Defensive Mastery Comparison

 

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.

 

Low-Tier 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:

30*(1+(Armor/100+MR/100)/2)=.01*Health

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.

High-Tier Masteries

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/200=3

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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 "Song" of the Day

31

Comments

  • #27 Pathoth

    if you take into account hp regen, heal summoner spell, flask, spell vamp, life steal, hp pots, things that damage you based on your maxhp... 

    maxhp bonuses don't look so good, especially early game. unless your champion has some scaling bonus with maxhp.

  • #28 GentlemanGustaf

    yup. Health isn't good. That's why no pro players stack health, even on champions who already have tons of health, like Cho.

    Sure, there's %HP damage, but it requires you to go out of your way to get it. %Pen is basically part of every AD's build now.

  • #24 PhilNye

    Yes, I'm glad someone put it into perspective on how mediocre legendary armor is.  The only time I can even remotely see it being useful (maybe) is it being applied on "hyper-tanks" that get high scaling for building heavily into resistances like Malphite, Rammus, or someone who can steal those stats like Trundle.

  • #21 ianzzz94

    If I didn't already calculate and post my version of it before, I would've loved reading this. 

    http://www.reignofgaming.net/forums/strategy/runes-and-mastery-discussion/30216-mastery-theorycrafting-ehp-and-the-defensive-tree

    Anyways, interesting conclusion. My last question would be: What would your ideal 0/21/0 page be? 

  • #22 Morkai

    There's no ideal 0-21-0 page just in general, it depends on the champion, matchup and even enemy team comp.

  • #25 ianzzz94

    The biggest reason I said this, was because he would see that one did not simply choose between  Hardiness and Resistance and Veteran Scars, since you would be forced to take Perseverance (And no-one ever does that anyways) or you would have to take Durability without Veteran Scars (And that is just plain stupid) 

    And that you would never be choosing between Defender and Juggernaut, since you wouldn't waste points on Legendary Armor. 

    Only thing in the conclusion that is actually a good statement is taking Defender over an extra point in Resistance or Hardiness.

    One thing he did not notice is that Legendary Armor at 450 Resistances (9 resistances) is actually still worse than Defender with 5 man (10 resistances). And he actually calculates the examples with 450 Bonus Resistances, while Defender works better than Legendary Armor at lower resistances. 

    For example:  you would have 1500 HP and 200 Resistance into mid game and you're dancing around mid lane poking and teamfighting etc. -- meaning 1.5% of Juggernaut would turn into 1.5% + 2% of your HP, while Defender would be an EHP boost of 10% of your HP 
    Meaning that Defender is better into mid-game and late game until you have around 850 Resistances. 
    Note: I am not sure if Gustaf actually calculated it this way or first divided by 2, because of lumping Armor and Magic Resist in one whole makes this pretty messy

    Personally, I would not prefer to use the term Resistances as a whole, since that kinda messes up the calculations. (I mean, come on 2% of your HP EHP per enemy boost on Defender sounds pretty OP, while actually it gives 1% on your HP EHP per type per enemy, while Juggernaut gives 1,5% of your EHP per type) For this reason, I split it up into PEHP and MEHP. 

    Also, for the completeness: Legendary Armors second and third points grant 1,5% and Juggernauts second and third points grant 1,25% 

  • #26 GentlemanGustaf

    I lumped them together, because then it's easy to make statements without appeal to team comp. 200 points in resistances increases your EHP the same, no matter what. yes, it increases PEHP and MEHP differently. But you can simply make the choice as you see fit.

    Also, Defender is never a 10%*HP increase to your EHP. With 5 people around, it's 5%*HP to PEHP and MEHP. Since your EHP is the average of your PEHP and MEHP, Defender at most gives 5%*HP as an increase to your PEHP.

    Juggernaut, on the other hand, gives 1.5%*HP*(1+(AVG RESIST)/100). This means that to beat MAXIMAL Defender, you need about 233 as your average resistance, or 466 total. So yes, Defender will beat Juggernaut during team fights, but for the previous 20 minutes, it will have been a bit more lackluster.

    Let's use that same example to prove the veracity of my math.

    You have 1500 HP and 200 resistances.

    Let us split this into three cases:

    • 150 Armor, 50 MR
    • 125 Armor, 75 MR
    • 100 Armor, 100 MR

    Your base PEHP/MEHP/EHP for each of the three are as follows:

    • 3750/2250/3000
    • 3375/2625/3000
    • 3000/3000/3000

    Now let's add 1.5% to your HP! Your HP is now 1522.5. Your PEHP/MEHP/EHP is now:

    • 3806.25/2283.75/3045
    • 3425.625/2664.375/3045
    • 3045/3045/3045

    3045 is a 1.5% increase in your EHP, or a 1.5%*HP*(1+200/2) increase in your EHP (Since your EHP IS HP*(1+200/2))

    Now let's add 5 Armor/MR. You now have:

    • 155 Armor, 55 MR
    • 130 Armor, 80 MR
    • 105 Armor, 105 MR

    What's your PEHP/MEHP/EHP?

    • 3825/2325/3075
    • 3450/2700/3075
    • 3075/3075/3075

    As we can see, this increase in Defender is 5% of 1500, or 75 EHP, not 10%. It is, with 5 enemies, greater than Juggernaut. However, with just 1 person around (laning, since I assuming you're not taking this on your AD Carry, and you're probably not taking it on support), that's 1%, or 15 EHP; well below the 22.5 Juggernaut gives you, even assuming no armor. Even in a gank, it only reaches 30 EHP, which Juggernaut beats with 66 total resistances (almost everybody starts with that)

    In the mid game, you have to be around 3 people to break even vs your 200 resistances example, and that isn't much at all, considering that base Armor will be close to 80, counting runes, and base MR will probably be above 50. This means that 1 resistance item would get you to 200 total.

    Don't get me wrong, I think that Defender is a one-point wonder. But if you're building it over Juggernaut, you're making a pretty big mistake, since you won't be using that advantage until 20 minutes into the game.

    I could maybe see taking it over the second 2 points of Juggernaut.

    But honestly, it's not the conclusions I care that much about (those are situational, and depend on much more than just burst EHP, factoring into account heals (including regen) and shields.

    It's the methods. And averaging Armor and MR does not make this messy. Moreover, I did not average them, I summed them, to represent that you had about 3 items worth of resistances, and could split them up as you saw fit. Mathematically, there's no difference. But representationally? It gives a very easy picture: if you buy 2-3 resistance items, this is the case.

    It is your methods that seem suspect, since they have yielded the answer that Defender is better until you have about 850 Resistances (I assume your calculations gave 866), when the actual number is 433 (exactly half that). There is no need (so long as you make those adjustments in game) to split up PEHP and MEHP mathematically, because points spent on health affect both, and points spent on Armor/MR affect your EHP equally.

    Yes, I agree that the choices are pretty obvious to those who have done the math. But not everybody knows that Legendary Armor sucks, for example. I watch many high-Elo streamers pick it up over Juggernaut still.

    And isn't that my job? To do/present the math, so others don't have to?

    Or is my job to make decisions for you, and to tell you how to play?

    I argue it's the former. My job is to crunch math because people can and will make mistakes (like your 'Defender would be an EHP boost of 10% of your HP'). Of course, I can make mistakes too, so there should be checks and balances, and there's nothing wrong with calling out my math (when people have done so in the past, I've made changes right away). I'm just not incorrect in this case.

    Last edited by GentlemanGustaf: 1/21/2013 2:16:53 PM
  • #29 ianzzz94

    Oh damn, I read your example wrong --  "As such, you gain a combined 9 resistances, or 4.5%*HP in EHP increase" 
    It is indeed an average and not a sum, so that is my bad. 

    I'm just saying, you are not giving Defender the credit it deserves. "Try to avoid Defender" -- Don't avoid it, embrace it, with 1 person against you, it is more or less equal to the first points of Resistance and Hardiness, with 2 people it outscales them, with 3 it is better/equal to a Juggernaut with 200 resistances. with 4 it outscales Juggernaut most of the times, same for 5. 

    Juggernaut would be the pre-teamfight mastery (and very late game if you build a lot of resistances) and Defender the teamfight mastery. 

    Still there is one part of my post left that you did not explain. How would you ever take Juggernaut instead of Defender or Hardiness instead of Veteran Scars? 

    The only way I can think of taking Hardiness instead of Durability + Veteran Scars is if you are jungling with 21/9/0 or 0/9/21. 
    For Juggernaut vs Defender you would have to take a lot of random/not very effective points. It is almost never a choice to get Juggernaut or Defender, more often a choice to get Resistance or Defender or Legendary Armor or Defender. 

    This brings me to the last part that I'm still wondering. Did you read my forum post before you made this article? 

  • #30 GentlemanGustaf

    The full quote is: Try to avoid Defender, but it's a decent one-point wonder if nothing's left (it's strictly better than Resistance/Hardiness).

    1. You answered your question for Veteran's Scars vs Hardiness in the next line, so move onto #2
    2. If you went utility heavy in the defensive tree, 9 points through Veteran's Scars, 5 points of CCR, 3 points in block, you now have 3 points left before 21. At this point, I'd probably put 2 in Juggernaut and 1 in Defender, or 1 in Juggernaut, 1 in Defender, and 1 in Reinforced Armor (if I thought I'd see a crit build).

    Nope, but it's possible that the person who asked me about Juggernaut vs Legendary Armor (being another RoGer) had.

    It's a pretty good post, though. I'm trying to decide whether I like unyielding/block explanation. I would have done them by how much damage you have to be taking for it to beat Resistance/Hardiness/Veteran's Scars, but that's a neat way of doing it. I just don't know how easy it is to compare, that way.

  • #31 ianzzz94

    Thank you, I was planning to compare the two of them in that way, but I got exams right now, so I didn't have time for that anymore. I was planning something in the way of:
    "When is Unyielding + Block worth building towards" (As I'm currently using pages like 1/13/16 and 14/16/0) and especially when is Block worth making, as it is a pretty situational mastery. 

  • #19 brbafkftw

    Great article Gustaf.

    I'm glad that my previous assumptions that juggernaut and veteran's scars are much better than hardiness/resistance, defender, and legendary armor (in almost all game situations) was confirmed by your math.

    Now I'm curious about unyielding, block, and reinforced armor. (perhaps this is planned for a future article - if so, disregard this question) I don't need any math proofs, but assuming I have 4 total points left to use that can go in hardiness/resistance, defender, legendary armor, unyielding, block, or reinforced armor, where would you put them? 

     

    I think the general opinion that health is best on Dr. Mundo mostly stems from the fact that his (non-ult abilities use flat values of health so if he stacks health they will be diminishing his overall bulk much less than if he was stacking resistances. Otherwise I completely agree that Mundo's bulk does not increase by stacking health over resistances when he's in a team fight with his ult on.

  • #16 Dudleydino

    "So Legendary Armor gives you an EHP increase of X/100%*HP."

    Is it supposed to be 2X/100 * HP because legendary armor gives 2% of bonus resistances?

  • #17 GentlemanGustaf

    No. This is just because of a convention I was using, where I lumped Armor/MR together. It's actually 2%*(X+Y)/2. I just replaced (X+Y) with X. Think of it this way: to get a 1% increase in tankiness, you need 1 point of MR AND armor. So if your total Armor + MR is 100, that's 50 of each, and 2% of that, is 1 point each, for a 1% increase.

  • #15 Millouis

    Ok I have a big question mark on my head... what about health % runes nowadays? I know nobody used 'em on season 2, what about now?

  • #14 Morkai

    I think that you're neglecting an important thing when discussing the defensive masteries, which is sustain. Mitigation increases the value of your heal, regen and lifesteal which is something that flat health does not do.

    What you are comparing here is not actual tankyness in the wider meaning rather the resistance to being bursted down. In the current assassin-heavy meta it happens to be the roughly the same, but once you get past surviving an assassin's burst resistances and regen/lifesteal/heal/pots help you regen so that you can possibly survive a second cycle of attacks.

    With warmog's being a trend as a first item you get to have not only good hp but also good regen with most champions that get it and there I think mitigation plays an important role. I also believe that riot has shown that they're generally good with balancing numbers(not being a fanboy, but they've generally kept a better balance in the game than others similar-or-not games have had), if the mitigation/sustain masteries were so clearly inferior I'm pretty sure they'd have toned them up a bit before releasing them.

    You are also not mentioning 1 other thing that I think is important: Max health only matters when you're at 100% hp(at which point regen is useless) and when counting passive's(warmog's passive, shen's and sejuani's damage, garen's passive etc) positive and negative (it also increases dmg taken from %max health things like malz's W, vayne's silver bolt's liandry's torment{first tick at least} etc) whereas mitigation is never a stat that can scale positively with anything the opponent can get, they can counter it with % and flat penetration but it can never scale in their favour.
     Which brings us to regen(or sustain to include pots/heals/lifesteal): it starts taking value the moment your health drops below 100%(which is pretty much all of the laning phase and most of the late-game though it's weak against assassin comps while strong against poke comps). It scales with mitigation and also can never scale positively for the opponent either.

     

    My point is that such an article is useful only in showing some things, but if you really want to make an analysis on defensive masteries the correct question to answer would be "which of them are useful in which cases" and not "which of them are stronger" and my example is again this: If your enemy runs a poke comp then mitigation/sustain is king since they can't poke you down and they waste resources faster than you waste yours. Against an assassin comp all the sustain in the world won't save you if you are dead within a cycle and your main concern is to survive first deal damage on their downtime later(or just catch them off guard).

  • #18 GentlemanGustaf

    sure, there's also % Pen, and shields.

  • #20 Ryvena

    Definitely insightful reply.

    GentlemanGustaf's is very organized though, it compares a single stat. Survivability in a 100% HP to 0 HP scenario. So yes it's limited in scope but it is a strong and clear comparison. We could include that "defender" allows people to detect enemies in brush as well (I don't know the range) but...

    But even with the simplified math, and simplified analysis, a lot of this stuff is over the heads of the average audience.

    In reference to Morkai's reply, one strong point ppl overlook is... 9 potions is 150hpx9 = 1350HP, 1 point def is 13.5HP, which is why Arm/MR flats are so strong at lvl 1. This is also why the Defender armor, and the flat MR/Arm Masteries cannot be too strong (it'll make lvl 1 def tree too strong). The legendary armor... really isn't very legendary though. (worst def point imo)

    Last edited by Ryvena: 1/20/2013 6:09:21 PM
  • #23 Dj0z

    Exception that confirms the rule: Trundle R.

  • #13 EuWGasgano

    I like how you mentioned that Defender is a one-point-wonder, in a 5v5 team fight you get 10 ressistances for only one point, thats cool.

    I like this article, altough its nothing new for me personally ;) Veteran Scars boosts your starting hp by atleast 5%, which is huge. Legendary Armor is easy maths. Thanks for the summary!

  • #11 outofinspiration

    You talked about legendary armor and split pushing. What about champions who naturally buff their resistances (Leona, Taric, Singed...)?

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