29 replies to this topic

[Trahas]

*EDIT* I added my workbook, it is not perfect but I really wanted to show my work. Enjoy

Hello, Leaguecrafters.


I was falling asleep last night after playing a few games of League, and I got to thinking when is it better to buy more AP and when is it better to buy a Void Staff. And as I drifted off to sleep, I was thinking of all the fun math I will get to do in the morning to figure it out.

I am now in the process of building a small Excel workbook that handles all the calculations for you, but here are a few notes I would like to share about my process and of course I am open to any sort of criticism, even the, "You're an idiot" kind.

First thing to note is I am looking at a pure damage output, so I won't be looking at items such as Rod of Ages. Instead, I am focusing on two items: Void Staff and Rabadon's Deathcap.

But wait a second, Trahas! Void Staff and Deathcap have two very different gold costs, so how can you compare them? Well, you are right, good sir or madame. So to make up the difference, I took the gold split between the two items, then I divided it by the cost of a Needlessly Large Rod and multiplied that by 80 AP, the amount you get from said rod. It comes out to be 65.25 AP. This is just theoretical AP you could buy with that gold, even though there is no actual item. I figured this was a close enough way of doing it. But just in case people don't like that, I also used a Void Staff + Blasting Wand + Amplifying Tome, which is 10 gold less and 5.25 AP less than a Deathcap.

So now to the math part. I figured there were three main variables to this problem (though really, there are five total variables).

The First Variable = how much Magic Resistance does the given enemy champion have?
The Second Variable = what is the AP ratio of your spell(s)?
The Third Variable = what is the base damage of your spell(s)?

The Fourth and Fifth Variables are AP and MPen, but because these two aspects are the two we are controlling, they are worth mentioning but not as important.

I will either attach my workbook when I feel it is good enough to publish or post a link to it so others can check my math and formulas.

One formula I have is Final Damage = (100/(100+(Mres*(1-Mpen))))*(BaseDmg+(AP*Ratio)).

If you plug in the two constants for AP and MPen for the different items and then set their Final Damage equal to each other to find the point where buying either gives you the same damage, all of this gives you a final formula of (5200*Ratio)/((20.8*Ratio)+(.4*BaseDmg)) = MRes.

Using this, you can plug in your base damage and ratio and find at what MRes does buying either give you the same result. Basically, if the given opponent's MRes is less than the said MRes, you should get Deathcap. When MRes is higher, it would be better to get a Void Staff.

So I used this formula on a few different champions to add together all their abilities' base damage and ratios at max rank. And to my surprise, the turning point for MRes is surprisingly low on almost all champs. A few that I did are below ... (Note: I only did burst damage, so while some champs can spam certain skills more often I only counted one hit. However, adding in more hits only changes the MRes slightly and has no real big impact.)

• Ahri 29.2
  
• Akali 17.8
  
• Alistar 27.5
  
• Anivia 29.6
  
• Annie 26.4
  
• Brand 23.1
  
• Cassiopeia 30.7
  
• Ezreal 22.1
  
• Fiddlesticks 25.1
  
• Fizz 33.1

So if you notice, most of them are around the 20-30 mark. And because every champion has base MRes of 30, it is almost always better to buy a Void Staff before a Deathcap.



If you have any questions or comments, please post them below or PM me. If I made any spelling or grammar areas, please PM me so I can fix it right away. English was never my strong subject in school.

Here are more technical notes about my process.

Spoiler

*I used Deathcap with no other AP added to the champion meaning I took 140*1.3 for its second effect. Since it increases your AP based on other sources if you already have a good amount of AP this could make Deathcap more desirable at Higher Mres.

*Deathcap's cost is 3600 gold
Void Staff's cost is 2295 gold

*To make up for this difference, I had two choices: one was taking (3600-2295)/1600*80 to get 65.25 extra AP, or 'buying' a Blasting Wand and an Amplifying Tome, which costs 1295 extra but only giving 60 AP. I chose for most of my calculations to use the latter because it is actually doable in game because you cannot buy a fraction of an item. The cost difference is only 10 gold that favors Void Staff and is close to negliable.

For my MRes Formula above here are my steps to solving for it.
Final Damage = (100/(100+(MRes*(1-Mpen))))*(BaseDmg+(AP*Ratio))
For Deathcap
Final Damage = (100/(100+(MRes*(1-0))))*(BaseDmg+(182*Ratio))
For Void Staff
Final Damage = (100/(100+(MRes*(1-.4))))*(BaseDmg+(130*Ratio))

(100/(100+(MRes*(1-0))))*(BaseDmg+(182*Ratio)) = (100/(100+(MRes*(1-.4))))*(BaseDmg+(130*Ratio))
Cleanup
(100/(100+(MRes*(1))))*(BaseDmg+(182*Ratio)) = (100/(100+(MRes*(.6))))*(BaseDmg+(130*Ratio))
Divide both sides by 100
(1/(100+(MRes*(1))))*(BaseDmg+(182*Ratio)) = (1/(100+(MRes*(.6))))*(BaseDmg+(130*Ratio))
Cleanup
(BaseDmg+(182*Ratio))/(100+MRes) = (BaseDmg+(130*Ratio))/(100+(Mres*.6))
Multiply both sides by (100 + MRes)*(100+(MRes*.6))
(BaseDmg+(182*Ratio))*(100+.6*MRes) = (BaseDmg+(130*Ratio))*(100+MRes)
Cleanup
100*BaseDmg+18200*Ratio+.6*MRes*BaseDmg+109.2*Ratio*MRes = 100*BaseDmg+13000*Ratio+MRes*BaseDmg+130*Ratio*MRes
Subtract 100*BaseDmg from both sides
18200*Ratio+.6*MRes*BaseDmg+109.2*Ratio*MRes = 13000*Ratio+MRes*BaseDmg+130*Ratio*MRes
Cleanup
5200*Ratio = .4*MRes*BaseDmg + 20.8*Ratio*MRes
Pull out MRes on the right side
5200*Ratio = (.4*BaseDmg + 20.8*Ratio)*MRes
Divide both sides by (.4*BaseDmg + 20.8*Ratio)
(5200*Ratio)/(.4*BaseDmg + 20.8*Ratio) = MRes

Attached File(s)

•  Trahas\'s Mathcrafting, AP vs Mpen.xlsx (1.43MB)
  Number of downloads: 13

Edited by Trahas, 28 July 2012 - 03:46 PM.

[SoupSoupMahGaa]

Cool story. Actually.

[Trahas]

Thanks for responding. Always nice to know someone reads what I write since it did take me a while to do. I am thinking of doing one also for Arpen, but I feel like there may be way to many variables for it. Do I do all abilities as well? or purely for the Auto Attacks. And then you have Attackspeed and Crit to deal with as well. But might be worth looking into.

[ReversedAura]

Too lazy to check the math, but if you're right, then wow, I knew Void Staff was good, but never thought it would actually be better than getting Deathcap first for damage.

Of course, the sheer volume of AP Deathcap gives is useful for more than just damage (for certain champions), but this is really good to know. Nice work.

[CHARLATON]

So, basically, assuming that you bought Sorceror Shoes and have 9 MPen from Runes, Void Staff is better than Deathcap when a character has roughly 60 MR for all champions.

Is this factoring in the 10% MPen from Masteries (too lazy to look)? Or Fiddle's passive MR reduction?

[Trahas]

CHARLATON, on 28 July 2012 - 02:33 AM, said:

So, basically, assuming that you bought Sorceror Shoes and have 9 MPen from Runes, Void Staff is better than Deathcap when a character has roughly 60 MR for all champions.

Is this factoring in the 10% MPen from Masteries (too lazy to look)? Or Fiddle's passive MR reduction?

This is not, also worth noting that the 10% from Masteries and the 40% from voidstaff aren't additive but instead you must multiply them together giving you only 46% pen.

I did not add in masteries and runes and boots because those aren't always standard. But say you had the 9 pen from masteries and 20 from boots, you would actually add 29 to those totals above to give you like you said around 60 Mres. Which is not hard to get on most champs. Since the base is 30 and all melee champs have a 1.25 MRes/lvl, people also pick up scaling MRes/lvl blues often and Merc treds give 25 Mres getting about 60 MR is no big deal at all.

As for fiddle's MR Reduction I did forget about that so it was not added in on him. I was just grabbing numbers for Damage and ratios for a handful of champs to use for examples.

[Feanor]

Wow. Just wow. This is soooo weird. I checked math and counldn't find anything weird. Most AP carries don't run Magic Penetration anymore these days so you don't have to incalculate runes. Why is everybody rushing Deathcap if Void Staff gives better damage. It puzzles me.

[kiwijunglist]

Assume you run the following

Mpen Reds = 8.5 Mpen
Sorc Shoes = 20 Mpen
Magic Pen Mastery = 10% Mpen

Enemy has 30 Base MR - No MR from Runes

Without Void staff, Enemy has (30-20-8.5) x 0.9 Effective resistance = 1.35 MR
With Void Staff, Enemy has (30-20-8.5) x .54 Effective resitance = 0.81 MR

Enemy has 30 Base MR + 12 MR from Runes

Without Void staff, Enemy has (42-20-8.5) x 0.9 Effective resistance = 12.15 MR
With Void Staff, Enemy has (42-20-8.5) x .55 Effective resistance = 7.42 MR

My Conclusion

Your totally wrong, no point getting void staff unless facing an enemy with high MR

[Trahas]

kiwijunglist, on 28 July 2012 - 01:31 PM, said:

Assume you run the following

Mpen Reds = 8.5 Mpen
Sorc Shoes = 20 Mpen
Magic Pen Mastery = 10% Mpen

Enemy has 30 Base MR - No MR from Runes

Without Void staff, Enemy has (30-20-8.5) x 0.9 Effective resistance = 1.35 MR
With Void Staff, Enemy has (30-20-8.5) x .54 Effective resitance = 0.81 MR

Enemy has 30 Base MR + 12 MR from Runes

Without Void staff, Enemy has (42-20-8.5) x 0.9 Effective resistance = 12.15 MR
With Void Staff, Enemy has (42-20-8.5) x .55 Effective resistance = 7.42 MR

My Conclusion

Your totally wrong, no point getting void staff unless facing an enemy with high MR

If you read further in the comments it was pointed out that if you run runes and masteries it becomes effective around 60 MR, but if they have the 30 base, plus runes/masteries and most champions get some form of MR in at least one item whether it be mercs, chalice, or whatever, it is very easy to get above 60, especially melee champions that have MRes per level.

Plus your math didn't prove me right or wrong because you never compared it to how much damage you would be doing with AP. You should also note that Mpen improves your Base damage and damage from AP ratios, while AP only helps your ratios.

[Feanor]

It's so easy to reach 60 MR these days. Runes, masteries, Soraka, Aegis.

[SoupSoupMahGaa]

kiwijunglist, on 28 July 2012 - 01:31 PM, said:

Your totally wrong, no point getting void staff unless facing an enemy with high MR

YOU'RE* DAMMIT.
And at what point of MR is that? Trahas's math says 60.

[Animality42]

To me, while the math is here and it proves that once a character has around 60 MR that void staff is better, it doesn't talk about the scenario in which it's the casters job to nuke down the carry, who has:
Ashe: 30
Caitlyn: 30
Corki: 30
Draven: 30
Ezreal: 30
Graves : 30
Kennen: 30
Tristana: 30
Twitch: 30
Urgot: 30
Vayne: 30
Varus: 30
Soooo yeah, this is why mages rush deathcap in 90% of scenarios before voidstaff, because unless there galio is the only one extremely fed, they need to be doing their job at nuking down low base health targets like AD carries

Like the meta is their for a reason and this has probably been theorycrafted before numerous times by highly skilled players

[Suzaku910]

Animality42, on 28 July 2012 - 09:16 PM, said:

To me, while the math is here and it proves that once a character has around 60 MR that void staff is better, it doesn't talk about the scenario in which it's the casters job to nuke down the carry, who has:
Ashe: 30
Caitlyn: 30
Corki: 30
Draven: 30
Ezreal: 30
Graves : 30
Kennen: 30
Tristana: 30
Twitch: 30
Urgot: 30
Vayne: 30
Varus: 30
Soooo yeah, this is why mages rush deathcap in 90% of scenarios before voidstaff, because unless there galio is the only one extremely fed, they need to be doing their job at nuking down low base health targets like AD carries

Like the meta is their for a reason and this has probably been theorycrafted before numerous times by highly skilled players

A lot of AD carries use scaling MR runes + 21/9/0 masteries.

That's an extra 11 MR at level 8 + 6 from Masteries = 17. So they're at 47 or so at level 8 already, not counting anything else they may have or built.

[Animality42]

Suzaku910, on 28 July 2012 - 10:59 PM, said:

A lot of AD carries use scaling MR runes + 21/9/0 masteries.

That's an extra 11 MR at level 8 + 6 from Masteries = 17. So they're at 47 or so at level 8 already, not counting anything else they may have or built.

And we said the turning point was 60 right, so by lvl 18 the AD carry should have +30~ mag res, which is exactly 60, which means, by the time their AD carry hits lvl 18 (Should have IE+PD in an average scenario), you should be building void staff, which means that in the ideal situation, someone like Ahri would have Sorc, 2 Dorans, Deathcap, and Void staff
Meaning that Deathcap offered more damage to explode carries midgame, and now can be followed up by Void staff to keep doing their job

To me, there is no scenario where a mage should build void before deathcap, because by the time AD carries have that MR, it's later in the game and the mage can itemize for it having deathcap and 1 other big item if they farmed well

[Trahas]

You miss understood what I was going for here, it was simply a test to see where the breaking point was for different AP ratios and Base Damage. And the turning point is around 30, not 60. It becomes 60 if you spec in both masteries, runes, and by buying sorc shoes. If we just say no sorc shoes alone the number needed is only around 40 which is very easily gotten by masteries and runes from the enemy.

But once again I am not saying rush voidstaff first every time, I was just wanting to figure out the turning point on when it is better to do one then the other. And if you download my excel file you can see when those turning points are and when it would be better to get Cap first.

Also to assume in a game that your only target will always and forever only be the carry then that is pretty far from the truth. It may be closer to that in extremely high level play, but that is not the majority of players and this is what I was aiming for. When an udyr who does get Mr early comes rushing at your face it would be nice to know you can turn on him and burst him down easier then you would if you built straight AP.