In recent news, we have this tale from the PlayDota forums of one man’s harrowing tale of taking a 2900 rated Dota2 account to 5400 in the course of 144 games with a 122-22 (.847) record. Some might say that this disproves the existence of ‘ELO[sic] Hell.’ But of course for some people it didn’t, and today I want to focus on one of the objections.

Juice, the player behind the experiment, prefers to play mid and carry and did so throughout the experiment. A common reaction then has been that all this experiment proves is that if you want to raise your MMR, you need to pick ‘high impact’ heroes, preferably mids. Juice seemed to prefer Ember Spirit, Storm Spirit, and Templar Assassin, though his picks overall were actually quite varied. In any case, I want to examine the idea that maining these snowballing mid heroes are some universal secret to raising your MMR.

1. Let’s start by looking at the overall win rates for some mid heroes:

Outside of our three exceptions, things don’t look so good for traditional mid heroes, and when people recommend picking a high impact mid, Zeus and Necro aren’t typically the heroes that get brought up.

Of course it’s true that some of these heroes do perform better in higher rated games. Ember, Storm, Tinker, Invoker, and Templar Assassin are all among the heroes with the greatest win rate improvement in Very High games (roughly >4000 MMR). But at the same time, none of these shifts are strong enough to get any of these heroes to +50% in that category. Furthermore, these heroes are only nearing that range of success in the hands of people with the mechanics to make it to >4000 play. If you can’t make it to 4k using the heroes you’re comfortable with, it’s extremely unlikely that you have the mechanics necessary to make any of these heroes your ticket out of the so-called trench. At least right now. If you aspire to learn everything there is to know about one of these heroes, then good, go for it. Just don’t pretend it’s going to be the fast fix that will carry you to the MMR you really deserve.

But I feel that this simple win rate examination fails to capture the entirety of what’s going on here, so…

2. Let’s step back and ask ourselves what exactly it is that hero win rates measure in the first place.

If you’d like to know, I can tell you that in your universe you move freely in three dimensions that you call space. You move in a straight line in a fourth, which you call time, and stay rooted to one place in a fifth, which is the first fundamental of probability. After that it gets a bit complicated, and there’s all sort of stuff going on in dimensions thirteen to twenty-two that you really wouldn’t want to know about. All you really need to know for the moment is that the universe is a lot more complicated than you might think, even if you start from a position of thinking it’s pretty damn complicated in the first place. I can easily not say words like “damn” if it offends you. -Mostly Harmless

Think of a hero win rate as a giant array of outcomes condensed into a single number. Two key dimensions within this array represent the probability that the hero will influence their team into a positive gold/XP state and the probability that a hero can take a positive gold/XP state and convert it into an even more dominant position. The heroes that we think of as supports tend to produce good outcomes of the first type while the heroes that we think of as carries tend to produce good outcomes of the second type.

Of course it’s more complicated than that. Lich likely has one of the highest public win rates in a large part because you can stick him into any dumb pub composition and he’ll accomplish something in the laning phase. Meanwhile, Shadow Demon has one of the worst public win rates because his early impact is extremely dependent on having someone take advantage of Disruption initiation. On the other end of the spectrum, Anti-Mage has possibly the strongest capability to convert GPM into total dominance, but his mere existence on a team makes it less likely to get to those stats. Viper has a much weaker gold conversion but has a dramatically higher win rate because he lanes well in general. Spectre provides a somewhat more puzzling counter-example, as she, like Anti-Mage, is a weak laner, and yet she still has had a consistent >52% win rate for several patch periods.

Anyway, We’ve got this idea of snowball or momentum heroes, so where do they fit in? We could say that they’re just a lot like carries since carries snowball too, but that feels off. Items do matter for heroes like Templar Assassin, Storm Spirit, and Outworld Devourer, but not really in a way that’s comparable to Anti-Mage or Spectre. Anti-Mage and Spectre aren’t dependent on momentum; they’re more like time bombs, with their rate of farm determining how much time you have to disarm them.

What I suggest is that the success of these snowball semi-carries isn’t about reaching some kind of item-based end state like it is with a traditional carry. Instead, the goal of a snowball semi-carry is to create a gap between their damage progression and the HP levels of the opposing team. The most straightforward example of this is Outworld Devourer’s ultimate. Sanity’s Eclipse does damage based on the difference between OD’s intelligence and the target’s. If OD gets an item and level lead, Eclipse will do huge amounts of damage in a large area of effect. Conversely, if OD falls far enough behind it won’t do any damage at all.

The central unifying feature to this class of heroes appears to be a specialization in burst damage that tends to be at least as level dependent as it is item dependent.

Templar Assassin can use the free damage and armor shred from Refraction and Meld to melt low HP heroes. Damage items like Desolator and Daedalus can be useful but aren’t strictly necessary and often skipped/delayed in favor of pickups like a Blink Dagger.

can use the free damage and armor shred from Refraction and Meld to melt low HP heroes. Damage items like Desolator and Daedalus can be useful but aren’t strictly necessary and often skipped/delayed in favor of pickups like a Blink Dagger. Storm Spirit thrives on hitting that point where any lone traveler is dead within the duration of Electric Vortex and Orchid.

thrives on hitting that point where any lone traveler is dead within the duration of Electric Vortex and Orchid. Ember Spirit gets right click damage scaling off of a 5-second AoE nuke with a very long range, but struggles to keep up with the sustained damage output of a true late game carry.

If any of these heroes get ahead, they can consistently blow up out of position targets and put their opponents on the defensive with a 5v4. If they fall behind, or even just fail to stay ahead, they can find themselves put into more prolonged fights that their kits are not as well suited for.

And that’s fine. Part of being a hero that depends on momentum is the downside of potentially becoming dead weight if you lose that momentum. The first choice you make in any Dota game is trying to pick a hero with a strong array of outcomes, but those arrays aren’t fixed. Wisp’s array in pub play is pretty terrible, but his array in competitive play has been stellar. Just like Shadow Demon, if you draft a positive environment for the hero, they can drastically outperform their performance in essentially random pub environments. Snowball mids are just another class of hero where a good environment is essential to success. Subsequently, their overall pub win rates kinda suck because pub teams in general are tremendously more self-centered than even the most marginal of competitive teams.

3. So if we accept that environment influences a heroes success, why can’t MMR (and matchmaking in general) itself play a huge role in shaping the expected environment?

Imagine that we have Juice, a ~5500 rated player, queuing into his first match on a 2900 account and playing Templar Assassin. What do we know about the match conditions?

You probably don’t recognize this graph from over a year ago, but it shows the distribution of game ending GPM for players in Dota’s three skill brackets back in 6.74. I’m going to run with the assumption that the shape of these distributions hasn’t changed dramatically since then, partially because it’s likely true and partially because I don’t want to go through the trouble of making an updated version right now.

The blue distribution is Normal games, which roughly correlates to < 3000 MMR. The red distribution is Very High games, roughly > 4000 MMR. Green is everything in between.

Thanks to the Dota2 blog we also have an idea of the shape of the overall distribution of MMRs.

5% 1100 10% 1500 25% 2000 50% 2250 75% 2731 90% 3200 95% 3900 99% 4100

With a ~5500 rating, the games Juice plays on his main account would be deep in the tail end of the red distribution. Based on the chart, we’d expect his games to fall around the 400 GPM per player mark per average. And what do we find when we take the average GPM of all the players in his last 10 games on his main account starting with 646057416? An average GPM of 406.41. We don’t have a fair measure the average GPM of the games at the start of this experiment because Juice’s presence in those games inevitably warps the results, but if we trust that my 6.74 data holds, it’s likely somewhere between 300 and 325. XPM likely has a similar, if somewhat less pronounced gap.

For a hero based on momentum this is a dream environment. If your potential as a hero is based on the difference between your stat progression and theirs, then with 100 GPM worth of a handicap that difference will practically never go away. On top of this, you get a guaranteed 1v1 lane against a player you almost certainly massively outskill, and there’s virtually no risk of ganks since you’re in a bracket where supports, if they even exist, largely have no idea what they are doing and believe that only mids gank. You give a top .1% player all those advantages and it’s not surprising that the immediate result is this:

So yeah, if you’re a player playing 2500 MMR below your true MMR, snowball mids might indeed be the fastest, most reliable way to maximize your winrate and MMR growth, but for the 99% of players playing at a relatively accurate MMR, there’s absolutely no reason to believe that these heroes are a fast fix to a positive win rate. Sure, with enough practice a hero like Storm Spirit can get you up there, but the operative word here is ‘practice.’ You’ll have to actually put in the effort to improve as a player, and you’ll be better for it than a player just trying to Flavor-of-the-Month it up the ladder.

4. Epilogue: The Origin of an Idea

Suppose that instead of MMR, matchmaking just threw 10 people randomly together into teams to create games for you. What would these games look like? Well to start we need to add ourselves, so let’s assume that we’re a vaguely defined ‘above average’ player with an MMR somewhere between 3500-4500. The other 9 slots would tend to be distributed pretty similarly to the distribution earlier from the official Dota 2 blog. This means that on average, 8 of the other 9 people are going to be below 3000 rating, and 5 of 9 are going to be below 2250. So if you’re a 4000 player in one of these games, most of your games are going to going to be you as a ~4000 rated player, and a bunch of other people 3000 or below. In other words, the games from your perspective would look an awful lot like the game’s Juice went through on his experiment.

I’m not going to claim to be an expert on the social structure of original Dota, but it’s likely that basic Battle.net custom games were pretty similar to this as the normal distribution has this pesky tendency to show up just about everywhere. This means that if you were a decent player in the Dota days, then just about every game you played was similar to the ones in Juice’s experiment. Is it any wonder that ‘play a snowball mid’ is common knowledge? It would have really been true in almost every game.

For better or worse (hint: better), matchmaking has killed this, but Dota players in their opinions are often the slaves of some defunct patch period. You can see the same effect when it comes to win rates. In a completely random system, a 60-80% win rate would be evidence of the equivalent of a 3000-5000 rated player. With Dota2’s matchmaking, win rates are no longer a direct predictor of player skill. But you still have this crowd longing for the regular assurance that they’re nominally above average that you would get in a completely random. And so you get complaints about ‘socialist matchmaking’ forcing 50% win rates.

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