Hand of Misuse

I originally wrote this post for a more gaming-oriented blog my friends and I created, Bloglomerate. It is exclusively concerned with the game Dota 2. I’ve reposted it here to ensure it lives on in case Bloglomerate is discontinued.

Pro teams are picking up Hand of Midas a lot these days. First, just a brief look at usage over the last year. All stats pulled from datDota.

General Midas appearance and winrate by patch

Here’s the funny thing: Midas was nerfed in 6.79c. Most of the games counted in 6.79 came before that patch, but it was valued much less in 6.78 for no apparent reason. While drafting strategy could explain some of it, it would appear that Midas has become a thriving trend across nearly a full year of use.

In any case, we can see that despite the nerf, players are picking it up nearly as fast as they did before it was more expensive, and they’re even using it more efficiently despite getting it later in the game.

Midas appearance, success, and usage across teams in 6.81.

But how effective is it in reality? This is where Midas usage is at among Tier 1 teams currently in 6.81.

Those results are not particularly favorable for Midas. While not large enough to be statistically significant, they raise the question of why players are choosing this item when the latest results are not particularly positive. It doesn’t even appear that earlier purchase times are resulting in better chances to win.

The mystery: where is Midas useful?

Midas is generally picked up on carries for the purpose of securing more farm. There was a brief fad where supports were grabbing it, but we haven’t seen much of this in 6.81. It’s an investment item, one that’s meant to pay off in the long run. Every caster will discuss a team’s choice to prepare for the late game by purchasing Midas. As such, Midas should be resulting in a higher win rate the longer the match goes on. Here’s the data for match length, separated out across the last few patches.

Midas success and usage by patch and game length.

We should be seeing winrate increase over time. Instead, winrate for teams with Midas is dropping over the length of the match. This is not easy to explain.

There are some clear trends. Purchase time is definitely correlated to win rate, but why do win rates drop for identical purchase times across increasing match lengths? More transmutes represent a strictly better return on value for the investment. Why is the win rate so astronomically high for short matches? Midas offers so little for such short time spans. Clearly we need more information. Maybe hero picks are part of the problem. How does Midas impact the most common Midas carriers?

Midas use by hero, between patch 6.80 and 6.81. Darkest shades indicate 95%+ confidence using chi-squared goodness-of-fit. Lightest shades indicate 75%+ confidence.

This data is all over the place. It doesn’t even make sense why it bumps some up and others down. Why should Shadow Fiend see such a huge increase? He’s a squishy right-click hero with no procs that depend on attack speed, and his ability to flash farm is naturally very, very high. Meanwhile, Faceless Void benefits strongly from attack speed and has no ability to flash farm – but Midas appears to have literally zero impact for him, possible even being negative.

Purchase time does seem to have an influence – everyone that manages a sub-8 minute Midas seems to benefit. But why should Weaver’s 8.2 minute Midas fail him while Doom’s 9.2 minute Midas still be worth it? Why does Lifestealer benefit so much more from the same Midas timing as Luna?

The answer, I believe, is in experience.

Experience vs. gold

Let’s look at the basics of what Midas actually does. Midas costs 2050 gold. Transmute is on a 100s cooldown. Transmute gives 190 gold and 2.5x experience. Transmute replaces the original bounty for the creep, meaning you have to add on the original value of the creep to the payback time.

The biggest factor to Midas payback time is using it every time it’s on cooldown. While it’s theoretically possible to use it instantly every time it comes off cooldown, deaths, distance from the lane or the jungle, ganks, and team fights will interrupt. There should be a way to calculate this using existing data, but I can’t find it. Let’s throw in a rough downtime of 8s between uses, which is fairly generous.

To limit downtime, most transmutes will be used on lane creeps. Ranged creeps are worth less xp and more gold, meaning they are always the inferior choice. The average bounty for melee creeps is 43 gold and 62 experience.

190 gold – 43 = 147 bonus gold per transmute
147 gold x 14 uses = 2058 gold (Midas paid for)
14 uses x 100s cd + (8s lag x 13) = 1504s / 60s =
25.07 minutes (Midas payback time)

62 exp (melee creep) x 1.5 = 93 bonus exp per transmute
93 xp x 14 uses = 1302 bonus exp at payback

Maximizing for experience means selecting only level 5 neutrals, which are worth 119 exp and 72 gold.

190 gold – 72 = 118 bonus gold per transmute
118 gold x 18 uses = 2124 gold (Midas paid for)
18 uses x 100s cd + (8s lag x 17) = 1936s / 60s =
32.27 minutes (Midas payback time)

119 exp x 1.5 = 178.5 bonus exp per transmute
178.5 exp x 18 uses = 3213 bonus exp at payback

Maximizing for gold is far less realistic, but for the sake of it – selecting only level 1 neutrals, which are worth 25 exp and 8g.

190 – 8 = 182 bonus gold per transmute
182 gold x 12 uses = 2184 gold (Midas paid for)
12 uses x 100s cd + (8s lag x 11) = 1288s / 60s =
21.46 minutes (Midas payback time)

25 exp x 1.5 = 19.8 bonus exp per transmute
19.8 exp x 12 uses = 237.6 bonus exp at payback

It’s impossible (or at least, beyond my ability) to measure the opportunity cost of not buying the items that could have sat in the place of Midas. The possibilities are endless and possessing a Midas changes optimal behavior for its carrier. The best we can do is assess the average benefits based on when players are acquiring their Midas (9 minutes) and how many transmutes they are able to execute (13.5). While this does indicate that players are usually getting back their investment on the item, that’s not really good enough. They need to be getting back much moreto make up for the opportunity cost of the item that Midas is delaying, and that has to come from the experience bonus.

Consider again the anomaly of Midas’ huge early-game win rate. While it is possible that few teams losing badly enough to concede in the first 20 minutes are able to afford a Midas (creating a bias in the data), according to current theory there should be many games lost early on because a team chose to orient towards the late game with a Midas. It is also possible that Midas is a “win more” item – if a carry scores an early first blood, it’s very likely that they’ll pick up a Midas. But again, according to current theory, Midas wouldn’t be contributing to that win because it could just as well be Drums or a Blink dagger – something that actively contributes to killing or pushing.

I suggest, instead, that Midas is actually relevant to these wins because of the insane early level advantage it can provide. Transmuting a level 5 neutral is an enormous quantity of experience – it’s half of the experience required to reach level 11, which is an important level for every hero in the game. This effect is further amplified for heroes that greatly values ranks in all of their abilities.

There is no other way to buy levels in the game. You can’t buy a gank, you can’t buy a Rosh kill, but you can buy an extra 90 experience per minute with a 2050 gold item. For some heroes, that means capturing invaluable killing power not otherwise available. Why does Shadow Fiend appear to benefit so much? I propose that it’s because reaching level 2 Requiem and multiple levels in Presence vastly amplifies his damage output, especially earlier in the game when armor values are low.

Similarly, Lifestealer is at his most potent when all of his abilities are max rank. Lower cooldown Rage, higher range Open wounds, and free damage and sustainability through Feast. Invoker’s utility increases directly with his levels. Outworld Devourer can right click like a monster with zero items, as long as he has max Essence aura and Arcane orb. Morphling’s survivability increases dramatically with levels, though he does require items to sustain his high mana costs.

I’m not sure experience explains all of the data we see here, but I think there’s a strong case to be made that for any hero for whom quick levels are important, Midas is a strong investment. This would also indicate that many players are not buying Midas correctly, and it seems very clear that Midas after 10 minutes for any core is not a good idea. I haven’t included any support heroes in my analysis here, so I can’t rule out that choice for supports like Witch Doctor or Dazzle that remain desperate for levels throughout most games. Further inquiry on that front requires more data than is currently available.