October 06, 2017

The Impact and Abuse of Stats

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This is the first in a short series of theorycrafting blogs I'm going to be doing. It's a subject that's been on the back of my mind for a fair while now, and since we're only (or still) a couple of weeks out from the much-anticipated 7.07, it seems pertinent to do this now
and then
link it to
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Why do this now? Well, a lot of what I'm going to bring up can be easily addressed and my points illustrated in terms of what we're expecting to see in 7.07. I'm going to break down the discussion into a few key points and try to keep this structured, rather than ramble on as I am wont to do.

Warning.

Maths.

Foreword 1: 7.07 predictions, and "leaks"



As with any leaks, take these with a really hefty grain of salt. A while ago on 4Chan (lul), there was apparently a "Valve insider" who leaked some of the changes that would occur in 7.07. It's a high chance these are completely false, but they do look really cool. What I want to focus on now is the proposed talents changes, which would take them from levels 10, 15, 20, and 25 to 9, 13, 17, 21, and 25, thereby giving each hero a fifth row of talents.

I'm going to come back to this later in reference to an upcoming point, so keep this potential leak in the back of your mind. For what it's worth, I really do hope this leak is true, because it'll be hugely impactful and open up a vast, vast amount of possibilities regarding hero strengths, weaknesses, power spikes, and scaling.

Foreword 2: Differentiating types of carries



The term "hard carry" has somewhat fallen out of vogue as the position one role has become less dominant in the lategame. Ever since 6.84, we've seen gold being redistributed more evenly across a team - supports are no longer dirt poor, offlaners are no longer sacrificial lambs, and the mid has shifted from a ganker and roaming role to a secondary (or in some cases, the primary) core. Dual core lineups have been popular since TI3 or even before, but these days it's extremely common to have two farm-dependent scaling cores.

"Hard carry" used to be your #1, who would vacuum up the farm on the map and scale into the lategame extremely well due to a massive gold advantage. Heroes like Anti-Mage, Phantom Lancer and Medusa were hugely popular in the role. However, since the gold has been redistributed, supports especially can now afford the tools to kite and slow down these hard carries enough to bring them down. This directly led to the rise of farming mids like Shadow Fiend, Storm Spirit and Sniper, who would be played alongside a more traditional #1. Obviously, I'm simplifying this quite a bit for the sake of clarity, but one statement stands true - in order to solo carry the lategame, you need to be very rich, and your opponent needs to be very poor. Supports can now afford things like Glimmer Cape and Lotus Orb to save allies from an attacking hard carry, or prevent themselves from getting instantly annihilated.

This has blurred the line between carry and hard carry. It's no longer about sheer scaling, since that's far less relevant in a world where 1v5s simply aren't feasible to execute even if you're 15k gold ahead of the enemy cores. What's it about, then?

Uselessness early-game? Not really. Slark isn't particularly effective early on, and I don't think anyone would consider him a hard carry. Likewise with Invoker. Early-game weakness, combined with incredible lategame scaling? Again, as mentioned above, due to gold distribution that just means you've got a carry with a weak laning phase.

The hard carry role these days is best defined by the lategame, when they are most relevant. And not necessarily in teamfights, although that is of course a factor. So to try and define a hard carry, let's look at the main topic of this article; hero scaling.

The Nuts and Bolts of Scaling



Scaling is a term that simply refers to how good a hero is later in the game. A hero that scales well will remain relevant well past 50 minutes; one that does not scale well, or 'drops off' peaks well before then, and fades off compared to other heroes.

So what constitutes and determines how well a hero scales?

I did a post a short while back with the endgame, fully slotted stats of most of the carries in the game. Now, while that post is all well and good in a vacuum, it's a bit misleading in a lot of cases; not everyone had the same net worth, and some item builds weren't standard - you wouldn't really get Manta Style on Arc Warden in a real game. Maybe maybe MAYBE as an 8th slot if you were really desperate. It's just way too hard to utilise on that hero for the little payoff. I'll come back to Arc in a later section, so he's another hero to remember for the moment. Regardless, that post can be used to illustrate how scaling works and how it functions lategame.

Multiplication is king in terms of scaling. Let's say you have two hypothetical effects - one gives +100 damage, and the other one gives 100% more damage. If you take a Dota hero, they might only have 50 damage in the early game, so +100 damage is much more impactful. But as the game goes on, heroes crack 200, 300, even 400 damage... so 100% more damage will result in a much larger net gain.

That's scaling at its absolute most basic form. Addition and multiplication to find out what gives the biggest numbers. Now, if you go through that post and thread to find all the stats, you'll notice something interesting.

Most heroes end up with comparable DPS, HP and armour with a balanced endgame item build. A fully kitted up Agility carry can expect to hover around 3k Health, 25-30 armour, and 2-3k DPS. This can seem especially strange when you compare heroes like Phantom Lancer and Clinkz. PL has 160% more damage from illusions, right? He's historically been one of the most dreaded lategame heroes. Clinkz gets +90 damage per hit from his Searing Arrows, and a burst of attack speed from Strafe plus whatever Death Pact gives him. That's additive. Multiplicative is king, right?

Well, the reason why heroes tend to have fairly comparable stats is because scaling in Dota 2 is very carefully balanced and capped. We can meme OSFrog all we like, but at the end of the day, Icefrog is damn good at his job and we're privileged to have him working on the game. Item stat bonuses such as that from Heart of Tarrasque are additive (and are thus applied before multiplication - another reason multiplicative effects are so powerful). Additive and multiplicative effects are balanced so as such that yes, in the lategame multiplicative effects come out on top, but it's not an insurmountable difference. This makes it impossible to brute-force combat based on hero picks alone.

So from this section we've concluded that multiplication scales better than addition. Multiplicative health and armour sources don't exist in the game, so we've just got damage to go on. Multiplicative damage steroids include:
  • Illusions - they deal a percentage of the main hero's base damage.
  • Critical strikes - their critical chance and critical strike multiplier work together to increase the hero's total damage by a percentage. Works on illusions, so if you want to scare the **** out of someone in a pub buy Daedalus on Terrorblade.
  • Base attack time improvements - due to the way attack speed is calculated in Dota, improved BAT will increase your attack rate by a percentage. This works out to a total DPS increase.
  • Clone effects. This means Divided We Stand and Tempest Double.
However, the game is tightly balanced so that multiplication does not ever outstrip addition by an insurmountable level. This is why Clinkz can go heads on with Phantom Lancer, at least in terms of numbers.

Stat Gain



This is one of the most misleading and misunderstood aspects of a hero's scaling. Good stat gain is touted as super-important to your hero, whereas in reality you either have to have greatly exceptional or greatly awful stat gain for it to be noticeable at all.

To illustrate this point, I'm going to look at Agility carries because those are the most common kind of carries you get. Point for point, Agility is the most impactful of all stats, but that's a subject for another article. The average Agility gain for Agility carries is 2.52, which is right at the level Medusa is at. She's actually a really good example for this, because she doesn't have the potential to abuse stats.

By 'abuse stats', I mean multiply the amount of stats you get via illusions or clones. Medusa doesn't do either of this - if you get Manta Style on her before your 5th or 6th slot, I don't know what to say, but you're really not playing the hero right.

Medusa's base Agility is 20, and she gains 2.5 per level, for a total of 80 at level 25. A common buff/nerf Icefrog performs is increasing or decreasing Agility gain by between 0.3 and 0.5 - it's happened to Sniper, Juggernaut, Spectre and Phantom Lancer as nerfs, and Morphling, Mirana, Clinkz and Luna as buffs. So let's up Medusa's Agility gain from 2.5 to 3.0 and see where that takes us.

It nets us an extra 12 Agility at level 25. That's 12 damage, 12 attack speed, and a touch under 2 armour. When you consider that carries are closing in on 300 damage and 25 armour by that point, it's not really a big deal, is it? You've got an extra 4% damage. More noticeable is the 12% reduction to incoming physical damage, but even that isn't going to be as valuable as a solid boost to your Health on most heroes.

Ok, but what if a hero can abuse stats? I had a similar discussion to this with Cuki, who is in the top 50 Arc Warden players in the world, where (after I'd absorbed as much knowledge as I could) we threw around ideas for buffs that would make Arc competitively viable. He said that a buff to Arc's Agility gain would break the hero; I wasn't so sure.

Currently, Arc Warden sits at a very below-average Agility gain of 1.8. If we apply Icefrog's usual buff of 0.3-0.5 (let's say 0.4 for simplicity's sake), that brings his gain up to 2.2. His level 25 Agility goes from 58.2 to 67.8. If we round those numbers off, we get 58 and 68. That's a much more noticeable increase because Arc's Agility is so low, but it's still only 10. With Arc attacking about three times a second in the lategame, you get an extra 30 DPS from that.

But he has Tempest Double, right? That thread you linked earlier with DPS calculations, you mentioned that it was a flat unconditional 100% more damage, right?

30 dps doubled is still not a lot on a hero that already cracks 3000 relatively effortlessly. It's 2%. Like I said, more impactful is the armour from a stats gain, but 1.5 armour and 60 DPS won't catapult Arc Warden to first-ban territory.

Relating to the Styles of Carries



So clearly, simple stats aren't going to show the differences between carries and hard carries. Have the roles just blended together?

Well, arguably, to some extent, they have. However, I believe that what defines a hard carry in the modern era isn't their stats, but their impact on the lategame. A hard carry will warp the lategame around them, fundamentally changing how it is played, on top of being a beast in scaling. Let's look at Arc Warden. It's almost impossible to siege high ground against him, he's one of the best splitpushers in the game, he offers double the utility of items like Bloodthorn and Scythe of Vyse, and he offers completely risk-free ganking through the use of the Tempest Double and a Silver Edge. Enemies playing against Arc have to constantly respond to his pushes without splitting up, or they risk getting slaughtered before their team can react. This becomes a mind game where the Arc player can control where the enemy team is at any one time, letting his own team take advantage of that.

Similar aspects are echoed in Morphling, who trades Arc's highground defence and item abuse for being almost impossible to kill even if caught out. Morphling retains similar splitpush and ganking capabilities.

Naga Siren and Terrorblade. Very much two sides of the same coin, with Naga being more defensive and Terrorblade being more offensive. Both are phenomenal split-pushers that bring a lot to teamfights, either in the form of Song of the Siren or Reflection. Naga Siren can drag games on indefinitely, whereas Terrorblade can end them in the blink of an eye if given the opportunity.

I'd also add Spectre and Chaos Knight to the list, and perhaps Faceless Void - though I'd say that one is based on how much your team can take advantage of Chronosphere and how impactful Time Walk's heal and Time Dilation's freeze are against the enemy team.

Scaling via Talents



This should hopefully be the last part of this rather long and wordy assignment. I mentioned at the very beginning the prospect of a new row of talents being added. Hopefully, from reading later sections, you've gotten an idea for how murky the distinction between 'carry' and 'hard carry' can be, and how it's mostly based on abilities rather than stats.

That's where talents come in. Uniquely in Dota, talents modify both stats and abilities, leaving a lot of options open for scaling a hero. A common criticism of a lot of talents is that they're very bland on a lot of heroes, providing mere boosts to damage, health, or stats as opposed to more objectively interesting ability changes.

An interesting avenue of balancing appears from this, one Icefrog does not seem interested in taking, but one that seems pertinent to discuss nonetheless. Hard carries are such because their abilities are so impactful on the lategame, yet they also maintain impressive scaling that's often at the very top end of statistics - again, refer back to the stats threat I linked earlier. If a hard carry as we understand them requires both of these prerequisites to be fulfilled, this means talents can be used to direct a hero in a certain direction. If the leak about a fifth talent row was true, we may well could be seeing something akin to this appear. Hard carries tend to have abilities that are complete on their own, and often a talent modification to that ability simply isn't better than piling on more stats. An example of this is Spectre's level 25 talent row, where +400 health is almost universally taken over the cooldown reduction of Spectral Dagger.

Should a fifth row of talents be added, we will likely see hard carries strip way ahead in terms of numerical scaling as their new talents are merely stat boosts. Recent design tends to lean towards spell modifications being focused on for talents - the removal and replacement of respawn reduction talents is a prime example. Whereas Shadow Fiend might get a talent that improves his Presence of the Dark Lord or maybe adds innate healing to Requiem of Souls, what talents could you assign to Terrorblade that alter his spells in interesting ways? Improving Conjure Image begins to open a scaling divide, and it's highly unlikely any talent affecting Reflection will ever be considered a viable alternative to a chunky stats boost. Similar phenomena occur in other hard carries - no matter how cool-looking Morphling's level 25 talents are, were one to be replaced with the standard +15 all stats, you'd go the stats every time. It might also work in reverse - take a function from an ability, relegate it to a talent in place of a stats boost, and suddenly your carry hero is a lot worse off than they were before.

Conclusion



I feel I got somewhat off of my original topic, but it was all loosely related in the end. Scaling in Dota 2 is a fairly complex aspect of the game that has had new layers of depth added with talents while still remaining close to its core concepts. Indeed, talents are the most impactful way to play with a hero's scaling - though, Icefrog's subtle touch and keen intuition leads him towards the more restrained alteration of attribute gain.

I ended up conglomerating two topics into one, addressing both scaling and the functions of different carries, so hopefully the next article I do will be more focused in its scope. I hope you found this topic as interesting to read about as I did to write about.