TI4: Farm Dependency and the Nature of Carrying [Director’s Cut]

July 12, 2014

Aside from the usual archiving, I thought I’d jump on the early access bandwagon and take yesterday’s TI4: Farm Dependency and the Nature of Carrying out of beta, including using this system to analyze some day 4 games.

The 2014 International Group Stage has been, for lack of a better word, perplexing.  Team performances have been volatile, with former favorites looking on the verge of elimination and completely written-off underdogs in competition for the top spots.  It’s safe to say that year represents the least pronounced hierarchy in International history.

At the same time, the current 6.81 patch also represents the fuzziest period of hero balance in Dota 2, and perhaps these two facts are related.  While last years International had a good degree of strategic variance, it was ultimately dominated by 4-protect-1 strats with heavy support jungling (and Wisp/Io).  But changes in 6.79 put an end to that dominance, and now we’re left with a TI4 metagame that has been all over the place.

And this same lack of clearly established hierarchy is also apparent in the heroes themselves.  Surprising many, Razor and Skywrath Mage have emerged as the most picked heroes of the tournament with a pick despite having a negligible presence in the months of 6.81 prior to the tournament.  But for all the attention that they’ve received, neither hero has been dominant thus far.  At the end of the 2nd day, Razor and Skywrath have win rates of 47.6% and 45.5% respectively, which certainly aren’t unreasonably low win rates given such a small sample size, but they’re still a far cry from 2012 when Rubick put up 62.5% over 80 games and Morphling 57.1% over 77 games.

All Data provided by datDota.com and accurate as of July 10th for TI2014 and July 1st for 6.81

If that history is a bit too ancient for you, we could go back to last year where Chen put up 62.5% over 64 games and an entire list of heroes (Visage, Weaver, Lifestealer, Dark Seer, Bane, Gyrocopter, Naga Siren, and Puck) filled the top 15 picked list with ~55% win rates.  By comparison, so far only 4 of the top 15 picked heroes in the 2014 Group Stage (Enigma, Shadow Shaman, Doom, and Wraith King) have put up a +55% win rate, and all of those are support picks or generalist utility heroes that fit into a wide variety of lineups.  It’s certainly not a new sentiment, but 6.81 is the most wide open hero pool in Dota 2 history.

And as cool as that fact is, the downside is it can make it extremely difficult to figure out what’s going on with hero picks?  Why do some pairings work while others flounder?  Why is a particular hero’s performances so extremely mercurial?  Why is Mirana such a bad carry?  Well, what I’m going to try to accomplish here today is to provide you with a framework that explains the mechanics that govern hero interaction in Dota, and to begin that we need to start with the concept of Farm Dependency.

Farm Dependency and the definition of “Carry”

A while back I came up with an extremely simple statistical test.  I take a ton of high level pub games, and I measure the correlation between a particular hero’s rate of farm and whether they win the game.  With some outside help, I now have a slightly more advanced version that you can read about here, but the general principle is the same.

People will of course complain about correlation != causation, but I feel quite strongly that the correlation here is not spurious.  You can find all kind of stupid correlations if you just rub two random sets of numbers together,  but it’s clearly not the case that farm and winning are unrelated variables I just picked out of a hat.  Every time we open the gold graph in-game we do so under the assumption that gold advantages create wins, and when we encounter major come-from-behind victories,  we measure them by the size of the gold lead that was overcome.  From there it’s an incredibly small step to theorize that certain leads are more or less stable by virtue of the heroes on the right and wrong ends of the deficit.  Here’s an example of what I found from patch 6.80:

FarmDepTiersThe ratings are just a represenation of the strength of correlation and have no particular unit of measurement.

Don’t get caught up in the particular rankings, as there’s a good degree of fluidity from test to test.  Partly this is an issue of sample size, and partly this is just Dota’s wonderfully hazy ambiguity that you eventually come to love.  There are certain factors that I feel might systemically over and underrate certain heroes.  And on top of both of those points there is also the issue of differences between pub and competitive culture.  But aside those concerns, there is a specific consistency in the heroes that populate the tops of these lists: they always have some form of innate right click scaling.

In a pattern that is infinitely repeated throughout all of Dota’s mechanics, there’s a tension between the flat damage potential of nukes and the scaling damage potential of right click.  During the mid game, nuke damage is high relative to HP pools, but you have extremely limited means to amplify it through gold.  As the game progresses and heroes continue to level up, these Nukes have a reduced probability of determining team fights relative to right click pressure.  Unlike Nuke damage, there’s a plethora of itemization items that boost right click damage, and what’s more they do it in an exponential manner because each new right-click stat stick amplifies the effects of the items you already have.  Carries are carries because they have some kind of ability that essentially acts like a free right-click item that gives them a headstart in the race.  The crit on heroes like Juggernaut, Wraith King, and Chaos Knight is like a free mini-Crystalys, Phantom Lancer’s Juxtapose is like a perpetual Manta Style machine, and Anti-Mage’s Mana Burn is like an innate Diffusal Blade, minus the active of course.

Aggressive right click damage also tends to trump defensive builds in the long run, and it’s easy to see why that is.

First, defensive itemization is, likely intentionally, not very optimized.  Most of your big armor items aren’t exclusively personal survivability items, but also come budgeted with a lot of additional utility, such as Assault Cuirass, Shiva’s Guard, Armlet, and Mekansm.  And Vanguard is very explicitly designed not to scale very well into the late game.

Second, long games tend to revolve around 5v5s.  A team that just invested a bunch of defensive items into say a Centaur Warrunner or Necrolyte will just find that the opposing team’s carry can outrace them in eliminating the other 4 members, leaving them isolated and helpless.  This is why when it comes to building defensively as a team, value pickups like Mekansm, Force Staff, and Ghost Scepter tend to be far more important than just big stacks of HP and Armor.

For an actual example of this effect at the International, you can look at the first game of the play-in match between MVP Phoenix and Team Liquid.  MVP Phoenix actually had a sizable gold lead early, but they spent most of it on survivability and utility items like the Mek, Blink, and Shiva’s on Doom, the Vanguard, Pipe, Blademail, and Heart on Bristleback, and the Skadi and Blink on Slark.  In a vacuum none of these are bad choices, particularly the Slark items, but MVP had a true tri-core team with relatively low scaling carries in Bristleback and Slark.  MVP desperately needed one of their three carries to build around personal aggression, probably either the Doom or Bristle, and both an Assault Cuirass and Vlad’s would have potentially been valuable given the three melee carries and for reducing the physical damage of Death Prophet’s ultimate through the armor auras.

For yet another example, try Na`Vi vs Titan.  Once again you have a lineup with a pair of low scaling carries in Viper and Bristleback, and they’re facing a sort of enrage timer in the Radiance Naga.  Na`Vi has a pretty sizable gold advantage as much as thirty minutes in, but that gold advantage is tied up in two Hearts, a Pipe, and an Aghanim’s for Viper.  Again, none of these are indefensible choices in isolation, but in the context of the match conditions, Na`Vi’s lack of some source of straight damage left them incapable of closing the game.

Finally, I’d just like to add that I hate the term “Hard Carry.”  The use of this term tends to revolve around discussions about a scenario involving a 6-slotted 1v1 that is so exceedingly rare as to be virtually non-existent.  There is, of course, a ton of variation within carries, but it’s far more nuanced than we give it credit for.

Furthermore, there’s something implicitly desirable in the standard conception of the hard carry, when extreme farm dependence is just as much a curse as it is a blessing.  Anti-Mage is in some ways the archetype of extreme farm dependence, but the dark side is that if an Anti-Mage player fails to crack 4 creep kills a minute by the end of pub game, they have something like a 25% win rate, which basically comes out to this massive bulge of risk that only Shadow Fiend even remotely approaches in degree.

And when we talk about hard carries, we often fail to distinguish between heroes like Anti-Mage that desperately need to consume more CS than anyone at all stages of the game to stay relevant from heroes that simply want the game to go late.  One potentially interesting example of this is LGD’s use of Spectre in LGD vs Fnatic.  Instead of trying to build a defensive pocket around Spectre, LGD drafts incredibly greedy with Doom, Razor, and Batrider.  The goal here is to create so much noise that Spectre will have the breathing room to find farm in the midgame.  Perhaps it only worked as a response to a Tinker lineup, but it demonstrates how thinking of Spectre as a “hard carry” might limit you conceptually when it comes to thinking about the types of lineups she might work in.

Scaling of a Different Sort: The Semi-Carry

“Semi-Carry” is an incredibly broad term that encompasses a wide array of heroes that probably have no business being grouped together, but I have no better terminology so here we go.  At it’s most basic, it illustrates the face that there exist plenty of heroes that are not carries, that is they do not have meaningful right click scaling, but still warrant a farming role.  Like I emphasized earlier, Dota is built around a tension between inert lumps of raw power and stronger yet speculative promises of limitless future potential.  Scaling doesn’t always win, because sometimes that inert lump robs you of your future.  What we’re seeing at TI4 is that the changes that nerfed the dominance of the defensive trilane has opened the door for strategies built primarily around semi-carries to take an increased role in the meta.

One recent example, though not from the International, was Alliance’s Aghs-Refresher Silencer at DreamLeagueSilencer does have a form of right click scaling in his Glaives, but it’s one that has never proven to be potent enough to run with the actual carries.  Maybe that’s changed some since his Agi buff, but regardless, Aghs->Refresher is not a carry build.  Instead, it invests a ton of gold into putting this big lump of global damage and silence into play.  If Silencer successfully gets to that point (which can be more difficult said then done) and you can’t survive through the brutal teamfights, then it doesn’t matter how much scaling his team has given up by investing in him instead of an actual carry.

Another, less investment intensive example is Necrolyte.  Let me answer a million stupid pug arguments by saying that Necrolyte is definitively not a carry, and yet the most successful pub hero in 6.81 still deserves a farming role.  For an illustration from TI of how this works, we have Necrolyte’s only appearance of the tournament as a safelane farmer in EG vs Fnatic.  EG recognizes that a Necrolyte/Dragon Knight/Tidehunter is not a monster late-game trio, but they have no intention of letting this go late.  Necrolyte’s Death Pulse both makes for incredibly sustained pushes, with Dragon Knight’s ult and Eidolons providing the bulk of the tower damage, and also amplifies an already monstrously bulky team given Dragon Knight and Tidehunter’s defensive passives, Enigma’s early Mek, and Abaddon for shielding and additional Mist Coil healing.  Oh, and you’ll be teamfighting into Black Hole and Ravage.  Necrolyte is, at best, a situational pickup, but he works perfectly here as the centerpiece for a low investment, extremely tanky push comp.

I alluded 6.79’s demise of the 4-protect-1 dominance earlier, and the biggest beneficiary of this shift is the high-investment semi-carry, or at least, high-investment semi-carries not named Storm Spirit.  And I begrudgingly have to admit that this shift has made Tinker a significantly more viable option.  I disagree with the people who consider him overpowered, he’s still extremely vulnerable to early disruption and any spectacular game can immediately be followed by disaster, but he does pretty well provided you can manage to  slip him into a draft without him getting banned or countered.

Ironically, my favorite Tinker draft of TI2014 so far comes from Team Liquid.  It’s ironic because my least favorite Tinker draft of 2013 was also Team Liquid.  But then again, if you had told me before the tournament that the most productive roaming support duo was going to be Bulba and waytosexy, I would have just assumed you had arrived in Seattle early and needed to kill some time.  In summary, Team Liquid is a land of many contrasts.

Anyway, the challenge to a Tinker draft is three-fold.  One, he needs to have space created where he can farm to get online.  Two, he needs a team around him that can accomplish things without him for long stretches at a time.  Three, that team needs to do this in a low farm environment while March of the Machines gobbles up entire lanes.  Good Tinker players will be mindful to try to not starve their team too much, but you’ll still be eating table scraps.

In Liquid vs Newbee, Liquid runs a well-tailored draft around all of these pressures.  Tinker’s complementary cores are Ursa and Brewmaster, both extremely low maintenance heroes both in terms of lane protection and farm needed.  This allows Liquid’s Wraith King and Skywrath duo to spend more of the early game running interference for Tinker at mid.  Meanwhile, Wraith King and Ursa put Ursa into play extremely early, which again, buys time for Tinker.  Finally, Liquid’s draft is perfect for dragging out fights with Reincarnate and Primal Split.  This gives Tinker ample time to teleport in and set up multiple Rearm combos.  It’s the kind of conceptually sound draft that you can’t just put together by looking up hero synergies on Dotabuff.

Two heroes that you might have found conspicuously missing from my earlier carry list are Ember Spirit and Naga Siren, so let me take some time to address them.

[Portrait]NagaNaga Siren never shows up very high on my farm dependency lists.  Perhaps this is because she gets played as support a lot; I can’t reliably differentiate between support Naga Siren and disastrous carry Naga Siren from an endgame stat sheet.  What I find though is that Naga Siren is relatively inefficient at turning massive amounts of farm into wins.  She shares this feature with Tinker and Nature’s Prophet, two other heroes who have the potential to farm in such a way that they starve the rest of their team out of gold.  So maybe the system underrates poor Naga because of the careless people playing here.

But I’m increasingly of the opinion that Naga Siren operates differently from the traditional carry.  Phantom Lancer in his prime also never scored that high in terms of farm dependency and people found this outrageous, but in a lot of cases, Phantom Lancer wins games through avoiding fights and creating tower attrition.  It’s quite possible that as a strategy this is much less farm dependent than winning a 5v5 and more of a Boolean check on whether the opposing team has the proper tools and disposition to exterminate rats.  My theory is that, in a vacuum, core Naga functions under a similar dynamic.  In the Na`Vi vs Titan game I mentioned earlier, Viper and Bristleback simply did not have the tools to deal with Naga in the lategame and they didn’t push early enough to avoid having to deal with the late-game.

But Naga isn’t especially popular right now, so let’s talk about Ember Spirit.

[Portrait]EmberEmber Spirit is the poster boy for not-a-carry acceptance, because being successful with the hero is absolutely dependent upon realizing that he should not be played as a carry.  Carries, as I’ve defined it, are heroes that have some form of innate right click scaling.  Ember Spirit only has Sleight of Fist, and Sleight operates extremely differently.  For starters, it provides no tower pushing or Roshan, which is a liability for any team foolishly running Ember Spirit as their only ‘carry.’

Possibly more importantly, consider what Sleight of Fist is.  It’s an incredibly ranged AoE attack on an eventual 6 second cooldown.  That cooldown is important because on of the things that right click damage scales with is attack speed, and not only does Sleight not benefit from attack speed at all, it also effectively sets Ember to only having one attack every 5 seconds, plus whatever other autoattacks you can weave between if the situation allows.  In terms of late-game damage potential, Sleight is garbage compared to any actual carry’s right click.

And this is fine because Sleight of Fist is a red herring and Ember’s real value lies in his crazy mid-game dives and damage.  Pair him with a standard carry in your safe lane and your team composition no longer cares about Ember’s weaknesses.

[Portrait]PugnaBut another interesting option that has made an appearance at TI4 is to simply force the enemy into a base siege at the height of Ember’s power curve, and this relies on another semi-carry in the form of Pugna.  One of the weaknesses of most semi-carries relative to standard carries is the lack of objective control.  Tinker, for example, is often seen as a pusher, but his actual building damage is anemic at best.  Pugna, however, is a little wrecking ball whose push lineups are perfect for forcing teams to make the decision between 5v5ing on your terms or not having a Barracks.

iG vs EG is a great example of this kind of Pugna push comp designed to force you into a very painful teamfight.  Pugna’s building assault creates an early push opportunity.  If you attempt to passively defend you’re dealing with the siege potential of Sleight of Fist and Elder Titan’s Astral Spirit.  If you charge, you face Doom and his ult Doom and the combo of Searing Chains into Skywrath’s Mystic Flare, all while in the range of Pugna’s ward and Elder Titan’s Natural Order.  It’s a brutal setup, and if it seems familiar it’s because DK ran the same Ember/Pugna/Elder Titan trio in the finals at StarSeries.  Good on iG for taking notes.

Shaping the Space Between “Carry” and “Support”

Since Semi-carry is a huge and impossibly vague label, I’d like to propose a few poorly-named sub-categories to make it easier to think about what’s going on.

Hard Semi-Carries: These heroes behave very similarly to standard carries, just with a greater emphasis on momentum over gold.  Examples: Ember Spirit, Tinker, Naga Siren, arguably Outworld Devourer and Storm Spirit

High Investment Utility Semi-Carries: These heroes don’t need as much momentum to fill their role, but they do require favorable laning conditions.  Examples: Pugna, Necrolyte, Silencer, Invoker, Kunkka.  Queen of Pain and Zeus might be halfway between this category and Hard Semi-Carries.  Puck might be halfway between this and the next category of…

Low Investment Utility Semi-Carries: These heroes neither need momentum nor a favorable lane.  A big part of their value is how capable they are of thriving anywhere.  Examples: Brewmaster, Dark Seer, Clockwerk, Batrider, Bounty Hunter, Tidehunter, Elder Titan, Centaur Warrunner, Nyx Assassin when run as a core.

Pseudo-Carry Semi-Carries: These guys look a lot like carries in that they tend to emphasize right clicks, but they either have weak or very situational scaling.  They make up for this by providing other valuable, and perform best in multi-core lineups.  You could alternatively think of them as Low Investment Utility Carries.  Examples: Nature’s Prophet, Mirana, Razor, Bristleback

Applying the Theory to Analyzing Actual Matches

The basic rule of thumb is that there is an investment hierarchy in hero roles.  At the top of the hierarchy are the Hard Semi-Carries and the most farm dependent Carries.  Below them are the mid to high farm dependent Carries, then the High Investment Utility Semi-Carries and the Pseudo-Carries, then the Low Investment Utility Semi-Carries, and finally the supports.

When laning, teams will tend to give their safest and most lucrative lanes to heroes at the top of the hierarchy, and conversely, opposing teams will more often lane aggressively with aggressive trilanes or duo mids or gank heavily against heroes at the top of the hierarchy.  When it comes to a team’s preferred win condition/ideal window of opportunity, heroes at the top of the hierarchy will exert the most influence.

So let’s apply this all to some day 4 matches

Arrow vs Empire

Arrow: Meepo, Axe, Mirana, Sand King, Dazzle

Empire: Lycan, Dragon Knight, Batrider, Vengeful Spirit, Bane

The lone Meepo game of the tournament, Arrow runs a variant of the 4-protect-1 around the hero.  Empire goes with a 2-core lineup with a heavy emphasis on pushing, and Batrider along as the primary initiator.  Arrow’s primary goals in the laning stage is to use an aggressive trilane built around Axe to jam Lycan’s progression long enough for Meepo to find the level advantage needed to suffocate Empire.  Empire wants to avoid fighting Axe head-on, and instead pressure Meepo in mid, hopefully getting kills that will both delay Meepo’s level progression and let Dragon Knight start pushing towers to buy Lycan the space to recover from Axe.

The precise details of these games are sketchy at best for me as I was trying to watch all four at once, but from what I recall, Empire was more successful ganking Meepo than Axe was at killing Lycan.  Dragon Knight and Lycan quickly pulled ahead in net worth off of that, and Arrow had little to no chance to stage a comeback without Meepo having a huge level advantage.

One possible variant for this game would be for Arrow to shift Meepo over to the safe lane to make him less vulnerable to support rotations, but the downside to this is a 1v1 vs Batrider.  Rock and a hard place, really.

Newbee vs Na`Vi

Newbee: Faceless Void, Timbersaw, Batrider, Shadow Shaman, Ancient Apparition

Na`Vi: Ember Spirit, Razor, Tidehunter, Enigma, Vengeful Spirit

Na`Vi with the Ember Spirit-Razor combo desperately needs to end the game early.  Newbee has scaling on their side, with the caveat that Newbee is basically all-in on Chronosphere.  Void’s scaling outside of Chronosphere isn’t amazing, and Timbersaw and Ancient Apparition are largely included for the wombo-combo potential with Chrono.

Na`Vi, having learned from their struggles winning with Ember earlier in the year, go all-out push largely through Eidolons and Vengeance Aura, with Black Hole and Ravage there to tilt the inevitable tower teamfights in their favor.  Newbee puts up a fight, but their Chronosphere coordination is off, and Na`Vi successfully takes their first set of barracks at around the 20 minute mark.  Things collapse for Newbee from there.  Good example of Na`Vi understanding quite well the expiration date on their team comp.

Alliance vs Na`Vi

Alliance: Storm Spirit, Naga Siren, Batrider, Skywrath Mage, Rubick

Na`Vi: Shadow Fiend, Razor, Tidehunter, Enigma, Vengeful Spirit

What we have here is two extremely different push strats colliding.  Na`Vi goes for an almost identical lineup to their previous game, only replacing Ember Spirit with Shadow Fiend.  They again want to push early as five and force Alliance to fight into their teamfight.  Alliance, on the other hand, wants to avoid any kind of a straight-up fight entirely.  Naga will use Radiance split push, provided she can pick one up in time, and Storm Spirit can use his mobility to keep lanes pushed out, slowly chipping away at towers while frustrating Na`Vi’s push attempts.  Meanwhile, it’s a very lonely game for Alliance’s supports.

Alliance puts Loda in mid on Naga while putting S4’s Storm Spirit in the safe lane.  This reflects that they want to guarantee that Storm Spirit has a strong early game because he can buy time for Naga to farm the rest of her Radiance, whereas she might not be able to control the midgame if Storm Spirit gets shut down.

Alliance succeeds in getting both on a timely Radiance and avoiding too much direct conflict.  Razor spends what must be the most frustrating game of his life trying to maintain a Static Link in the face of three Force Staffs.  It’s exceedingly appropriate that this ends in a base race.

DK vs EG

DK: Ursa, Nature’s Prophet, Brewmaster, Juggernaut, Lion

EG: Tinker, Faceless Void, Beastmaster, Mirana, Bane

Tinker warps every game around him.  Knowing from the start of the draft that they’d be facing Tinker, DK goes for a very low investment early game oriented tricore built loosely around  Ursa.  Prophet’s Treants allow them to 5-man push early, with Brewmaster’s ultimate providing the teamfight support.  Juggernaut is picked so that Healing Ward can help maintain pushes and help mitigate Missile spam.  Rather than invest heavily in ganking the Tinker, they hope to force him to respond to their pushes so often that he can’t create the farm separation he needs to take over the game.

EG has some laning aggression in the Bane/Mirana support combo, but there is a concern that their teamfight has many forms of ultimate based CC without a lot of damage to take advantage of it.  EG also has Beastmaster for Tinker airdrops, but like so much else in this comp it is absolutely dependent on Tinker finding the farm to become a threat.

Long story short, Tinker for a variety of reasons ends up struggling to find farm, and things collapse for EG.

This game is an example of one easy-to-make mistake in the TI4 meta:  devoting too much of your draft to utility without the damage to take advantage of said utility.  Another example of this is [b]the pairing of Brewmaster and Batrider[/b].  Both heroes are initiation specialists thanks to their ults, but put them together you have too much initiation (and not especially complementary initiation) and no one available to take advantage of it.  In all of 6.81, Batrider has a 53.4% win rate and Brewmaster is at 49.2%.  Combined, they’re 32.1%, including an 1-3 showing at the International so far.

And finally a bit about supports!

This is a very core focused article, because cores usually exert more pressure on team with supports often being complementary to your cores.  There are exceptions like Wisp, but in general your support picks do not define your team.  But one interesting wrinkle is that some supports are actual carries that were buffed to such a high base potential that they’re capable of functioning in both roles, and even capable of transitioning between them midgame.

The “classic” example of this is Alchemist.  People realized that Unstable Concoction was extremely good, and suddenly, support Alchemist became a thing.  But one extra benefit to this is that Alchemist still had right click scaling, and a unique sort of scaling in the form of Greevil’s Greed.  The downside to running Alchemist as a carry is that he would often find so much farm that he would 6-slot extremely early in the game and then run out of progression.  In the farm dependency graphs mentioned in the PDF I linked earlier, Alchemist was unique in that he looked like a typical carry until the 45 minute mark, at which point he would fall off relative to other carries.  But from a support position, Greed offers Alchemist the potential to catch-up in farm during passive midgames and essentially become a 4th core.

And following in this tradition we have Wraith King.  Over the past year he saw large buffs to both his ultimate, giving hima much stronger slow upon its activation, and his Lifesteal Aura which now works for ranged heroes.  Combined with his stun, he now provides enough utility to be viable as a support.

At the same time, he still has all the features that made him a capable, if not spectacular carry.  He didn’t work at all in a 4-protect-1 framework, but as a support that can farm abandoned lanes with relative impunity thanks to Reincarnate and teleport reactions, Wraith King gives you the potential to do all those support duties while also offering you an extra Mjollnir or an Assault Cuirass carrier for any game that goes late.

Faceless Void in this tournament is a similar story.  Void has received, among other things, baseline buffs to the availability of Chronosphere and Time Walk.  These changes allow him to function in the offlane role, whereas before he would have never found the farm there that he would need to be relevant at a lower baseline level of power.

These examples also touch upon an idea that Kupon3ss calls Dynamic Farm Allocation.  During the laning phase, Faceless Void and Wraith King can fill the 3 and 4 roles well enough, but by having them on your team, you have the option to shift their farm priority up as the laning phase ends.  This might provide you a bigger bang for your buck than say, getting another item for your Razor or Clockwerk.

The Symphony of Yin and Yang

Team synergy in high level Dota revolves around eternally searching for a perfect balance between two forces.  Between the scaling potential of a carry and the strong early and mid game that ensures that you will be able to secure that potential.  Between the reliable but predictable power of right clicks and the overwhelming yet elusive potential of a carry-less lineup.  Between the initiator and the one who capitalizes on the initiation.  A good draft finds a complementary balance between the forces, and a good team has enough draft concepts available so that the opposing drafter cannot anticipate and eliminate your source of balance (by, say, finally realizing you should just immediately ban Nature’s Prophet and Io every single game).

The art of drafting is in some ways similar to musical composition.  First you learn your scales, and come to perceive the basic chord patterns that follow from the understanding of the scale.  Like 4-protect-1, slight variations of I-IV-V can make for you a relatively successful career, at least for a while.

Eventually you feel a force compelling you to push beyond your basic fundamentals, whether it be integrity, market forces, or a new set of patch notes.  You find new things that break your old rules by integrating different modes, or a sus chord that shouldn’t ‘belong’ in a song but yet works.  You find that in the multitude of permutations between notes, your old ruleset was adept at finding good-sounding combinations, but it was leaving you deaf to an untold number of beautiful progressions simply because they failed to conform to your beliefs of how music was supposed to work.

So you seek a more expansive logic, because there still is am underlying logic there that in some way resembles your limited initial understanding.  And armed with this logic you are now capable of compositions that you never would have imagined possible.

The source of the drive for musical evolution may be unknown to us, but in Dota it is much more simple.  To be able to create a working draft out of the unknown gives you a competitive edge.  This edge won’t last forever, as teams can and will copy you or simply ban a particular hero out, but like support Naga last year, that evolutionary edge can be enough to win you a tournament like the International.


1v1 Top 8 and Matchup Chart

June 23, 2014

I spent a couple days last week trying to replicate DotaMax’s VH match list under the new sans-date_max regime, and the good news is that their results appear legitimate.  I was able to create a list of VH (and even High) games that exhibited a proper match duration distribution.  The bad news is that I did it the day after 1v1 matchmaking was released, so I have to filter through yet another set of unwanted match types.  But 1v1 is a unique environment where certain aspects of standard games happen in complete isolation.  Even if you’re disinterested in the mode, it might be worth a look to see if it can tell us anything about standard 5v5 play.

The Radiant Advantage Continues

In previous samples that I’ve looked at, Radiant has always had the net advantage, and that trend continues here.


The two most likely drivers for Radiant advantage in 1v1 are the midlane topography and camera perspective.  It’s important to keep in mind that this is likely only part of the puzzle, as there’s no time frame for 1v1 that enjoys a huge +55% advantage like the Radiant does in 20-30 minute games in 5v5.  In this case, the slow shift towards a Dire advantage as we reach 20 minutes probably indicates that if a Radiant player hasn’t already capitalized on their advantage by that point then it’s slightly more likely that the Dire player is in the stronger position.  I can’t imagine that there is anything comparable to Roshan that would provide the Dire a ‘late’ game advantage.

On a related note, Radiant vs Dire has been a hot topic as of recent, and I’ll have a bit more to say on it in a couple days over at liquiddota.com, so keep an eye out for it.

Shadow Fiend is Pretty Popular

It’s not much of a surprise, but Shadow Fiend tops the usage list with 14.36% of the players in the sample using that hero.  In general, 1v1 is a pretty top heavy mode when it comes to hero usage.  The top 3 most played heroes (Shadow Fiend, Invoker, and Pudge) combine to make up 26.36% of the heroes picked; the top 10 (the three from before and add Viper, Sniper, Queen of Pain, Windrunner, Puck, Templar Assassin, and Skywrath Mage) make up 47.70%.  Given that hero usage drops off so rapidly, I’ve decided to focus primarily on the top 25 most-used heroes, as they’re the most likely to have a statistically significant number of matches recorded.


So with the top 25 established, I decided to put a little thing together.  It’s only a proof of concept because the sample size is lacking, but maybe you’ll find it interesting:


And based off it, I bring you…

The Top 8 Heroes of Day 1 VH 1v1


#1: Broodmother

Finally, after years of struggling, Broodmother has a mode to shine in.  She’s put in the top win rate so far at 71% , and it’s no wonder why as she has positive matchups across the board, including absolutely brutal matchup advantages over Invoker and Pudge.  The spider queen only has one negative matchup in the entire list, a 44% against Death Prophet, and even that is mitigated by the fact that I only have nine Broodmother vs Death Prophet matches on record.  Queen of Pain is another tight matchup, and Shadow Shaman, Shadow Fiend, and Kunkka all put up decent fights.

#2: Bane

Coming in at 2nd with a win rate just short of 69%, Bane is the first of the two caster specialists with no real push power in the top 8.  Bane’s big call to fame is having the best recorded matchup against Shadow Fiend, which is nice when he happens to be the most likely matchup you’ll run into.  Bane generally does best against right-click specialists, I assume largely due to Enfeeble, but Templar Assassin and Outworld Destroyer put up tough fights.  Where Bane struggles (or at least dominates less consistently) is against top end pushers.  Broodmother wrecks him, and both Shadow Shaman and Death Prophet are near even (Pugna, for whatever reason, struggles).  Invoker is also a very even matchup, perhaps in part because Forge Spirits bypasses Enfeeble?

#3: Templar Assassin

Templar Assassin has positive matchups almost across the board.  Bane is slightly negative at 46%, and besides that, her three bad matchups are all heroes with ways to strip away her Refraction charges, Broodmother, Viper, and Venomancer.  She also has the best overall win rate against the popularity trinity of Shadow Fiend, Invoker, and Pudge.

#4: Shadow Shaman

Shadow Shaman is the first of the top 8 push specialist trinity.  He’s one of the most consistent hero in the top 8, in that he has no dramatically bad matchups but less dominant matchups than the top 3.  Broodmother and Templar Assassin are the worst, but both are just above 40%.  Shadow Shaman’s best matchup is surprisingly Outworld Devourer.  OD is supposed to dominate 1v1s vs Intelligence heroes, but so far he is struggling against every Int hero in the top 8.

#5: Death Prophet

Pretty similar to Shadow Shaman, but her one downside is she’s only a 50/50 matchup against Shadow Fiend, Invoker, and Pudge.

#6: Viper

Viper is a peculiar case.  Once you move past the dominating duo of Broodmother and Bane he does pretty well, but he doesn’t dominate the bottom half of the 25 most common nearly as consistently as the rest of the top 8.  Outworld Devourer is an even matchup, along with Tinker and Silencer, and of the three only OD has one other matchup against the top 8 that’s better than 40%.  Viper also struggles against Phantom Assassin and Pugna.

#7: Pugna

Of the push specialist trinity, Pugna is the most feast or famine.  One interesting tidbit about the trinity is that they have a bit of a rock-paper-scissors thing going on.  Pugna has a slight advantage against Death Prophet,  Death Prophet has a slight advantage against Shadow Shaman, and Shadow Shaman has a slight advantage against Pugna.  But none of these heroes are extremely popular, so this could all just be noise.

#8: Skywrath Mage

Skywrath is the hero I’m most surprised to see in the top 8, but he does pretty well against most of the 25 and has one of the top win rates against Shadow Fiend and Pudge.  Unfortunately for him, all of his matches against the top 8 are 50:50 for worse, and his win rates against Broodmother, Bane, and Templar Assassin are dreadful.

Other Dark Horses and the Complete Stats

I’m sure some of you are interested in heroes that didn’t make the top 25, so here is the complete stat dump.

1v1CompleteStatsSome lesser played heroes to keep an eye out for

Brewmaster: Narrowly missed the top 25, and has a respectable 58.75% win rate.

Jakiro, Witch Doctor, Warlock, Disruptor: Still small sample sizes, but all 4 supports are putting up +60% win rate so far.

Earth Spirit, Leshrac, Night Stalker, Legion Commander, Enigma: 57-59%, but small samples

Lone Druid, Lina, Lich, Tusk: ~55%

And worst 1v1 hero goes to Spectre, with both the fewest games played in the sample and the worst win rate at 17.5%.

Random Ability Draft: Hero Win Rates

June 11, 2014

As a bit of a curiosity and side project, I put together the hero win rates in Random Ability Draft from my last 6.80 sample back in January.  It may be a bit outdated, but the base hero values didn’t change drastically in 6.81, and the stats come from the period before Divided We Stand’s reign of terror.  While I don’t have much interest in the mode myself, it’s an interesting look into how the basic stat values contribute to a hero’s viability independent of their abilities.

The special caveats here:

  • My RAD match collection is a byproduct of my actual match samples.  As a result it’s fairly small at just under 20,000 games total.  Mitigating this, because the hero selection is randomized, all hero samples are around 2,200 games.
  • The matches are separated into Normal, High, and Very High.  I do not know if they actually correspond to anything.  My best guess is that RAD unranked MMR but then becomes separate.  In any case, I averaged the Win % across all three brackets in an attempt to mitigate sample size issues.
  • I tried to revert the 6.81 changes in my stat charts, but I might have missed some.
  • There might be other errors.  This was new, hectic, and I’m not extremely invested in it.

Oh, and if you’re prone to getting angry about being assigned “bad” heroes in the mode, you might want to look away.


And that’s well and good, but the more interesting question is what makes a hero a good or bad platform in RAD?  Silencer far and away at the top is a relatively easy outlier due to his intelligence steal, but beyond that it gets more complicated.  One intriguing fact you might pick out by the hero shading is that Intelligence heroes tend to do the best overall in RAD.  In terms of average win rates, Intelligence heroes come in at 51.33% with Strength at 49.49% and Agility at 49.01%.

But that’s not good enough because we want to break things down by individual stats.  To approach this, I imported the hero attributes table from dota2wiki, and found the average win rate for the top, middle, and bottom third percentile of each stat group.  Or some Excel facsimile of that.  It’s at least a relatively consistent division for above and below average.  I wouldn’t rely on it for precision, but it gives us a general idea of how influential each stat appears to be on the overall win rate.  And here’s the results:


So for stats, Intelligence actually appears to be the most valuable stat in both base and scaling, but Strength Scaling is close.  This likely explains a good portion of why Intelligence heroes do best overall in the mode.  Having good overall base stats and stat growth are arguably the two strongest predictors for a strong RAD hero.  Movespeed and Base Armor are the next two strongest predictors, and ranged heroes as a whole tend to outperform melee heroes.  What’s somewhat surprising is that short cast points provided no noticeable advantage whatsoever.

But don’t take my word for it.  I made a (rather huge) graphic that includes a percentile ranking for each stat for every hero.  For example, the movespeed for all heroes fall between a minimum of 280 and max of 330.  Heroes with 280 are treated as 0%, 330 is treated as 100%, and 305 is treated as 50%.  Extreme stat outliers are kept separate.  For example, I treat the range in average level 1 avergae autoattack damage is 44 to 69.  But Treant Protector’s damage is 85, which gets treated as 174% so he doesn’t warp the listing for everyone else.  It’s also available in spreadsheet format so you can download your own copy for sorting.


6.81 Hero Stats, kinda

May 29, 2014

With my former method for interacting with the API increasingly appearing to be permanently disabled, there’s not a lot left for me to do.  But people still want to know what’s going on in the new patch, so I’ve taken a look at DotaMax, a Chinese site that claims to have hero stats with skill bracket information.

I say “claims,” because I have no way of personally vouching for the quality of their data.  I have a suspicion as to how they get it, and if my suspicion is correct there are likely gaps in their match records.  These gaps might be innocuous, or they might actually warp the results.  They definitely appear to have less total matches on record than Dotabuff.  In my 7 day test, Dotamax only had 88% the match volume of Dotabuff.  6.80 looks even worse, with Pudge for example having only 55% the Dotabuff numbers.

The better news is that the numbers themselves tend to conform to my expectations from other sources.  This doesn’t prove that they’re good, but they’re at least not obviously bad.  So far.

One last caveat.  This was an experimental project done over the course of a couple days.  I used DotaMax’s Last 7 days setting for the 6.81 numbers, but because this wasn’t done all at once there may be discrepancies.  These should usually be small, but if a hero’s win rate changes between sections, it’s because of this.

Normal/High/Very High Match Distribution

According to the DotaMax numbers, it was 75% Normal, 15% High, 10% Very High.  This is a larger Very High section than usual, which could represent matchmaking maturing over time, but as I mentioned, DotaMax appears to have an incomplete set of games.  If my suspicion from earlier is correct, it’s a lot more likely for them to drop Normal and High matches, which would artificially compress the distribution some.

As a reminder, it’s theorized that public approximations have Normal as being somewhere around < 3000 MMR and Very High being > 4000.

Ranked vs Unranked Match Distribution

People have speculated that the N/H/V distribution is significantly different for ranked matches only, and DotaMax appears to agree with them.  In only ranked matches the distribution I found 51/26/23.  ~57% of VH matches in the Dotamax results take place in ranked compared to 18% in Normal and 26% overall.  These trends represented by these results are likely factual even if the particular numbers might be warped by unevenly distributed dropped matches.

VH Top 25 by Win Rate


Hero Shifts by Skill Level


No surprises, but a couple things to point out.

First, Terrorblade and Phoenix took their hits in the patch, but they’re both looking competitive in higher skill games, especially Phoenix.

Lycan is another hero whose 6.81 nerf might have been exaggerated by his predominantly low skill performances in Dotabuff.

The people saying Earth Spirit would be competitive in Captain’s Mode might have a point.  Despite having the worst overall public win rate in Dota 2 history, he’s consistently putting up the strongest VH trend since 6.78 Wisp.  It’s true that at 42.61% Earth Spirit still doesn’t have the greatest of VH win rates, but neither does Shadow Demon and SD sees plenty of competitive play (though perhaps a bit more than he ought to).  And if you look exclusively at VH Ranked games, Earth Spirit’s win rate goes all the way up to 45.30%, albeit with a small sample of just under 10k games.

Necrolyte (technically -phos but whatever) has the latest case of Spirit Breaker syndrome.  Necro still isn’t getting much competitive attention, but pubs are mostly ignoring him too so he might be able to evade nerfs for a bit longer.

I won’t trust Legion Commander‘s results until I have proof that people have stopped skipping Overwhelming Odds to max Moment of Courage.

Hero Popularity: China Versus the World

One interesting feature of this site is that it also provides results exclusive to the Chinese servers.  This gives us a glimpse into the shifts in hero popularity between China and the rest of the Dota 2 servers.  The end result is pretty large, so I’m just going to thumbnail them.

<-Very High | Normal ->


Lower level Chinese pubs appear to be much more conscientious towards team composition than their predominantly Western counterparts.  The top 10 less-played heroes on the Chinese side starts with Pudge and then goes entirely pub-carry with Drow Ranger, Phantom Assassin, Riki, Ursa, Sniper, Faceless Void, Bloodseeker, Meepo, and Troll Warlord.

In both brackets, Chinese players show a big affinity towards Axe, Earthshaker, Slark, Doom, Skeleton King and Kunkka.

Bloodseeker and Viper are surprisingly popular in VH pubs.

Besides Earthshaker, Ancient Apparition appears to be the support of choice.

Invoker is present in 56.76% VH games.

Concluding Remarks

As a reminder, I can’t completely vouch for these results.  They look believable, but that doesn’t preclude them from being warped in some subtle way.  Do with them what you will.

On a final note, I had to mess around with a Chinese translator to navigate the site and came across a hero translation I’ve never seen before.  I guess in the Chinese backstory he’s a disgruntled Counter-strike grognard.


[TI4Quals-CN]Brewmaster: Drinks Are on You (link)

May 23, 2014

In the continuing series of the hot heroes of the International Qualifiers we have a look into Brewmaster’s meteoric surge in popularity along with his struggle to produce results.

Previous Entries in this series:

[TI4Quals-SEA]Treant Protector: Into Forest Shade

[TI4Quals-Americas]Mirana: A Wild Mirana Appears


Also there’s our TI4 Qualifier Hero Comparison Chart, which will be updated tonight with the playoff results from the China Qualifier.

TI Qualifiers: Hero Usage by Region[Link]

May 21, 2014

Curious about how hero preferences differ between regions?  Well, I took the Pick/Ban stats for each of the TI4 Qualifiers and compared them the overall hero stats of 6.81 before the Qualifiers began.  Come marvel at Americas love for Shadow Demon and Fiend or SEA’s complete and utter refusal to sync up with anyone.

Available Here: http://www.liquiddota.com/forum/dota-2-general/3335-ti4-quals-by-the-numbers

Encyclopedia Pudge and the Case of the Strangely Surging Win Rate

May 13, 2014

As you might recall, last week I published a thing on the hero win rate shifts of 6.81.  At the time, I said that the biggest mystery of the patch is Pudge’s win rate increase.  Well, that mystery has not abated over the past week, so I want to take some time to examine the potential suspects and see how their alibis stack up.

The Scene of the Crime, as it were

The Scene of the Crime, as it were

First the facts.  At the time of this draft, Pudge has exhibited the largest win rate boost on Dotabuff in the 6.81 patch period at 3.94%.  This is odd because the usual culprit for shifts this large are official balance changes, and Pudge received none.  He also, as far as I can tell, received no direct or indirect buffs bugfixes that would have driven an improvement of this magnitude, and I can find no reported bugs in 6.81 that Pudge would benefit from.  Of course, just because I cannot find them doesn’t mean that they’re not there, but at this point it’s safe to say that on this front I have no leads.

For now, let’s assume that Pudge’s recent success has nothing to do with a mechanical power boost and examine some alternative explanations.

Theory 1: Pudge is being played by better players in 6.81

The typical explanation goes like this.  There are a lot of bad Pudge players.  These Pudge players get distracted by new shiny things in the patch, so they play heroes other than Pudge.  Pudge’s win rate goes up accordingly.

There’s some support for the idea that popularity trends can influence win rates.  The most clear and consistent example is how every new hero introduced to the game has had huge day 1 usage rates that quickly fall off, and as they fall off the hero’s win rate always creeps upwards.  Some of this win rate improvement, especially for newer and more complicated heroes like Earth and Ember Spirit, is players just learning how the hero works.  Still, even with more basic heroes there tends to be a tourist effect.  It’s not even much of a surprise; people who pick a hero because they like them tend to outperform people picking the same hero out of a sense of novelty.

The problem then is that there’s no real evidence that this effect makes much of a splash in the opposite direction, and even if there were, there’s no reason to believe it would effect Pudge dramatically more than every other hero in the game.  And on top of that, Pudge’s use rate didn’t even decline post-patch.  It actually hit a month high 39.24% last Thursday up from his usual 35-36%.

Verdict: Implausible

Theory 2: Pudge is taking advantage of trendy strats like Aghs-rush Lich and KotL

This theory we can actually test.  Using the Dotabuff Pudge matchup page we can find out how often he plays against different heroes during different patch periods and his win percentage in each head-to-head matchup.  Has Pudge fed off of a sudden surge of sloppy play?


In terms of usage rates, 6.81 did not shake things up dramatically.  More important to the theory is that the heroes Pudge is facing more often in 6.81 aren’t exactly favorable matchups.  Only Invoker, Keeper, and Phantom Assassin are better than average matchups both pre- and post-patch.  Not by much in the case of Invoker and Keeper who are 42 and 45 respectively out of 106 in 6.81.  Phantom Assassin was Pudge’s 11th best matchup in 6.80, but her6.81 buffs have improved her to 33rd.  On the other end of things Wraith King was tied for Pudge’s worst matchup in 6.80, though things have improved for Pudge such that it’s now 104 out of 106.  Ursa and Lich are also amongst Pudge’s top 10 worst matchups.

It’s also worth pointing out that this group is, if anything, outperforming Pudge’s overall win rate shift of 3.94%, thanks in a large part to buffs to Huskar, Faceless Void, Phantom Assassin, and Silencer.

Verdict: Implausible

Theory 3: Pudge is benefiting from a favorable meta-game shift, and his win rate comes from a handful of advantageous matchups

This explanation gets trotted out to explain any otherwise inexplicable win rate shift, and while it sometimes is valid for competitive play, things are rarely that responsive in pub Dota.  Competitive Dota is a highly self-aware system where teams work to respond to specific matchup threats and any seemingly successful strategy will get integrated at-large as a counterpick option.  By contrast, picks (and lane assignments) in pub Dota are essentially random dice rolls weighted by the innate popularity of the heroes in question.  As a result, the influence of the metagame on pub win rates tends to be rather weak.

To demonstrate this, let’s use a thought experiment.  Invoker is Pudge’s most commonly seen foe in 6.81 Dota, so let’s simplify things and just say he shows up in 1/5 of all Pudge games pre and post patch.  In 6.80 Pudge’s win rate vs. Invoker is the same as his overall win rate at 48%.  In 6.81 his win rate jumps four percentage points to 52%, but this increase is solely because of a favorable development in the Pudge vs Invoker matchup.  As a result, his win rate in the 4/5 of games without Invoker stays at 48%.  What would Pudge’s 6.81 win rate against Invoker have to be to make this possible?

The answer.

So yeah, you’ll basically never see a win rate shift this large determined by a single match-up, at least in pub play.  At a tournament like TI3 you can see a single hero like Outworld Devourer sunk entirely by counterpicks like Razor, but that was an incredibly small environment where teams had a very specific gameplan involving these two heroes.  Pub play is a bit under a million games a day being played players that, on average, either have no concept of a Dota metagame or have an incredibly wrong one.

But perhaps there’s a broader explanation at work here.  A cluster of heroes that are working in concert to lose to Pudge.  Well, if there is, I’m sure not seeing them.

Using the Dotabuff matchup page again, I compiled the win rate shift in every individual matchup against Pudge between the two patch periods.  60 out of 106 of the heroes fell within a +/- of .75 from Pudge’s overall win rate shift of 3.94.  Of the 46 that did not, the vast majority were heroes that had their own win rate shifts thanks to buffs and nerfs they received in the patch, with their Pudge shift being a rough summation of the individual win rate shifts.  In short, Pudge’s newfound win rate appears to be distributed relatively evenly among the entire cast.  I can’t completely rule out that there isn’t something more complex going on, but it’s definitely not a simple question of 1v1 matchups.

Verdict: Very Unlikely

Theory 4: With recommended items changed in the patch, Pudge players are now spending their money more effectively.

This…actually might have some merit.  Maybe.  I can’t actually determine if Pudge’s recommended items did change with the patch, as I can’t find a reliable source on what his recommended items were pre-patch.  What I can say is that there has been some interesting item trends going on with the hero.  Two in particularly actually.


I’m skeptical that the Force Staff -> Blink Dagger is the big driver here.  From what I can tell using (Last Month – 6.81) to get an estimate of late 6.80, this trend towards Blink Dagger has been a gradual once ever since Pudge received the ability to use Blink Dagger in 6.79.  If Blink Dagger was the source of Pudge’s win rate, we would expect his win rate increase to have also been gradual and not suddenly surge on patch day.

The Boots shift is much more likely to be due to recommended items.  My estimate of (Last Month – 6.81) puts Phase Boots at a ~29% usage rate, which fits the profile for a precipitous dropoff in 6.81.  Tranquil Boots is also definitely a part of Pudge’s current core items.  It’s also worth mentioning that Pudge has a lower win rate with Phase Boots despite Tranquils being much cheaper, so there’s a case to be made that reduced Phase Boots usage should actually increase his overall win rate.  The question though is whether this boot choice alone could drive a 4% win rate shift.

Verdict: Plausible, but possibly only a partial explanation

And that’s the case as it stands.  It could be that Pudge stands out as the somewhat surprising biggest winner of the 6.81 recommended item changes, but I’m skeptical that this is the entire story.  As I’ve pointed out, Pudge’s win rate increase in the patch was the largest of any hero, and a boot switch doesn’t seem like it would be enough regardless of the fact that Phase Boots are Pudge’s least successful Boot upgrade.

So we still have an open mystery on our hands.  In the meantime, strongly consider skipping the Phase Boots when trying to get that Pudge compendium win.