Hello, hello! DiffTheEnder with some more mathcrafting for you today. I'll warn you right now -- if you don't like rainbow graphs, you might want to skim through to the conclusions. However if you're a fan of them -- enjoy the ride!
So what is today's analysis about? The pinnacle of Ability Power items -- the Void Staff and the formidable Rabadon's Deathcap. Both of these items exist purely to boost your damage output and it's time to figure out at exactly which points each item is better for your damage!
Let's remind ourselves what each of these items do first.
Apart from the raw Ability Power each item gives you, the real complexity in figuring out which item is better lies in the passives. Does 35% Magic Penetration outweigh 25% bonus Ability Power significantly?
There are a couple of assumptions that must be made to make this analysis more representative of real-game situations.
- The mage in question has taken the standard 21 points in the magical offensive tree.
- The mage has built Sorcerer's Shoes before building either a Deathcap or a Void Staff. which gives 15 Magic Penetration.
- The mage has taken Magic Penetration marks.
There's not much more to be said other than the forewarning about the complexity of the analysis. There are several factors to take into account when trying to answer a question such as this. Namely, they are:
- The mage's Ability Power (current AP) before building either a Deathcap or a Void Staff. This is important because of the % multiplier passive of the Deathcap.
- The AP ratio of your spells. Spells with higher AP ratios do more damage if you have more AP and a Deathcap provides more AP.
- The base damage of your spells. The base damage of your spells only scale off Magic Penetration and this means higher base damage spells favour the Void Staff more.
- The enemy's Magic Resistance. The more magic resistance they have, the more effective the Void Staff's passive will be.
Each of the four above factors are variable and therefore we'd need a multi dimensional graph to fully encapsulate the data. Believe me when I say, I've simplified it as much as I could to produce simpler contour difference plots instead (aka rainbow graphs). This is a math heavy post so I'll stop babbling on and let you see the results. There are A LOT OF GRAPHS coming up so I'll try to explain how the graphs work before unloading them on you.
If there is a simpler way to display the data, I still haven't figured it out after a year. So here's a picture that will try to explain how to read a rainbow graph using an example of an upcoming graph.
You'll have to click and enlarge the image to view the text clearly. Now that you've hopefully understood how to read these graphs - let's dive in.
As I mentioned, there are 4 dimensions of data and I don't want to use a more complicated graph than a rainbow graph. So I've made several rainbow graphs to span a set of realistic values to give you an idea of how effective each item is. Apologies for the visual assault.
You'll have to view the enlarged version to read it clearly. Without running through each graph, we can see that the results match what we expected. Void Staff is more effective with higher base damage and higher enemy magic resistance.
From the above data, the Void Staff is shown to be an effective purchase over Deathcap against enemies who have built at least a bit of magic resistance. However, there is a large difference in the damage difference against low Magic Resist targets.
There is one key factor we are missing however and that is the cost of the items. The Void Staff is 1,305g cheaper than a Deathcap and that is a HUGE amount. Huge enough, that you could buy a Blasting Wand and an Amplifying Tome with that money and have an extra 60 AP. So the question we should really be asking ourselves is, can a Void Staff + Blasting Wand + Amplifying Tome out do a Deathcap in damage? The answer, is a resounding yes. Here's a comparison of the damage across the 100 MR bracket.
Once again you'll have to enlarge the image to see the results clearly.
If you've read those graphs right, you, like me, would have been mindblown at how strong the Void Staff really is. It significantly outdamages the Deathcap regardless of what your base damage is at 100 MR. Remember that Void Staff scales better when the enemy has higher MR. In other words, Void Staff + BW+ AT is > Deathcap for anyone with 100 MR or above. However, now you're thinking, "My goal is to 100 to zero the squishy carries and I could care less about tankier enemies".
I would answer, "You're right, a Deathcap does deal more damage to lower MR champions, for anyone under approximately 80MR depending on your AP scalings and base damages." I don't want to bombard you guys with more rainbow graphs, but I can tell you that the graphs for Void Staff + 60 AP look similar to the ones without the +60 AP.
Let's move in to the conclusions so that the readers who skipped the graphs can get something valuable :)
Welcome to all the readers who skipped past the graphs for fear they would go blind with the colour overload -- fear not, I'll recap the results.
A Void Staff proves to be a competent damage output alternative to Rabadon's Deathcap when the enemy has over 100 MR, your base damages are high and your AP ratios are decent. However, short of having obscene amounts of base damage or MR, the Deathcap can provide you with a better damage boost.
The above is accurate BUT that does not take into account the item's cost or build path discussion.
The Void Staff is cheaper than the Deathcap. This means you have enough of a gold difference to buy a Blasting Wand and an Amplifying Tome which give you 60 AP. A comparison of a Void Staff+Blasting Wand+Amplifying Tome versus a Rabadon's Deathcap does the comparison more justice.
The results when you take into account the extra AP are significant. The Void Staff option becomes the higher damaging build against enemies who have greater than approximately 80 MR depending on your AP ratios and base damages. You might be thinking that only tanks have MR values greater than this, however that's not true. Here are the resist values from a game at MLG Dallas.
Thanks to ELOBUFF for the data. You'll see that short of the supports and the squishy Orianna, everyone had at least 70 MR.
Another advantage for the Void Staff is that since it's cheaper and the components are cheaper, there is a greater option in build flexibility as the game goes on. You can decide to change your build and not have it hurt you as much since you've invested 1300 gold less than a Deathcap. A Void Staff also complements Magic Penetration builds a lot better, take note Elise players. Finally, a majority of mages have at least one damaging AoE spell, and having a Void Staff maximises the damage of this spell to every enemy hit regardless of whether they are a tank or not which in my opinion is a better route to take.
Tl;dr - Void will usually be better against enemies with >80 MR (read above to understand what affects "usually")
Regardless, the facts have been laid out and my opinion has been voiced. It's up to you to make the decision on which to buy. I know I'll be buying Void before Deathcap more often now.
If you enjoyed this analysis - I'd appreciate your support in helping spread the word about Void Staff!