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
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.
Trahas\'s Mathcrafting, AP vs Mpen.xlsx (1.43MB)
Number of downloads: 13
Edited by Trahas, 28 July 2012 - 03:46 PM.