How OP is pOPpy's Passive?

Introduction

One of the first things most people think of when you talk about Poppy is her passive. Everyone can think of one situation where a favourable fight has turned horrendously bad due to underestimating her passive.

For those who need their memory jogged -- meet Valiant Fighter, one of the most sought-after passives.

The Aim

By the end of this post I'll be hoping to answer the question posed in the title: how OP (over powered) is the passive?

I may or may not be able to definitively give an answer -- but rest assured you'll learn quite a bit along this journey. So ready your eyes, I've got some rainbows for you today.

For readers new to this blog -- my affectionate term for contour plots are "rainbow graphs," for reasons that will become obvious.

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Doing the maths

Let's get some things clear

The damage reduction is applied after resistances have been taken into account. So if you're being crit for 1000, and you have 100 armour which reduces that to 500 damage, the passive will reduce that further to 250 damage.

For reasons unbeknownst to me, the tooltip description on Valiant Fighter is misleading -- damage is not actually reduced by 50%. I dug through some old posts and found this equation to explain how Poppy's passive works:

Let's use some basic substitution to try and express this in a simpler form:

To finally end with:

For those who have completely skipped the maths -- the point to take from this is that the passive does not reduce incoming damage by 50%, but slightly less, as 5% of your current HP is added to 50% of the incoming damage.

Source for equation: See FeralPony's Riot post (#3) on the original League of Legends forums thread.

So now that we've sorted out the equation for the damage reduction -- let's do something meaningful with it.

Something meaningful

The easiest way to visualise how effective Poppy's passive is: figure out how much further damage reduction you gain by having it active.

First, let's take a look at how much damage you'd deal without Poppy's passive active.

How to read the above and following graphs: Y axis (Armour/MR) -- Poppy's Armour/MR X axis (Damage) -- The damage of your attack Z axis (the colour fill) -- How much damage you actually deal (use the key on the right to read values)

(Important note: I assumed that Poppy's HP was 300 in these calculations.)

Now let's take a look at the same graph with the damage reduction from the passive as well as armour/MR taken into account.

As you can see -- there is a huge difference in the actual damage dealt.

The following shows the difference in damage between having the passive active and not having it active:

It cannot be denied that the passive makes a huge difference. Let's try to put this in perspective of something we all understand -- resistances. How much more "invisible" Armour/MR does Poppy gain while her passive is in effect?

The whitespace is where there is no difference -- Valiant Fighter will not be active at those values as the damage dealt to Poppy is too low to meet the condition.

So I imagine your reactions after seeing this would be one of the following:

• "Oh wow -- she gains a lot of free resistances -- MUST NERF POPPY" -- would be the first reaction for most people who get to this point.
• "Diff -- you've gone mental" -- would be the reaction of people who actually went in-depth and understood these calculations.
• So why am I mental? -- Because the 300 HP I assumed near the top actually does matter quite a lot.

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The 5% is huge

Recall our friendly simplified formula:

5% of your current HP is added on top of the damage taken -- so if you were at 3000 HP, 5% of the HP would be 150, which is by no means a small amount.

Let's skip all the lead-up graphs and bombard you with rainbows for the effective extra resistance you gain at various HP values:

As you can see, the whitespace grows -- you'll need to deal more damage to activate Valiant Fighter.

The whitespace becomes most pronounced in the final graph:

There's a linear line determined by resists/damage for each HP that determines when Valiant Fighter will be active.

If you noticed -- the effective resistance you gain from having Valiant Fighter active decreases as you gain more HP, and increases as you gain more resistances. However, the highest increase in damage reduction occurs when you have the least resistances and least HP.

Therefore it is quite clear that to make the most of Valiant Fighter -- you should build Poppy as a glass cannon.

Disclaimer: I'm not saying you should build glass cannon Poppy -- but I am merely stating the fact that the highest rewards from the passive are reaped when Poppy has low resists. Just a fact.

From looking at the graphs -- in most realistic situations, the effectiveness of Poppy's Valiant Fighter is anywhere between 15 to 150 Armour/MR on top of your base resistances. Quite a hefty amount. Let's take a look at how Valiant Fighter compares to other abilities.

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Comparisons

I'll only be comparing the damage reduction portion of the abilities.

Jax's Ultimate

This beats Poppy's passive for armour but won't match up for MR if you build AD bruiser Jax. However it can be used to negate burst, which is valuable. It's close -- but Valiant Fighter loses.

Kassadin's Passive

No contest here. Valiant Fighter wins.

Olaf's Ultimate

Barring the CC immunity -- Valiant Fighter ties.

Wukong's Passive

Once again, Valiant Fighter is far stronger than this. Valiant Fighter wins.

Graves' Passive

He'll need to remain in combat for a while, and even with unlimited stacks he can't compete with Poppy. No contest. Valiant Fighter wins.

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Conclusion (with a fair bit of opinion)

It's quite clear that Valiant Fighter is very strong. It outdoes every other similar passive and compares very nicely with ultimates like Ragnarok. From the numbers and graphs above -- it consistently offers significant amounts of effective resistances. Combining this with the fact that she is all but immune to one damage source for up to 8 seconds, you have a ridiculously tough champion.

It can be argued that Poppy needs the survivability to be able to get in and assassinate a target while walking out alive -- but it is my opinion that Valiant Fighter is OP. If I had to take a stab at what value the passive should be at -- I'd say reducing incoming damage by something like 35% instead of 50%. However I am no designer and that is another matter entirely :)

Cheers, -- DiffTheEnder