In this post (very long) I will show a detailed comparison of the 2 items and the cut-off MR value for when Void becomes better than all Shadowflame penetrations. I will leave the TL;DR just below this:

TL;DR:

If the enemy has over 50-65 MR depending on your items/AP total then Void staff will always be better for damage than Shadowflame. As you gain AP and have items like Sorcs the MR cutoff lowers and makes Void the better option at relatively low MR values. This assumes Shadowflame is always dealing 20 pen but it doesn't always do that. So even at 35-40 MR at 3+ items void CAN be better.

Crossover depends on if you believe the 200g should be compensated in the comparison. I am unsure.

## INTRO

The new item Shadowflame is being built frequently now that we have another source of flat magic penetration. Previously we only had sorcs + ludens+ rocketbelt, but now we have a rival for void staff in mid game?

AP10065
HP200
Magic Penetration10-20 (Based on target's current health) 20 when target =1000hp* and 10 when target is 2500.45%
Cost3000g2800g

*and/or if the they were affected by a shield within the last 5 seconds.

For the purpose of dmg calculations I am going to omit HP value. However Void staff is 200g cheaper and therefore I will offer 2 sets of numbers, the first set comparing the items vs each other and the second set will compensate the 200g cheaper void staff with 200g worth of AP which is equivalent to: 9.1954 AP. This is referred to as 'Void comp' throughout

Magic Penetration vs Magic Resist

Magic penetration is how much of the Magic resist will be ignored. Magic resist CANNOT go into negative values using just Magic penetration items. So ludens/shadowflame/sorcs will never put a targets MR into negative values. It will always be set to 0 if it's theoretically below 0.

Magic Resist formula :

📷

MR formula. Magic pen can't pen below 0 MR. Only MR shreds like Trundle R

We can test the dmg when varying the MR value and see how each performs.

## Test 1:

Target has 100 MR and 1000HP

If the damage in a spell is 500 dmg how much will the items penetrate. Shadowflame will ignore 20 MR and Void would ignore 45MR.

Table shows target MR and the effective mr (MR which effects the damage value) = MR – Magic Pen

Item / MR10203040506070
Void5.51116.52227.53338.5

If we were to assume Shadowflame always did 20 pen the exact MR value Void overtakes is 44.444.

However this is simply comparing the two items penetration and does not consider any of the AP on the items which is what this post is mostly about.

## AP difference

Shadowflame gives 35 more ap. Or just over 25 if we include the 200g compensation AP. This changes the point at which Void overtakes Shadowflame as the Δ AP = Δ damage.

To calculate damage of most spells in league we do:

Spell Damage = Base Damage + (AP ratio * AP)

i.e A spell does 200 base dmg, the ratio is 0.5 and you have 100 AP. The total spell damage will be 250.

So if we have 2 builds, one with Shadowflame and one with Void. The builds will have a difference in 35/25AP. Which means the spell damage will differ between the builds by:

35 * AP ratio = Difference in damage between the 2 builds

For most builds the delta in AP is the only important factor. However if we had Deathcap or infernal dragons which have multiplicative effects on your AP the difference will change. Having any of these multiplicative effects will push Shadowflame into being more favourable.

## Builds

I have experimented with numerous builds but will show a standard season 12 build. *

* These builds do not show the 200g correction of AP but will include in results.

2 item build with no compensation for void price

So the total AP values are 224 and 189 respectively. With 18 Magic pen base from Sorcs. And if we added a Cosmic Drive + it's combat passive for a 3rd item we would have AP values of 353 and 328. Due to the variety of builds there is not really a x item = y ap value but we can plug and play whatever ap value as long as we maintain the correct Δ AP to get a rough guess Which will be 35 or 25*.

## Test 2

So let's look at a spell. I will use Orianna q. Base dmg of 180 and an AP ratio of 0.5.

Ori q dmg with the 3 builds* with 2 items completed

Now we can plot this damage value vs a range of MR values.

Orianna q 2 items w/sorcs damage vs various MR values

So here we can see the damage decrease as MR increases and Void starts to overtake in damage around 55-60 if Shadowflame does the maximum pen of 20 at 1000HP (Red line) but if the target has 2050 HP. The two Void builts overtake at an MR value of just 40-45MR.

8 values going to the same damage value is because with all the pen of sorcs + shadowflame the MR is 0.

To calculate the overlap we can do some algebra and form an equation. (Each build can change the equation as it depends on the amount of pen you have, removing sorcs changes it etc…)

Simple DMG calculation

We then set both "Damage" to be equal we find the overlap and we can solve for MR at which the post mitigation damage is the same.

eq 1 and 2. Finding the MR at which both builds/pen do the same Post mitigation damage

These could be simplified but I kept it like this so I could track where things came from etc… Feel free to simplify and make simpler equations.

So using eq (1 & 2) we can solve the overlap MR exactly for all testing for this one.

With sorcs

Void overtakes Shadow(20) at: 60.80 MR

Void comp overtakes Shadow(20) at: 56.03 MR

For people wondering what removing sorcs does to to the overlap.

Without sorcs

Void overtakes Shadow(20) at: 63.56 MR

Void comp overtakes Shadow(20) at: 57.99 MR

## Test 3

What about a full combo using the same items as test 2. I used Orianna qwr which has an AP ratio of 2.0 combined and a base damage of 650. Initially you may think that this would have the exact same outcome however the changing AP ratios of spells shifts the overlap. Shadowflame loves high AP ratio spells and void loves base dmg spells. There is a ratio to be found between base dmg and ap ratio. For the whole combo we can do 650/2.0 = 325. And q's ratio is 180/0.5 = 360. These are fairly close and MOST champions fall roughly in this range. This value is the ap required to double the spells pre mitigation damage. You will notice that we require less AP to double the damage of the QWR combo and therefore the increased AP in the shadowflame build will marginally shift this build to being more favourable.

NOTE: IF you are a champion like Elise and have an AP %HP ratio not like 0.5AP. Then the increased AP helps a lot. Don't have the exact numbers but it'll help get past the % thresholds.

Orianna qwr 2 items w/sorcs damage vs various MR values

With sorcs

Void overtakes Shadow(20) at: 62.01 MR

Void comp overtakes Shadow(20) at: 56.86 MR

Without sorcs

Void overtakes Shadow(20) at: 64.98 MR

Void comp overtakes Shadow(20) at: 58.96 MR

Important: I will not detail further about this as you can endlessly make combos and look at the AP ratios and just make weird stories. This data suggests if you only use q on Orianna you should build Void and if you only use qwr combo you should have shadowflame.

## Test 4

Increasing the AP with a 3rd item and looking at the qwr combo again. Previously I mentioned we can plug and play any AP as long as we maintain the same Δ AP which is only good for a guess. Now as we increase our AP the difference in AP between the builds does stay exactly the same BUT the %difference in AP will shrink and shrink as we increase our AP. Meaning the ap portion of our spells being stronger because of shadowflame is less important. So as we increase our number of items and AP we will favour Void more and more and more.

3 item build with total AP values. Void Comp again ~9AP more.

Orianna qwr 3 items w/sorcs damage vs various MR values

With sorcs

Void overtakes Shadow(20) at: 57.739 MR

Void comp overtakes Shadow(20) at: 53.93MR

Without sorcs

Void comp overtakes Shadow(20) at: 55.53 MR

So as we transitioned from 2 item to 3 item we have reduced the threshold at which Void becomes better by 3-4MR. This will continue as we get more AP.

We can make an equation to calculate how much AP you need to shift the crossover higher or lower . Maybe this is important for you to calculate AP needed vs certain comps/MR values. First we need to derive a DMG ratio between the 2 builds. (eq3-4) And then do some more math to get an AP value.

https://preview.redd.it/bqkuocxvnc181.png?width=690&format=png&auto=webp&s=7f620b580640ab2402a6005dbca07b53008c25e2

Equations to solve for the AP

So with equation 3-4 we can plug in our desired MR value where we want the overlap to be. Let's plug in 50 for this 3 item build. The using eqn 6 we use the damage ratio of 0.9778. And therefore we would require 782AP to make this difference in AP (void comp) to get the MR overlap to 50.

Proof of concept for having 782 AP on Shadowflame build, 747 and 756 for the Void builds. Overlap with Void comp is 50 MR

## Deathcap and Infernals

As stated these multiplicative effects on AP help Shadowflame substantially. Let's start with Dcap as this one is a 35% increase in AP whereas infernals are 4/8/12/16% respectively. So always less of an effect but you will see how that works. Let's say we build it 3rd and have these builds. Which is not that uncommon on many mages.

3 item build with deathcap

Now we can clearly see the established 35 AP difference between Shadowflame and Void has been broken. Now the difference in this build is 47.25 (35*1.35) and for Void comp the difference is 34.836. This means we have a shift towards higher MR values and Shadowflame being favoured.

## Test 5

Orianna qwr 3 items w/dcap and sorcs damage vs various MR values

With sorcs

Void comp overtakes Shadow(20) at: 56.51MR

Without sorcs

Void comp overtakes Shadow(20) at: 58.55MR

So comparing the two 3 item builds we don't see that dramatic of a shift but also remember we have a lot more AP, so the dcap build AP value is similar to that of a normal 4 item (no dcap) build. So if you have Deathcap in your build the shift is approx 2-3MR. But if you had 4 items and similar ap the shift is approx 4-5 MR towards favouring Shadowflame.

## Conclusion

Sorry for the wall of text, I got carried away investigating this and thought I'd share most things.

Big take aways. The changeover from which item is better is somewhere between 50-65MR when (considering shadowflame always has 20 magic pen which it doesnt) depending on items/runes/dragons and your champions AP ratios. If you are a champion with very good AP:Base dmgs you should maybe consider Shadowflame more. Not because of the 2MR shift but because you will be doing a lot more dmg to squishes too. This is not a post to tell you to always build one or the other, every game of league is different.

Builds which include both shadowflame + void can become overkill a lot of the time as you cannot reach into negative MR values with just pen items. So please do not build sorcs+ ludens + shadowflame because you want to give them -19 MR it doesn't work like that.

Crossover threshold for Orianna QWR

BuildsSorcsNo sorcs
2 item62.01 MR64.99 MR
2 Item with void comp56.86 MR58.96 MR
3 item57.74 MR59.99 MR
3 item with void comp53.93 MR55.54 MR
3 item with dcap59.84 MR62.45 MR
3 item with dcap and void comp56.51 MR58.55 MR

Every champion + their combos will shift these values but this is merely to show that changing the builds through the game will change the threshold.

So if their team has 0 mr items/runes/masteries or mountains Shadowflame will be better is most circumstances but if they have high HP maybe not. But if they have atleast 1 null magic mantle then void is usually better and as you increase your AP void will become more and more favourable.

Ludens + sorcs + shadowflame is overkill and the crossover is still 53-55 MR at 3 items. Despite doing close to true DMG to anyone below 50 MR. Void + Sorcs +Ludens does the same job.

Building them together is super good in mid/late game on lots of champs but I think other items could be better. Will run the numbers to check later!

If you notice any mistakes or want to discuss anything just let me know!

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