Who is the Most Farm Dependent Hero?

November 28, 2012

People will often ask “What hero is the strongest with max farm?” and it’s really a pretty pointless question. I don’t have hard statistics on this, but I’d guess less than 1% of games end with even just one person on the team maxing out their inventory. If you just like to ponder silly hypotheticals then knock yourself out, but if you’re trying to learn about Dota there are more practical ways to go about it.

“Who is the strongest carry?” is a little better, but it’s also impossible to answer. Even if we simplify it to ask “Who is stronger, Clinkz or Antimage?” Well, it’s definitely Clinkz if he has a 10-minute Orchid and can concentrate exclusively on making Antimage’s farming life a living hell. Conversely, it’s likely Antimage, provided he get to 30-40 minutes with some strong items, including a Manta Style to nullify Clinkz’ Orchid. So then we have to ask which scenario is more probable…but probable given what? There are 8 other heroes in the game. That makes for a lot of possible team comps, some of which will be favorable to Antimage and others will be favorable to Clinkz. If we’re most concerned with the highest levels of play, we probably only care about Clinkz’ ideal comps vs Antimage’s, but even that is a mess of finding the ideal teams, then finding possible counters to those teams, then counters to those, then eventually tying up the whole thing in some kind of probability map. And even if you pull it off you’ve only compared two carries. To each other. In a vacuum. With ~40 more carries waiting to be addressed.

In short, it’s not a question worth tackling head-on.

I want to approach the question a different way. Forget talking about “best” or “strongest,” I want to instead simply find out which heroes need farm, and which heroes do not.

This is my first attempt.

The idea is that I take a hero and make a list of all their games, ordered by how much CS/min they achieved in the game. I divide the list into 5 equal sections. I calculate the win rate of each section, and then measure how much their win rate increased in the upper sections and decreased in the lower sections. Farm dependent heroes should see their win rate correlate highly with their CS/min. Farm independent heroes should see little correlation at all.

It’s still very much an alpha project. I’m not satisfied with the methodology yet, but the bigger issue is that the sample size I have is not sufficient for every hero. This can be addressed eventually, but in the meanwhile it makes it difficult to judge which methodology is more accurate.

For those who don’t want to traverse the spreadsheet, here’s a summary of the overall rankings:

1 Anti-Mage
2 Luna
3 Faceless Void
4 Drow Ranger
5 Lycanthrope
6 Lone Druid
7 Huskar
8 Outworld Destroyer
9 Phantom Assassin
10 Clinkz
11 Weaver
12 Morphling
13 Bloodseeker
14 Lifestealer
15 Shadow Fiend
16 Storm Spirit
17 Riki
18 Skeleton King
19 Sniper
20 Templar Assassin
21 Juggernaut
22 Ursa
23 Bounty Hunter
24 Viper
25 Chaos Knight

Some other well-known carries barely missed the cut. Dragon Knight and Spectre came in at 26 and 27 respectively.

At the bottom end of things we have

80 Sand King
81 Dark Seer
82 Nyx Assassin
83 Treant Protector
84 Ogre Magi
85 Clockwerk
86 Wisp
87 Shadow Demon
88 Rubick
89 Earthshaker
90 Keeper of the Light

Now for analysis

Most of the top end entries aren’t too surprising, but there are a few curious placement quirks.

Anti-mage, Luna, and Faceless Void as the top 3 might be correct, but it might also reflect that these three have a pretty high potential of being able to farm once the game is already won.

–Speaking of Anti-mage, this is a 6.74 sample. I expect he would drop significantly if this were repeated in 6.76c. Base hero performance in the bracket matters, perhaps more than it should. Alchemist performs poorly in this sample, and should see a much higher placement with the post 6.74 buffs. This probably also plays into why Outworld Destroyer shows a higher farm importance in Normal than he does in the other brackets, as it’s much easier for him to simply out-carry the other team at lower levels of play.

–I expect Lycan to drop even harder than Anti-mage post 6.74.

Huskar scores a lot higher than I feel most people would expect. He’s often painted as a ganker, but I have to wonder if he’s not optimally played as a full-on hard carry.

Bloodseeker seems like a less pronounced version of Huskar, but with much emphasis on “less pronounced.” Bloodseeker’s farm importance falls off hard in the Very High bracket, which I think offers the most accurate picture.

Clinkz being as high as he is isn’t surprising in the least. In the Normal bracket he’s only the 51st most prolific farmer, which is part of why he does so poorly in general matchmaking win%. I see Clinkz as the most extreme case of the time sensitive hard carry, in that his farm at 15 minutes in is way more important than his farm at 50 minutes in. Weaver at one spot lower probably functions similarly.

–Int characters are an interesting study
Outworld Destroyer is clearly the most definite Int Carry in the game.
Storm Spirit is fairly close. This makes sense because of his unique ability to turn excess mana regen into both damage and survivability.
Nature’s Prophet works as a carry in Normal, but falls off hard in High and Very High. In Very High he has the 2nd highest average CS/min, but only the 48th highest farm sensitivity. That pretty much says everything you need to know about Nature’s Profit.
Invoker and QoP stay reasonably high, but they’re beginning to push my definition of carry.
Necrolyte, in my opinion, is not a carry. He’s 68th in the Very High sample. GPM just doesn’t appear to be a priority for him (and for me, dependence on GPM is the most important aspect of a carry. If you want to call Necro a semi-carry, fine, but that’s a very different archetype.)
Silencer appears to me to have a better case for carry-dom, but his farm dependence scores are even a bit lower. Granted, this could reflect player attitudes toward Silencer as much as it does anything about Silencer’s kit.
Tinker also doesn’t see a farm dependence, though it’s possible what’s happening here is that a Boots of Travel-wearing, March of the Machines-spamming Tinker player can actually harm their team if they’re not careful by taking farming opportunities away from the actual carries. Keeper of the Light has a similar issue, and it’s not terrible surprising that he’s far and away the least farm dependent hero in all three samples, despite having the (I cannot believe this. Literally. Did I screw up the programming?) 10th highest CS Average in the Normal bracket.

–Moving on, I’m skeptical about Slardar’s carry potential. I think he makes more sense as an initiator/carry buffer, a la Magnus (who is not in this sample unfortunately). Kinda wonder if he can hang as a suicide solo. This would help him fit into lineups with a hard carry much easier, and might make him an interesting 3rd slot pickup for teams.

–Besides hard supports, initiators score really low on farm dependence, especially junglers. This makes sense because it’s really hard to shut down Dark Seer and Enigma’s farm, but neither of them get much out of farm once you have the basics like Soul Ring/Blink/BKB on Enigma. Earthshaker, Treant Protector, Tidehunter, Sand King, Enchantress, and Omniknight are similar cases, with the one odd exception being Chen. For now I attribute Chen’s performance to sampling error.

Broodmother’s results are all over the board from bracket to bracket. I don’t really care anymore. I’m nearly convinced at this point that she’s the worst character in the game if the enemy team is even half-competent in shutting her down.

Tiny is a weird case because he has two distinctly different playstyles. Carry Tiny appears to be much more of a thing in Very High, but I have to wonder if he’s been eclipsed by the recent Sven buffs. Sven is another case where the 6.74 to 6.76c comparison will be an interesting one.

I think that does it for now. Check out the spreadsheet yourself and come up with some opposing conclusions.

(I don’t know which WordPress Suggested Tag is better: ‘Farming Life’ or ‘Pointless Questions’)

Advertisements

Dreamhack 2012 EG vs Na’Vi Game Two: a Ban/Pick Analysis

November 23, 2012

I don’t intend on straying into the pro game too often. Plenty of other people do that better than I do, and my stat work is focused on public matchmaking and maybe occasionally extrapolating that to amateur organized matches. But today’s game was an interesting (and rare) case of Na’Vi definitively getting outpicked. It also shares some themes with an upcoming post about the double-edged sword of carry potential and carry risk.

The match is https://dotabuff.com/matches/67112954 and is viewable in-client either temporarily or indefinitely, I don’t know which. There’s likely also a VOD somewhere, but I’m sick so do your own googling.

Ban Phase 1:
Na’Vi — Magnataur
EG — Bounty Hunter
Na’Vi — Dark Seer
EG — Batrider

Pretty standard bans. Looking at the most banned/picked characters for the last month on Dota-Academy you can see that Bounty Hunter, Dark Seer, and Batrider are the 5th, 2nd, and 1st most banned/picked characters. Magnataur is a much more recent trend. Looking at Dreamhack specifically you have this list which is kinda crazy in its uniformity. 8 heroes have been picked or banned at least 30 times (possibly out of 32 games) this tournament, and we’ll see all 8 of them get picked or banned before the second ban phase.

EG knows that Na’Vi gets first pick, and I feel they target their bans accordingly. Of the top 8, Bounty Hunter and Batrider are arguably the best combination of flexible and impactful. Magnataur has been comparable, but he was Na’Vi’s initial ban so it’s not like EG ever had a chance to ban him.

Dark Seer is, to my understanding, a ban targetted at EG’s playstyle. His performance this tournament hasn’t been great, but the ban makes sense as a targetted one. Interestingly, the Dark Seer ban was the ban in this phase that took the longest for either team to decide on. Part of this is probably because Na’Vi is also deciding which heroes to leave in the pool for their upcoming first pick.

Pick Phase 1:

Na’Vi — Templar Assassin
EG — Jakiro
EG — Sven
Na’Vi — Faceless Void
Na’Vi — Vengeful Spirit
EG — Undying

Here is where I would argue things went wrong for Na’Vi. The Templar Assassin pick makes sense for both teams. She’s arguably the most desirable hero remaining in the pool, but from EG’s perspective I would rather risk giving her to Na’Vi than Magnataur, Bounty Hunter, or Batrider. Bounty Hunter and Magnataur have been very successful this tournament, and they’re both very flexible and more than capable of being a suicide solo. With TA you’re immediately declaring your mid, which cuts down your options in later picks. This is because there are far more viable mid heroes and setups than there are for the suicide lane. Batrider is also a character that could potentially handle a suicide lane or mid (or even jungle). The other important factor is that TA is the most farm dependent of these 4 heroes.

EG responds with the Jakiro/Sven pick. This appears to be the declaration of their carry and safe lane support. Both are trendy picks right now, and Jakiro also helps make the EG draft more flexible since he can be built either to push early with points in his tower slowing passive or exclusively for AoE control through his nukes.

Na’Vi responds with Faceless Void and Vengeful Spirit. It is my argument that these picks lost them the draft.

With Faceless Void and Templar Assassin you have two heroes that both need farm and both share a similar set of lane vulnerabilities. TA is definitely the more self-sufficient of the two thanks to refraction, but if there’s a lane that TA cannot handle, then Faceless Void likely cannot handle it either short of a defensive tri-lane.

Vengeful Spirit doesn’t help matters. She’s an aggressive but risky support capping off what is an extremely aggressive but risky first 3 picks. There’s nothing wrong with having a strategy that goes all in, but you should go all in with your 4th and 5th picks so that your opponent doesn’t get the chance to counterpick. It’s not as though VS was a terribly likely ban at any phase in the game. Na’Vi could have grabbed Windrunner here and not tipped their hand at all, though it’s admittedly likely that a Windrunner pick wouldn’t have deterred EG’s next pick. I think grabbing Chen here instead of VS would have been Na’Vi’s best move if we’re only making slight adjustments to their overarching pick strategy.

EG fires back with a relatively quick Undying pick, which basically screams offensive trilane. Name a value of x where x + Vengeful Spirit + Faceless Void beats Sven + Jakiro + Undying. I can’t come up with a good one, and two of the least bad options I can think of get banned by EG in the next phase.

Ban Phase 2:
Na’Vi — Wisp
EG — Enigma
Na’Vi — Brewmaster
EG — Broodmother
Na’Vi — Rubick
EG — Chen

EG has a really good ban phase, whereas Na’Vi bats, in my opinion, 1 for 3. But it’s easier to have a good ban phase if your opponents are more committed to their lanes, so this really shouldn’t be surprising.

From EG’s perspective, Enigma and Chen are basically the strongest junglers in the pool that could help shore up the Faceless Void safe lane without committing to a full on tri-lane vs tri-lane battle. EG also knows that Na’Vi absolutely needs a suicide solo. I honestly think Broodmother is a really weak hero competitively right now, but I think EG is thinking ahead. They know precisely who they want to send to their safe lane, and Broodmother is the only effective counter that will fit Na’Vi’s lineup.

Na’Vi on the other hand bans Wisp and Rubick. Why? EG’s support picks have been telegraphed already. I don’t think Rubick is a great solo mid option anymore, and of all the big teamfight ults, Chronosphere is the least valuable to Rubick now that it doesn’t freeze Faceless Void himself.

Brewmaster is an ok ban. He’s pretty similar in role to what EG ends up running in mid. It’s not a gamebreaker for EG, but it at least qualifies as a relatively likely pick.

Pick Phase 2:
Na’Vi — Windrunner
EG — Beastmaster
Na’Vi — Lycan
EG — Clinkz

Ok, Windrunner, whatever. Kinda an inconsequential formality. I don’t think she helps Na’Vi’s lineup, but they were in pretty dire straits regardless.

Beastmaster is an interesting pick, because by sending him mid EG basically declares “We don’t care what happens mid.” Yeah, PA is going to outfarm him, but he’ll get his quick six and enough axe farm for a relatively quick bottle and soul ring. He can use his boar to stack a camp and his axes to catch up on farm.

True, PA will get farm, but who were they going to pick to stop that? Instead, they put a relatively weak laner with a strong early ult in a position where TA can’t force them out of exp range, kinda akin to how suicide lane Tidehunter usually works.

There’s also the added benefit that losing out creeps to mid-pulling isn’t going to hurt a Beastmaster nearly as much as it would a traditionally exp hungry solo mid.

Moving on, we get to Lycan. It’s out of nowhere and I chalk it up to a desperation pick.

And finally we get to Clinkz. EG knows for sure that nothing Na’Vi has can stand up to their tri-lane of Sven, Jakiro, and Undying. The eventual response will be to send Faceless Void and Vengeful Spirit to the suicide lane. Given this, Clinkz accomplishes two things:

1. Faceless Void now has no safe lane to farm. His best option is to go mid with Vengeful Spirit, but this would force TA to a sideline which won’t be much better for her than it was for FV+VS.
2. EG now has two big carry threats on opposite sides of the map. Maybe Na’Vi will find a way to slow one of them down (spoiler alert: they don’t) but it’s impossible for their lineup to hinder both. Whichever one that gets off to a good start will have a strong enough midgame (combined with the potent early teamfight of Jakiro, Undying, and Beastmaster’s massive stun) will easily be able to buy the other one some room to catch up.

Now we can look back at the Broodmother ban and see how smart it was. If there’s any hero that could give Clinkz some issues in a 1v1, it’s Broodmother. She can win the lane by attrition, and Clinkz has poor tools for dealing with her spiderlings. Either she’ll push down towers in a big way or she’ll devour the entire Dire jungle. Possibly both. EG knows in advance what they want to do, and they smartly target the one counter to their strategy.

Should Na’Vi have banned Clinkz? Well it’s easy to look back with hindsight and say “Yes!” but I think it’s something to consider for the future. If the other team is obviously running an offensive trilane, Clinkz in safe lane is a very dangerous complement to that. I’m also not really big on the Enchantress pick, in most line-ups I feel Chen outclasses her, but if Na’Vi had taken Clinkz out of the pool Enchantress might have been a good option to buy Faceless Void some space. Either she can help keep the offensive trilane in check, or she can switch over with Faceless and Vengeful and offensive jungle. It certainly would have given their lineup a hell of a lot more flexibility than Lycan brought.

Na’Vi is kinda known for being a bit greedy in their drafts, and this time it really came back to haunt them. It’s an important lesson for pubbing too. If you’re picking Templar Assassin, Lycan, and Faceless Void, you run the risk of having one or more of them become underfarmed and essentially useless. It can be nice to have some farm…agnostic characters in a lineup. What I mean is heroes like Beastmaster who can function splendidly with little more than a decently quick level 6, but who can also help out your late-game with a maxed attack speed aura and a Necrobook 3. This gives you more room to adapt to how well the enemy team does or does not shut down your early CS.

I’d argue that this is also why you rarely see true carries much higher than 53% at best on the hero win percentage charts. 6.74 Lycan and Ursa were possible counter-examples, but they behaved quite differently from actual carries like Na’ix and Lone Druid. Also there’s +6.75 Drow, but she’s stupid overpowered in the bottom half of matchmaking, which I suspect accounts for a lot of her ~59% win rate.


Addendum to Radiant Advantage

November 21, 2012

Ran some Radiant vs Dire numbers looking at the final kill differential. Basically I divide the games into Radiant wins and Dire wins and by games that end in less than 30 minutes (but longer than 15 to filter early abandons) and games that last longer than 30 minutes. The number represents the average number of kills the winning team is up by at the end of the game

Very High
under 30 minutes
Radiant — 19.13 || Dire — 11.76
over 30 minutes
Radiant — 14.44 || Dire — 13.92

High
under 30 minutes
Radiant — 19.41 || Dire — 11.22
over 30 minutes
Radiant — 15.30 || Dire — 14.27

Normal
under 30 minutes
Radiant — 17.89 || Dire — 12.02
over 30 minutes
Radiant — 15.38 || Dire — 15.02

Radiant appears to have a significant advantage in kills during the laning phase, but there’s still no clear answer as to why or whether it’s the kills themselves that are the source of the Radiant win advantage.

Re-created the test in two different ways. Both disagree markedly with the above results, and a bug was isolated. New results are:

Very High
under 30 minutes
Radiant — 19.13 || Dire — 18.50
over 30 minutes
Radiant — 14.44 || Dire — 15.28

Kill differential as a cause or symptom now appears to be a non-starter. Radiant win advantage in < 30 minute games remains.

Edit: Trying out average team creep score per minute

Very High
under 30 minutes
Radiant Win: Winner — 16.05 || Loser — 10.69
Dire Win: Winner — 15.71 || Loser — 10.97
over 30 minutes
Radiant Win: Winner — 16.94 || Loser — 13.80
Dire Win: Winner — 16.64 || Loser — 14.40

Minor shifts and nothing conclusive.


The Radiant Advantage

November 18, 2012

Interesting post here about a 59%-41% advantage for Radiant in league matches since 6.75: Did 6.75 disrupt the balance between Radiant and Dire?

The two big relevant changes in 6.75 as described in the post were the shortened Aegis reclaim time and the realignment of the ban and pick phase.  My first thought is just do a test of 6.75/76 matchmaking games.  If the trend isn’t repeated then the most likely culprit is the pick/ban change.

Unfortunately I can’t do this while the API is still down, but it occurred to me that I had never done a Radiant vs Dire test on my own 6.74 sample.  So I threw a remarkably quick one together and came across some interesting results.

First, we have the Radiant win rate for all games in the sample (with a > 15 minutes duration check to purge out most of the games ruined by abandons)

Norm/High/VHigh

51.6/53.3/54.0

Sample Size:

9833/9915/9829

An interesting shift.  If you account for the fact that Normal games are 4 times more common than High+Very High, the adjusted average Radiant win rate is very close to 52%, but the advantage seen in the top two brackets is considerably higher.

So what happens if we only look at games that last at least 30 minutes

Norm/High/VHigh

51.1/52.0/52.3

Sample Size:

9024/8433/7874

Much of that Radiant advantage dissipates in longer games.  Does this trend continue indefinitely?  Let’s look at games that last 45 minutes or longer:

Norm/High/VHigh

48.3/49.4/49.7

Sample Size:

4496/2967/2473

If anything, the trend away from the Radiant advantage appears to accelerate as the games go longer, so let’s go the opposite direction and look at games that are shorter than 30 minutes.

Norm/High/VHigh

56.9/61.0/61.1

Sample Size:

787/1457/1930

The trend continues in dramatic fashion.

So what can we take from all this?

  1. For starters, whatever advantage Radiant has is strongest in the laning phase.  The fact that this erodes away as the games draw longer suggests that Dire has a late game advantage, which is consistent with the theory that the location of the Rosh pit favors Dire.
  2. But unless the game goes longer than approximately 45 minutes, Radiant’s advantage is stronger than whatever benefit the Dire get from Roshan.
  3. Both the Radiant early advantage and the Dire late advantage appear more significant in the High and Very High brackets.
  4. Valve may or may not have a built-in matchmaking advantage for either side.  For example, there could be a pro-Radiant matchmaking handicap designed to compensate for the Roshan advantage.  If this handicap overwhelms the Dire during laning then Rosh doesn’t matter.  If it doesn’t overwhelm the Dire then the game becomes a toss-up.

No definitive conclusions can be reached other than to say that match duration appears to play a pretty significant role in Radiant vs Dire balance.  Hopefully future samples and tests will be able to expand on this base.


My Take on the ‘DotA 2 Team Composition Statistics’

November 17, 2012

A few weeks ago there was a post on reddit advertising this site: http://siyobik.info.gf/misc/dota2/

Basically they grabbed a bunch of matches off Dotabuff and found the win and usage rates of a bunch of different team compositions.  They split the team compositions in a variety of ways, including Ranged vs Melee, Strength vs Agility vs Intelligence, and using the in-game hero descriptions.

Because they were grabbing matches off of Dotabuff, they couldn’t separate the matches by skill level.  My sample, on the other hand, is divided by skill level, so I decided to recreate their Carry data (the category I found to be most interesting and worthwhile) by skill level to see what would happen.  Instead of finding out anything interesting about how the importance of carries varies by skill level, the results have led me to question the validity of their results.

First, their results:

        Win Ratio   Popularity

0	64.1%	         0.4%
1	57.5%	         7.5%
2	54.1%	        30.6%
3	49.2%	        38.3%
4	44.2%	        19.4%
5	38.2%	         3.8%

We all joke about AP pubs picking too many carries, but these results were still astonishing.   Carries appeared to be complete poison to a team’s win chances.   And keep in mind that they claim to be using the in-game definition of carry which includes nearly half of the currently released heroes.   Check it out for yourself.

So I ran (what I believe to be) the same test on my sample.  Here’s my results:

Normal
        Win Ratio   Popularity

0	48.84%	         0.66%
1	48.49%	         9.37%
2	51.25%	        32.37%
3	50.08%	        37.05%
4	49.08%	        17.58%
5	45.85%	         2.97%

High
        Win Ratio   Popularity

0	54.63%	         0.55%
1	51.41%	        13.05%
2	50.68%	        39.53%
3	49.92%	        35.03%
4	46.51%	        10.93%
5	42.54%	         0.91%

Very High
        Win Ratio   Popularity

0	46.24%	         0.88%
1	49.42%	        15.27%
2	50.25%	        40.46%
3	50.47%	        33.82%
4	48.64%	         9.01%
5	46.79%	         0.56%

Comparing their total sample with my normal sample shows that the popularity percentages are reasonably close with whatever differences falling within a reasonable amount of sampling error.  The win rates on the other hand bear no resemblance whatsoever.  Their win rates essentially claim “less carries = better”.  Mine show a series of normal distributions where the ideal number of carries (as defined in-game) is 2, with either 1 or 3 being fairly acceptable.

So I decided to try again.  This time I used # of Melee on a team.

Their Results:

        Win Ratio   Popularity

0	55.3%	         1.6%
1	51.8%	        14.1%
2	50.5%	        36.5%
3	50.0%	        34.7%
4	46.3%	        11.8%
5	42.6%	         1.3%

Again, a fairly simple story: “less melee = better.”

My Results:

Normal
        Win Ratio   Popularity

0	42.53%	         2.03%
1	44.80%	        15.43%
2	49.52%	        37.75%
3	52.19%	        33.89%
4	53.94%	        10.05%
5	49.39%	         0.84%

High
        Win Ratio   Popularity

0	42.60%	         3.07%
1	48.18%	        20.79%
2	49.46%	        41.80%
3	52.29%	        27.60%
4	52.69%	         6.38%
5	58.57%	         0.35%

Very High
        Win Ratio   Popularity

0	44.83%	         4.14%
1	48.94%	        26.32%
2	50.55%	        42.97%
3	50.57%	        22.55%
4	53.47%	         3.82%
5	48.72%	         0.20%

Again the popularity results are similar, but this time the win ratio results are even more at odds with each other.  In fact, if you look at their win ratios and my High win ratios the trends are almost perfectly inverted.

But unlike in the carries test, my claim here is more startling.  My stats tell me that a 3 or 4 melee team is at no significant disadvantage, and this is squarely at odds with conventional wisdom.  Can I really be confident that I just didn’t screw up somewhere?

So I did some double checking.  I found out the expected win rates of melee heroes based off of this test.  The method was pretty simple.  If I had 30 games in the sample with 2-melee teams, and they went 10-20, then I know the melee characters collectively had a record of 20-40, because 2 melee heroes won in each win, and 2 lost in each loss.  Repeat this for 0, 1, 3, 4, and 5 and you have the total win rate, which in normal ended up being just over 51%.

Then I went to the hero spreadsheet that I posted about previously.  I filtered out the ranged heroes and found the melee exclusive win rate, and it was very close to 51% both with and without adjusting for usage rates.  The numbers appear to check out.

And realistically why shouldn’t they?  Are melee heavy line-ups really that bad?  There are plenty of viable melee mids.  Several melee junglers.  Many of the best off-laners are melee, including Bounty Hunter, Dark Seer, Tidehunter, and the potential up-and-comer Magnus.  All you need is a decent all-melee safe lane like Phantom Lancer + Ogre Magi and you have a perfectly viable all-melee team.  And if you allow for a single ranged hero your options open up dramatically.  The real problem with melee heavy line-ups is when you do something like send Juggernaut and Anti-mage to the off-lane against a proper safe lane setup and jungler, which is bad for a multitude of reasons beyond just being double melee.

So we have two tests in disagreement with each other.  One possibility is that at least one of the tests is flawed.  The other big possibility is that the disagreement is just a reflection on different samples.  Mine are purely early 6.74.  His samples could be from 6.75, or they could have come from a different hero release.  If his sample came from the day of Meeepo’s release, that could easily warp the results tremendously.  If his sample came from 6.75c (which I’m almost certain it didn’t, but hypothetically) then it wouldn’t be that surprising if his melee vs ranged results differed from mine given the surge of Drow Ranger in popularity and performance.

At the moment I don’t have the information to do much more than speculate.  But what I can say is that I wouldn’t put a lot of stock in his more exotic categories.  For instance, the win rate of 5 Durable teams is 61.4%?  That’s great, but they make up .2% of his sample, which comes out to about 80 games.  If I counted correctly, there are 33 different Durable heroes currently in Dota 2.  You can figure out the number of combinations if you want, but I can guarantee you that 80 games is not an acceptable sample.  And don’t even get me started on the absurdity of adding up Carry/Disabler/Initator points.  Carry works as an evaluator because it estimates farm requirements (and farm availability is a fairly zero-sum game).  Melee vs Ranged works as a category because it estimates lane control.  Initiator as a category includes characters as absurdly varied as Faceless Void, Meepo, Tidehunter, Sand King, and Silencer.  You might as well categorize teams by how many of their heroes have names that begin with letters in the first third of the alphabet.


Creep Kills per Minute by Bracket and Hero

November 14, 2012

As a complement to the previous post, I have some creep killing stats.   GPM (and Net Worth, but Net Worth is a pain for me to calculate given the API information so I ignore it) is the better metric for evaluating a team performance, but isn’t so great for providing a benchmark for individual farming.  Creep Kills per Minute is also a better way of evaluating how teams distribute their limited farming opportunities between different heroes.
For all players in the sample, the CK/min stats are as follows:

Very High/High/Norm
3.01/2.79/2.36

When we restrict it to just the top farmer on each team:

Very High/High/Norm
5.10/4.66/3.87

So we see a 25-30% increase between the Normal and Very high brackets.

It’s difficult to test for and I don’t have any definitive results yet, but from what I have seen my suspicions are that the typical farm rate of a successful carry tends to increase as the game goes on.  This effect is most pronounced in the Normal bracket, but still exists in a lesser degree in the higher brackets.  Given this, I would say that 4 ck/min is a solid benchmark to shoot for by the 15 minute mark in a relative free farm situation for someone who wants to be able to play a hard carry at an acceptable level in the upper brackets.

 

Changing gears, I also have some charts that display the distribution of the ck/min stat for every hero in every bracket in my sample.  In lieu of trying to get WordPress to play nice with them, I’ll just provide the external links.

Very High Skill Bracket: http://jsfiddle.net/8vFdN/89/embedded/result/
High Skill Bracket: http://jsfiddle.net/FcRgh/8/embedded/result/
Normal Skill Bracket: http://jsfiddle.net/9HDRz/13/embedded/result/

All Three Skill Brackets, kinda unwieldy, contains all 270 entries grouped by hero: http://jsfiddle.net/QtTrP/16/embedded/result/

Just select the heroes you want to compare in the legend.  Supports will tend to have very high peaks early in the graph.  Carries will have lower peaks as they tend to be spread out over a much wider range of farm performances.

For example, Crystal Maiden, Ancient Apparition, and Wisp (among others) all have very similar extreme early peaks, marking them as heroes that tend to be played as hard supports or a 5 slot.  Tidehunter, Omniknight, and Sand King have support oriented distributions, but they’re slightly more shifted towards farm, indicating a greater propensity to play a 4 or even sometimes a 3 in team compositions.


Very High Skill Hell is a REAL place where you WILL be sent at the first sign of success.

November 7, 2012

Some of the more conspiracy-prone Dota discussion areas are pretty skeptical that Dota2’s matchmaking is effective, and in some extreme cases they doubt it even exists. So I did a bit of analysis on the types of games each bracket and can demonstrate that there are definite trends in player performance between the brackets. This in no way proves that Dota 2’s current matchmaking is flawless, but it does suggest that it’s been successful in sorting by player skill level.

One inconvenience you’ll have to forgive, due to technical difficulties these charts are legendless. In all the charts, the red line is the Very High bracket, the green line is the High bracket, and the blue line is the Normal bracket.

One other tiny, almost irrelevant factor: the ends of the distribution tend to be larger as an easy way of handling extreme outliers without warping the graph. As far as I’ve been able to determine, this simplification is entirely inconsequential.

Disclaimers aside, I give you the distribution of games by duration:

The mean match duration for the sample is:

vh = 38.46 minutes
h = 40.22 minutes
n = 44.10 minutes

Normal games, on average, last significantly longer than games in both the High and Very High bracket. No real surprises here. More highly skilled players tend to emphasize push and gank strategies over farm strategies, and they’re more capable of closing games once they have a significant advantage.

Moving on, we have average GPM:

The mean GPM for the sample is:

vh = 344.75
h = 330.19
n = 307.27

Again, no real surprise. From what I’ve seen, last hitting is the skill that is the most consistently improved as you move up in the skill brackets. You often see complaints about low skilled players leaking into the High and Very High brackets. In most cases, this is simply the result of group queuing, but it’s possible that there’s a class of player who wins more often than not in the Normal bracket simply by having superior last hitting mechanics than the competition. This moves them into the higher brackets where their relatively undeveloped game sense gets exposed by the shift towards more aggressive strategies.

Now for XPM:

Mean XPM in the sample:

vh = 445.51
h = 435.67
n = 422.20

This increase is less pronounced than GPM, which again, isn’t very surprising. An XPM increase mostly reflects an enhanced game sense for finding time to farm. This might entail using a TP scroll to a tower that’s about to receive a creep wave. This might come from remembering to stack and pull as a support. This might come from knowing when and how to use neutral creeps to enhance your farm. All these are important skills, but they’re skills that are already reflected in GPM. GPM adds in the mechanical aspect of last hitting, so GPM will be the stat that’s more sensitive to player skill.

Finally, we have Deaths per Minute:

Average Deaths per minute:

vh = 1.72
h = 1.65
n = 1.60

Of all the statistics, Deaths per Minute sees the smallest shift between the Normal and Very High brackets. Does this contradict what I was saying about Very High players being significantly more aggressive? No. Instead what’s happening here is that Very High players are better at playing aggressive, but they’re also significantly better at playing it safe. The skill increases counteract each other, but aggression gradually edges out safety to make for a slight trend towards higher kill scores.

One possible curiosity that stands out is that in this graph, Normal and High have very similar lines. In all the other graphs, High and Very High had the most similar lines and Normal was the outlier. A tentative interpretation is that as a player learns more about the game and moves up in the brackets, they’re more likely to first improve their farming skill and death prevention than they are their aggression and ganking. Exceptions would exist of course, possibly in great numbers, but the cautious farmers would still be the majority in the High bracket and therefore have the largest statistical footprint.

With this out of the way, it’s likely time to move on to one of the more interesting, and possibly most misleading metrics, creep kills per minute.