Wednesday, January 16, 2013

Why You Should Love Magic Resist Glyphs in S3

There was a time in Season 2 when flat magic resist runes were so strong that Riot Games felt it necessary to nerf them and buff magic penetration runes. Many players still continued to use magic resist glyphs on their mid-lane champions, but others - maybe you? - did not. Recently, the pre-Season 3 patch introduced several changes that made early magic resist more appealing. If you already use the glyphs, then you probably don't need to read this article beyond a need to satisfy your curiosity (or maybe you just like numbers, like me). However, if you are not the MR-loving type, then maybe I can convince you of becoming one.

I think we all already know of the benefits of MR: it mitigates magic damage. Flat magic resist is often useful in the mid-lane because your opponent will typically be an AP carry (though AD champions are rising in popularity there, but that's another subject you can read about here). However, I am not going to be writing this article about why MR runes are good in and of themselves - rather, I will explain why they are better than they were in Season 2, which might encourage you to pick them up if you thought they weren't quite worth it before.


Magic Resist Runes Were Left Untouched


The first thing to note is that while magic resist and magic penetration stats were both nerfed across the board, magic resist runes are unique in that they were left untouched. This means that although the enemy AP laner now starts with only 8% + 7.83 magic penetration, which is less than the old 10% + 8.55, you can still start with the same 42 magic resist as before. The preseason patch also changed the way magic penetration is calculated as to make it more beneficial (percentage before flat), but because MR values in the early game are relatively low, this is not enough to compensate for the nerfs. So even if you start with the same MR as before, that MR has gotten relatively better than it used to be.

Let's use some numbers to illustrate: In Season 2, starting with 42 MR gave you an effective 30 MR against somebody with magic penetration marks and the 10% mastery (which was essentially every AP carry). In Season 3, starting with 42 MR will give you an effective 31 MR against somebody with the same setup. For now, this is just 1 bonus MR - not much, but it does show the glyphs are on their way to being better than they used to be before (and they were already pretty damned good). If you think that's disappointing, don't worry, as there is much more to it than that.


Sorcerer's Shoes Were Nerfed


Sorcerer's Shoes only grants 15 magic penetration now, as opposed to the old 20. This means that when you had only 12 effective MR in Season 2 after the enemy laner bought his tier 2 boots, you now have 16 effective MR instead. That bonus 1 MR has now increased to 4 MR, though this has more to do with magic penetration nerfs than the glyphs themselves. And there remains other and and even reasons you should consider the glyphs.


Scaling Ability Power Was Nerfed


Scaling ability power glyphs are the typical alternative for those of you who wish not to pick up magic resist (assuming you are also playing an AP champion). These glyphs are designed for maximizing lategame AP power - yet because of the nerf to Rabadon's Deathcap, scaling AP glyphs have also lost a bit of their strength, dropping ever slightly from 36.4 to 35 effective AP. Not a lot, but it adds up. And remember that this just shows how flat MR is stronger than it was in Season 2 - it would still be good even with no changes at all.


Consumables Are Insane


Finally, the main reason you should be using MR glyphs in Season 3 turns out to have very little to do with magic resist or even magic penetration changes, and everything to do with consumables. Season 3 introduced the Crystalline Flask and changes to movement speed, resulting in very sustain-oriented starts that go well beyond the traditional boots and 3 potions we saw in every Season 2 match. Consumables are essentially extra HP, which is further boosted by resistances.

In Season 2, a standard start offered you an extra 450 HP from health potions, which meant that with 42 MR, an opponent needed to do 554 damage to burn through all of your health (calculations not including Sorcerer's Shoes, as those would not be present on 1st buy). That was a bonus of 104 effective sustain from the consumables, granted by the MR.

In Season 3, although there is no "standard" start just yet, 1st buys tend to vary between Flask and 2 potions, or Flask and 3 potions (no more Flask + 5 potions after the nerf, unfortunately), along with other potential items/consumables. That's a bonus of 600 - 750 HP from consumables, which means that your opponents needs to do 742 - 927 damage to counter it after magic pen/resist calculations are considered. That's a bonus of 142 - 177 effective sustain thanks to the MR glyphs. If you start with 9 potions and 2 wards, you get a 1350 bonus HP from the pots and an extra 318 from the MR.


Conclusion


In short, with MR glyphs you will have:
  • 1 more MR than in S2 against a standard mid-laner
  • 4 more MR than in S2 against a standard mid-laner w/ Sorc Shoes
  • 38 - 214 more effective HP than in S2 based on consumables

And this is all on top of the extra mitigation that they already provide on your base HP. Simply put, get magic resist!

(If you want to see all of the numbers above in a spreadsheet, here you go).

Thursday, January 3, 2013

Bruisers & AP Carries in the Mid Lane

The Season 3 pre-season patch has brought a lot of changes that have shaken our conception of the metagame. One of these changes revolves around the middle lane. In Season 2, AP carries dominated the mid lane, in part because of their heavy reliance on levels and the safety of the short lane, but also because of the easy accessibility to the golem buff and the roaming capability that the lane's position offers.

In the current patch, AD assassins, and especially AD bruisers, have seen increased play in the mid lane. In this post, I will explore the reasons for this new trend, as well as whether we can expect AP carries to completely disappear from the lane, as some have been postulating in League of Legends forums.

The Mid Lane Matchup


AP carries are known for being fragile. In fact, their "squishiness" is one of the reasons they prefer the middle lane over any other lane - its short length offers more safety from ganks and chases. Their fragility is in part due to their base stats, but also because of their limited escape options. Bruisers, on the other hand, have the durability and mobility that lets them compete in the jungle or in harsh attrition lanes like top. They will almost always win trades with AP carries as long as they can get in melee range - not normally a problem thanks to gap-closers - and will have an easier time recovering after a trade.

In short, bruisers tend to dominate most AP carries in lane. Please note that I do say "most" and not all, as some mages such as Ryze or Syndra do have the kits to handle themselves against bruisers. However, in most cases, bruiser vs. AP carry matchups are fairly one-sided in the favor of bruisers. Let's look, in detail, at why this is the case.

Base Stats


Bruisers benefit from superior armor - both base and scaling - which makes them less susceptible to auto-attack poke, especially from AP carries, who have low base AD and typically do not start with any armor penetration. Furthermore, they enjoy scaling magic resist, allowing them to slowly become more resilient to magic damage even without purchasing items. They also have higher base and scaling hit points. All of these base stats are extremely important factors in the laning phase, and bruisers are the clear winners in this category.

Early Itemization


There are several great build options for bruisers looking to counter magic damage. For example, Null-Magic Mantle - a cheap, magic resist basic item - builds into Mercury Treads, Hexdrinker, Wit's End, and Guardian Angel, all of which are viable choices for bruiser champions. Hexdrinker in particular is very powerful against an AP lane, and builds into Maw of Malmortius. A bruiser who rushes Mercury Treads, Hexdrinker, and some HP item becomes very difficult to kill for any AP carry who doesn't have high sustained damage, at a fairly low cost.

On the other hand, AP carries have few early itemization options to help them lane against bruisers. Cloth Armor - the armor version of Null-Magic Mantle - does not build into anything AP carries actually want. Banner of Command is alone in providing AP and building out of Cloth Armor, but is designed for supports. Zhonya's Hourglass is the only good armor item AP carries will consider in most games - with the exception of Guardian Angel in some - but buying that initial Chain Vest is a moderate investment that doesn't provide any damage.

Catalyst of the Protector is a decent buy, though it delays the AP carry's damage, which may not be ideal vs. the early-game strength of a bruiser. Not every AP carry wants to build Rod of Ages, either.

Sorcerer's Shoes


I believe the existence of Sorcerer's Shoes in its current form contributes to the weakness of AP carries. Consider this: when an AD caster or bruiser wants to upgrade his tier 1 boots, he has many choices: Mercury Treads against an AP-heavy or CC-heavy team, Ninja Tabi against an AD/autoattack-heavy team, Boots of Mobility for roaming potential, and even Boots of Lucidity in some cases. There are no "core" boots on AD casters or bruisers - the only thing they lose by picking any of the above boot upgrades is the missed attack speed from Berserker's Greaves, but attack speed isn't typically that valuable of a stat to them anyway.

On the other hand, AP carries have a lot to lose by building anything that isn't Sorcerer's Shoes, because magic penetration is so strong that not having it is a noticeable loss in damage. When I play a bruiser, it feels good buying Mercury Treads to counter that AP champion I'm laning against. But when I play an AP carry, it feels awful having to buy Ninja Tabi to counter the AD champion in my lane. I think it would greatly benefit AP carries to offer early magic penetration somewhere else (unless Haunting Guise is enough), and change Sorcerer's Shoes to offer a stat that isn't quasi-indispensable.

Season 3 Changes


So far, everything I've said has been applicable to Season 2 as well as Season 3. Bruisers have always done well in lane against AP carries and have always had better counter-itemization options. So what has changed? Why are mid-lane bruisers suddenly so much more popular in S3?

Movement Speed


In Season 2, every champion in the game had a base movement speed between 300 and 330, and basic Boots granted an extra 50. Because movement speed is so strong, by the end of S2 every player except the support would start with Boots and three health potions. In the new patch, base movement speed was buffed across the board by 25, and Boots were nerfed by the same amount. This is important because it is a huge buff to weak early laners, who can now start with sustain items like the Crystalline Flask and wards to offset their difficult lane - even Nasus is seeing more play thanks to this change.

Crystalline Flask


This item makes lane sustain easy and cheap, and is the main reason the movement speed change was so significant to mid lane matchups. In S2, the best way an AP carry could handle a bruiser in lane was to abuse the bruiser's biggest weakness: melee range. This was done via heavy auto-attack harassing. In S3, this is a lot harder to do, if not impractical, because most melees will start with a Flask, one or two wards, and health potions.

Armor Penetration


Finally, S3 also revamped The Black Cleaver and reworked armor penetration mechanics (see my detailed post about armor penetration here). Armor penetration is now stronger than ever, and also more readily available. Consequently, bruisers and assassins are now less easily countered by armor and have the opportunity to scale into the late-game better than they ever could, which used to be one of their main weakness. This means that AP carries have lost the scaling advantage they used to bring over bruisers, and also means the necessity for magic damage has diminished.

Lategame Items


As Doublelift pointed out in this video, AP carries are inherently weaker than AD-based champions because they have cheaper late-game items. A six-item AP champion will have invested less gold into his build - and thus will have less stats - than a six-item AD champion. This is in part due to the Rabadon's Deathcap nerf, which hurt AP carry scaling and especially burst casters, who were already considered slightly weak in the S2 competitive scene.

Pros of AP Carries


Despite all that has been said, let's not undervalue AP carries. They still bring superior crowd-control over bruisers, and even with the waning strength of armor in S3, magic damage is still a nice addition to any team. AP carries are also typically ranged, which means they are less susceptible to poke and typically better at farming and poking. If you've ever played an ARAM, you know that getting an all-melee team with no poke can be an awful experience.

Nevertheless, it is no question that the value of bringing an AP carry has decreased in S3. Many teams are now happy to let the AP champions fill the support and jungler roles - this way they can still provide the utility and magic damage for which they are valued - and to let the AD champions take over the carry roles. A few specific champions, such as Anivia or Orianna, may survive this trend by merit of their incredible kits.

Conclusion


AP carries are noticeably weaker than they were in Season 2. "Utility" mages may still prove to be irreplaceable assets to competitive teams thanks to their sustained damage and exceptional utility, but there is now arguably no reason to pick burst mages such as Brand or Veigar - who were already unpopular in S2 and never picked in tournaments - over AD bruisers.

Bruisers have several advantages over AP carries in lane, among which are base stats and early itemization options. Furthermore, one of the main downsides of picking mid lane AD champions in S2 - poor scaling - is now greatly diminished in S3 with the changes to armor penetration.

Changes in the metagame are healthy and welcome. However, the decreasing popularity of AP carries is alarming. One of the main reasons AP carries were played mid was because they were, in most cases, already outclassed in other lanes. If they suddenly cannot perform in the safest, best-located lane in the game, what will become of them?

Sunday, December 23, 2012

Cleaving Through Armor Penetration

The combination of The Black Cleaver and Last Whisper is a hot topic right now, so I decided to put my calculator to work on some armor penetration calculations. In this post, I will discuss the two items' cost and gold efficiency, as well as their role in the diminishing value of armor.

Before I begin, however, I need to establish some of the fixed numbers and concepts I will be using. Each champion statistic in the game has a certain gold value, calculated based on the most efficient basic-tier item (or advanced-tier, if the former doesn't exist) that provides that stat. These gold values are the basis for evaluating item cost efficiency.

For example, the most efficient basic item that provides armor is the Chain Vest, which grants 40 armor for 720 gold. This means armor has a gold value of 720 / 40 = 18. In other words, 1 armor costs 18 gold. If an item grants more armor per gold than this, its efficiency is greater than 1. If it grants less, its efficiency is less than 1.

Here are the gold values of the stats we'll be using in this post:
  • 1 armor = 18g
  • 1 armor penetration = 12.59g
  • 1 attack damage = 34.44g
  • 1% cooldown reduction = 35g
  • 1 hit point = 2.5g
Source: VVinrar's Item Efficiency Spreadsheet

Now that this is established, let's talk items.

Last Whisper

Last Whisper grants 40 AD, 35% armor penetration, and costs 2135g. Out of that amount, 1378g is devoted to AD, and the remaining 757g is sunk into the passive. Whether the passive is worth the cost depends on the target's armor. Last Whisper needs to penetrate a little over 60 armor to become cost efficient. It takes a target with 172 armor for the item to penetrate that amount.

In other words, Last Whisper becomes worth the cost when your target has 172+ armor, and increases in value as your target's armor goes up. This isn't nearly as good as the old S2 Last Whisper, which offered more armor penetration and was the subject of much complaint.

With the old Last Whisper, you paid for a value of about 30 armor penetration and met its gold efficiency when your target had 74 armor. This was substantially better than the current iteration of the item, but it is offset a little by the way armor penetration is now calculated. That 74 armor requirement would have been calculated after flat penetration - so if you had 25 armor pen, you would have needed your target to have at least 99 armor before making Last Whisper a good buy. Riot Games intended to nerf Last Whisper because it was too strong, and they succeeded. But then they reworked the following item:



The Black Cleaver

This item costs 3000g and grants 250 HP, 50 AD, 10% CDR, 10 armor penetration, and an armor reduction passive up that stacks up to 25%. You get 2697g worth of stats alone without even counting the armor penetration, which means the remaining 303g pays for the flat armor penetration and unique passive. This item needs to penetrate a mere 24 armor to become cost efficient, but it already grants a flat 10 armor pen, which means the % armor pen only needs to penetrate 14 armor. This requires a target who has barely over 56 armor.

To sum up what we know so far: the old Last Whisper was worth its cost when the target had at least 74 armor after flat armor pen. The new Last Whisper is worth its cost when the target has at least 172 armor. The new Black Cleaver is worth the cost when the target has at least 56 armor.



The Last Cleaver

Let's put these two bad boys together in our inventory. This costs 5135g, 1060 of which is completely devoted to the armor penetration. But remember that the passive on The Black Cleaver is armor reduction, not penetration, which means that it is calculated before Last Whisper's penetration, thus essentially being added multiplicatively and reducing a small amount of Last Whisper's potential power.

But not enough, however, to make it any bad. In fact, you are still effectively getting 51.25% armor penetration at max stacks. With the 8% armor penetration mastery, you're up to a whole 55.15% arp, and that's before applying flat penetration. In Season 2, you could only get up as high as 46% armor penetration, which was calculated after flat.

With armor penetration marks and quintessences (19.2), armor penetration masteries (5 and 8%), and The Black Cleaver and Last Whisper, you deal true damage to anybody who has less than 76.3 armor.

At this point, I think it's safe to say that %-based penetration is far too easily available. On Last Whisper, you pay a little under 22g for each 1% of penetration. This is fairly low compared to most stats, and barely higher than the gold you pay for 1 point of armor (18). However, this isn't too bad and the value is lower than in S2. The real culprit here is The Black Cleaver, which barely makes you pay for its % penetration.

You'd think there was a catch. After all, percent-based penetration is wholly dependent on the armor of the target, so it might be a better idea to simply stack health instead of armor when your opponent builds Last Whisper and The Black Cleaver. Ideally, this would make them waste their gold on an unnecessary stat.

Yet, as demonstrated above, it doesn't take a lot of armor for their investment to become worthwhile. The moderate amount of 145 armor is enough to make the items worth purchasing together, even if their passives don't stack additively. Champion base armor at lv. 18 varies between 61 and 90, so enemy champions should have acquired some extra armor to make it worth buying both items. But as already mentioned, someone with The Last Cleaver does true damage to anyone below 77 armor if he has armor penetration runes anyway, so high base damage physical abilities may be enough to warrant buying the two items, even if no one on the enemy team has purchased any armor.

Furthermore, The Black Cleaver is loaded with stats. 250 HP, 50 AD, 10% CDR, and 10 armor pen are great stats to have against anyone, even if - especially if - your opponent is stacking health and leaving you with the minimum amount of armor to penetrate. Finally, you may not even need to purchase The Black Cleaver to benefit from its passive, as it is armor reduction and not penetration. If you're playing an AD carry, you could let the AD caster/bruiser on your team buy the item, while saving gold for another and still reaching that 55.15% armor penetration.



Tons of... armor?

Let's begin wrapping things up. I've gone over a lot of numbers, but what is the verdict? Is The Black Cleaver - and, to an extent, its combination with Last Whisper - good or bad for League of Legends?

There's probably more than a few reasons one could say it is bad. The first is that building armor against someone equipped with The Black Cleaver and Last Whisper feels counterproductive, as you are mostly just increasing the value of his armor penetration while the value of your armor remains static. You'll gain some survivability, but not at the same pace that your opponent is gaining damage, and over half of your armor is being penetrated.

Let's say you're a level 18 Amumu with no runes and masteries. You've bought a Sunfire Cape and a Frozen Heart, both of which are excellent items on him. That's 135 bonus armor, which, on top of your base 77.4, gives you a total of 212.4 armor. Now as shown above, the gold value of armor is 18, so 135 bonus armor has a value of 2430 gold.

But against any player – Caitlyn, for example – with a Last Whisper and The Black Cleaver (again, not counting runes and masteries), your effective armor is reduced to a little under 94, which means the two items have essentially provided Caitlyn with 119 armor penetration. The value for this is a whole 1498g.

This is very powerful. To explain, Amumu spent 5600g on two defensive armor items, 2430g of which is completely devoted to armor. On the other hand, Caitlyn spent 5135g on two offensive physical damage items, 1060g of which is completely devoted to armor penetration. Yet because Amumu invested so much gold in armor, he ended up multiplying the value of Caitlyn's armor penetration by a factor of 1.4, and she gained nearly 438g in armor pen thanks to the mummy. No wonder he's so sad.

Now we must ask ourselves this question: is that too much? Other items scale in similar ways, after all. Frozen Heart's aura becomes better and better as the enemy players gains more attack speed, and even benefits your team. But then again, The Black Cleaver also benefits your team by reducing your target's armor by 25%. Free scaling or power isn't necessarily bad, but it should be limited somehow - either through pure numbers or through some gameplay mechanic. For example, Frozen Heart may not always be desirable on champions who do not benefit from the mana, and Vayne's Silver Bolts ability is gated by attack speed.

One other problem that should be mentioned is the lack of flat armor penetration options. There are no items that provide it other than Youmuu's Ghostblade, The Black Cleaver, and Last Whisper. The latter two options both offer a hefty amount of %-based penetration, and The Black Cleaver actually offers both flat and % penetration. It may have been wiser for Riot to simply provide flat armor pen options and leave the work of piercing armor by a percentage to a single item.



Increasing returns

Armor penetration is an interesting stat to consider because it has increasing returns. The reason is that armor has diminishing returns. Every point of armor you acquire is less beneficial than the previous. The first 50 points of armor you have grants an extra 33.33% damage mitigation. The next 50 points bumps you up to 50% damage mitigation, though this was only a 16.67 % increase - half of the previous increase. The next 50 armor only grants 10% more mitigation. This is why armor stacking is less beneficial than buying both armor and hit points to increase your effective health.

It's also why armor penetration has diminishing returns. Let's say you are against a target with 150 armor. This gives him 60% physical damage mitigation. Your first 50 armor penetration will reduce him to 100 armor, or 50% physical damage mitigation. Your next 50 armor penetration will reduce him to 50 armor, or 33% damage mitigation. The more you have, the better it gets. It also means that champions who already have a source of free armor penetration (e.g. Darius, Wukong) benefit from additional armor pen even more. It also heavily benefits champions with high base physical damage or damage based on the target's HP.

Let's apply this to a Season 2 vs. Season 3 comparison. Your target has 150 armor (60% mitigation), and you have the 46% armor penetration from S2. This reduces him to 81 armor, or 44.76% mitigation. You've reduced his mitigation by a little over 15%. Now let's say you have the 55.15% armor penetration possible in S3 - 9.15% more than previously possible. This reduces your target to 67.272 armor, or 40% mitigation. That extra armor pen in S3 is more beneficial than any of the previous points of penetration, and the gap only increases because flat armor pen is now applied after % armor pen.



Conclusion

The Black Cleaver offers a lot of stats for its cost - probably too many. Last Whisper isn't necessarily too strong, but becomes a problem when combined with The Black Cleaver, granting a total of 55.15% armor penetration before applying any sort of flat penetration. It's a little strange that Riot Games allowed this to happen, as they sought to nerf the strong 46% penetration possible in S2, only to add % penetration on another item that, when combined, provides more total penetration than ever possible before. On top of this, armor is more expensive, armor penetration is calculated in a more beneficial way, and the extra armor pen is amplified by increasing returns.

Furthermore, actual flat armor penetration options are limited, though right now they would have to be overpowered to be desirable over The Black Cleaver, which provides everything a physical-damage dealer might ever want.

Armor is a noticeably weak defense against a Last Whisper + Black Cleaver combination: a champion with armor penetration marks, quintessences, and masteries can reduce a full 300 armor tank to a mere 100 armor with these two items (as opposed to 121 armor in the last patch - including the old Black Cleaver, which would never have been built (145 without it)).

Not only is armor penetration easier to acquire, but the stats that come with the main armor penetration item are also more desirable, making physical damage dealers considerably stronger.