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
Now that this is established, let's talk items.
Last Whisper
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
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
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?
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.
I read your whole article and I have to say it's very well presented. I think a problem does exist with BC and your article really does illustrate the issue with solid maths and forms a compelling argument.
ReplyDeleteI only have a problem with your "increasing returns" section. I think you may be approaching that section from the wrong angle. Every point in armour increases your effective HP by 1% of your total hp, this doesn't change whether you have 0 armour to begin with or 2000 armour. This means that armour scales with your HP but otherwise adds a set amount, hence flat armour pen reduces by a set amount.
effective HP = total_HP + total_HP*((armour*armour_mod - flat_pen)/100)
where armour_mod = 1 - percentage_pen
I'm fairly certain the above equation is true until you reach negative armour, but anyway the point is that percentage penetration attacks a multiplier in the effective HP equation which makes percentage pen highly destructive. I find this an easier way to look at it rather than looking at the percentage of damage blocked.
As someone who plays tanks a lot, what this really changes is when I switch from building armour to building flat hp. There has always been a point where building HP increases effective HP more than building armour. With the increase to percentage penetration and weaker armour items, that switching point where HP is more attractive comes earlier.
However, I can see how Riot tried to balance BC, the old one actually shred more armour. 45 flat pen is only outdone by the new BC when the target has 140 armour or more [yeah, I know, almost everyone manages to get that much armour and I've not counted the mastery, just BC alone]. The issue as I see it is that the new BC is just loaded with useful stats. I think the itemization problem would be better solved through additional penetration items rather than a few massive ones. For contrast, magic penetration can be accomplished through 5 very different items whereas armour pen is covered in three [not counting brutalizer and haunting guise as they upgrade]
If you actually look at it right now, the new Black Cleaver is actually weaker than the old one until a target has 194+ Armor. Otherwise, the 45 shred on the original is actually stronger than the current 25% on the new Black Cleaver.
ReplyDeleteWhile it may have more desirable stats for champions that rarely saw play (Pantheon, Talon, etc) that was the entire point of changing the item; to make the AD Caster sub-type actually playable instead of completely abandoned on the side of the road.