I get a lot of questions about the new masteries, so I thought I'd do a quick series on the value of masteries. Typically, these valuations are done with gold, but I thought I'd try something new: how much tankier do they make you? Turns out the math is easy to do for some, hard to do for others, and WAY TOO SPECIFIC to do for some. So here's a comparison of health and armor in masteries.
First, let's compare the early defensive masteries.
You've got Durability, which gives you Health/lvl. How much does this increase your tankiness? Well, it gives you 1.5 points of health per level (per point). How much does this contribute to your Effective Hit Points (EHP)?
The formula for EHP is Health*(1+Resistance/100). For now, we'll assume an even physical/magical split; you'll obviously have to adjust when this isn't the case. Just remember that these numbers are for summed resistances (Armor and MR), not for individual resistances. This means that you get 1.5 times 1 plus the average of your Armor and MR (divided by 100): 1.5*(1+(Armor/100+MR/100)/2)/lvl. At level 18, this is 27*(1+(Armor/100+MR/100)/2).
Compare this to Hardiness or Resistances: the first point gives you 2 armor/mr, the next points; 1.5. The first point of these masteries increases your EHP by 1% of your Health; the next points, by .75%
Finally, you've got Veteran's Scars, which gives a whopping 30 health (yeah, it's a bit OP). This gives you 30*(1+(Armor/100+MR/100)/2) EHP.
Let's start by comparing Veteran's Scars to Hardiness/Resistance. One point in Veteran's Scars gives you 30*(1+(Armor/100+MR/100)/2) EHP, and one point in resistances gives you 1% of your Health. So we can set the two equal to each other:
Health=30*(100+(Armor+MR)/2). So if your Health equals 30*(1+(Armor+MR/2)), you can get either. If Health is greater than that, get hardiness/resistance, and if health is lower than that, get Veteran's Scars! So where's the break-even point?
Turns out Veteran's Scars is pretty much always better; it's better until you have 3000 Health and 0 resistances. The red side indicates the area where you should start get Resistance/Hardiness over Veteran's Scars. So, given that you'll get at least 60 Armor/MR naturally, unless you plan on having 5000 health and no Armor/MR items, go for Veteran's Scars.
So what's the catch? Well, to get Veteran's Scars, you have to get the 4 points of Durability. And how much are those worth? Well, at level 18, 27 HP, or basically Veteran's Scars. But that's exactly the catch. You have to wait for level 18. So how long do you have to wait for it to be worthwhile? I argue not long at all. For example, here's a graph of level 4 Durability vs Resistance:
An easy breakeven point to see is at about 1k health and 66.7 resistances. Most people will start with at least 42 MR and at least 30 Armor, and about 400-600 health. We can see from this that the early health will start being worth it right away. Basically, this confirms everything we know about stats; Health is a REALLY GOOD early game stat. As such, I pretty much always recommend getting Durability and Veteran's Scars over Resistance and Hardiness (especially since their third point is worth less.
The other major comparison to be made is between Legendary Armor, Juggernaut, and Defender. First, let's compare Legendary Armor and Defender.
Defender gives 1 resistance for each nearby enemy.
Legendary Armor gives 2% in additional BONUS resistances. This means if you have 3 resistance items (about 200 points in resistances), you're getting 4 points in resistances for that first mastery point, or the equivalent of 2 nearby enemies. It seems like Legendary Armor is strictly inferior to Defender. Why? Because Defender will apply most of the game, whereas Legendary Armor won't give you even one nearby enemy's worth of resistances until you have 100 points in resistances, and by then, team fights will cause Defender to give you more resistances. The only champions I could see Legendary Armor beating Defender on would be tanky split-push champions.
With that out of the way, let's compare Legendary Armor and Juggernaut.
The first point of Juggernaut increases your health by 1.5%, which will increase your overall tankiness by 1.5% of your EHP.
The first point of Legendary Armor, on the other hand, will increase your EHP by 1% of your health times 2% of your average resistances.
To avoid more math, let's do the next best thing! Since I think Juggernaut is better, I'll assume Legendary Armor gets the EXTREME benefit of the doubt. You now have 450 total bonus resistances. As such, you gain a combined 9 resistances, or 4.5%*HP in EHP increase. Juggernaut is giving you 1.5%*HP*(1+(450+BaseResistances)/100) already. Assuming base resistances of 100-ish, that's 9.75% times your HP in an EHP increase.
We can actually simplify that. Assume your bonus resistances = X. Divide X by 100. You get that number, as a percent, multiplied by your HP in an EHP increase. How much does Juggernaut buff your tankiness? Well, it increases your HP by 1.5%. Then, you multiply that HP gain by 1+your total resistances/200.
So Legendary Armor gives you an EHP increase of X/100%*HP.
And Juggernaut gives you an EHP increase of 1.5%*HP*(1+X/200).
What's the breakeven point?
X/100%*HP = 1.5%*HP*(1+X/200) -->
X/100%= 1.5%*(1+X/200) -->
2X/200% = 1.5%+ 1.5%X/200 -->
.5%X/200 = 1.5%
X=600. So until you have 600 total bonus points of resistances, stick with Juggernaut.
Notice one thing? The value of % Health doesn't scale with Health any more than Resistances. This is the root of my past claims that % Health abilities (like Mundo's ultimate) don't scale any better with health than with resistances.
The New Style - Health Stacking
This shouldn't come as a huge surprise to us. Resistances saw a sizable nerf; % and Flat Pen stack better, and Health items are at a premium right now, with Warmog's being one of the strongest items in the game. Why should masteries be any different? The simple answer is often the best, and this case is no exception. So get Veteran's Scars and Durability over Resistance and Hardiness, and get Juggernaut over Legendary Armor. Try to avoid Defender, but it's a decent one-point wonder if nothing's left (it's strictly better than Resistance/Hardiness). And if you have to choose between Resistance/Hardiness and Legendary Armor? Just consider that Legendary Armor won't start to do anything until you have already stacked resistances. It may be twice as strong late game, but it's 0% as strong to start.
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