard choice. I'd say they're very equal in lategame. His midgame damage will be higher with a crit build though.






Make your own graphs!

Want to compare the damage of two items, different rune types or anything else? Follow the instructions below!

You can download the graphing program I use here.
I'm gonna mention some formulas so that you can use them to make your own comparisons.
I use an estimated base AS and AS per lvl in the formula with AS.

If you can't; just ask me and I'll try to help you or even make the graph myself. I will not upload pics of the graphs unless I think it will help though.
  • Damage with crit and AS at level 18 = (AD*%CrD/100*%CrC/100+AD*(1-%CrC/100))*0.66*(1.5+%AS from items/100)*100/(100+(x-ArP)*(1-%ArP/100))

  • Damage with crit = (AD*%CrD/100*%CrC/100+AD*(1-%CrC/100))*100/(100+(x-ArP)*(1-%ArP/100))

  • Damage without crit = AD*100/(100+(x-ArP)*(1-%ArP/100))

  • Physical ability = (AD*ADratio+flat damage)*100/(100+(x-ArP)*(1-%ArP/100))

  • Magical ability = (AP*APratio+flat damage)*100/(100+(x-MrP)*(1-%MrP/100))

Just add all the stats from your items and base stats and you'll be making nice graphs in no time!
Also worth noting is that the starting point of your line/function should be the same as your flat penetration(because it can't go negative) and that it should always end at max 300(because getting more armor/MR than that is stupid).[/center]


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Quote | PM | +Rep by DEWO » January 26, 2011 12:07am | Report
GREAT stuff.

Somethin i was always wondering could be done on graphs too (if you have time ofc)

Builds for Karthus ultimate vs Mres.

Basic builds will consist of:
4xStaff/Sorc boots/Rabadon's Deathcap
vs
other builds (like consisting Void Staff and so on, and maybe the value of sorceror boots vs CDR boots for ultimate.

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Quote | PM | +Rep by Searz » January 26, 2011 1:22am | Report
DEWO wrote:

4xStaff/Sorc boots/Rabadon's Deathcap
vs
other builds (like consisting Void Staff and so on, and maybe the value of sorceror boots vs CDR boots for ultimate.

I'll make 2 graphs for that. 4xstaff vs others and Sorc boots vs CDR. Tho 4xstaff is kinda stupid.. It's insanely easy to counter. 3xstaff is the only thing I think may pay off.

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Quote | PM | +Rep by DEWO » January 26, 2011 1:29am | Report
Well 4x Staff is still best for building raw AP, and btw what do you mean by "countering" a staff build?
It is ******ed idea but works on Karthus and it is mainly for the Ulti calculations.

Also i was wondering about the utility of Void staff on Karthus, since you cant rely on Abysal Scepter due to AoE range.

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Quote | PM | +Rep by Searz » January 26, 2011 6:48am | Report
Why can't you rely on Abyssal Scepter?

4xStaff is incredibly easy to counter with magic resist. One MR item will drag the damage below the damage a Void Staff+3xStaff gives.

I will make this graph for you since I've already started, but it would be great if everyone learned how to make their own graphs. Try it yourself and I'll fill you in on anything you don't get.

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I don't want the same thing I have fond memories of doing when I was little. Because chances are that my view of it is clouded in the thick mist of nostalgia.
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Quote | PM | +Rep by DEWO » January 27, 2011 12:36am | Report
Becouse Abyssal Scepter has an AoE Aura, and its not globas as your ulti is :)

Most common MR is Banshee so if we take 50MR
4th staff will give you about 250AP
Void gives 70AP

so do you think that 40% mpen on som1 that bought banshee with 50MR will be better than 180AP?

this are the questions i'd love to see answered with your graphs :)

I just aksed you for the graph since you already had expirience with it. Ofc will try to make mine too coz i think it is a great tool, just didnt have enaugh time.

Thx for some usefull topic read (at least one once a year happens here :P )

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Quote | PM | +Rep by Searz » January 27, 2011 6:07am | Report
DEWO wrote:

Becouse Abyssal Scepter has an AoE Aura, and its not globas as your ulti is :)

Oh my god >.> I totally forgot about that. I can't believe I didn't think about that..

Quoted:
4th staff will give you about 250AP

It actually gives almost exactly 200AP.

Quoted:
so do you think that 40% mpen on som1 that bought banshee with 50MR will be better than 180AP?

I know it is. I've made the graphs, but they're at my stationary comp. I'll upload them as soon as I can. If I remember correctly Void Staff deals more damage above about 60MR, so one cheap MR item is even enough.

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Quote | PM | +Rep by DEWO » January 27, 2011 6:24am | Report
Searz wrote:



It actually gives almost exactly 200AP.




Did you count the Rabadan bonus with it? I am more than sure that it will give about 250

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Quote | PM | +Rep by nand » January 27, 2011 8:29am | Report
It's exactly 201.5 per staff.

@DEWO: The 30% increase is unique

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Quote | PM | +Rep by Searz » January 27, 2011 11:33am | Report
DEWO wrote:

Did you count the Rabadan bonus with it? I am more than sure that it will give about 250

I'm counting that on the total amount, not on each item. After all, the bonus is from deathcap, not the staffs.

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