Talk:Hand of Midas

Midas paying for itself
Hopefully this clarifies things, as there have been several recent edits.

BLUF: Midas will pay for itself in 21:40 (14 uses) if used on melee creeps or 30 minutes (19 uses) if used to maximize experience on large creeps. It can pay for itself in 20:00 (13 uses) if used to maximize gold on small creeps, but this isn't worth mentioning on the main page because the difference between this and melee creeps is so slight (and because people don't use Midas like this). Note that the only factors used in these calculations are the cost of Midas, the gold from creeps, and the 100-second cooldown; all other factors are ignored. So these times could be slightly lower or significantly higher in practice (significantly higher if frequently dead or otherwise having Midas off cooldown).

Notes/assumptions: 1. This might be obvious, but dividing 2050 by 190 doesn't cut it. A given creep normally gives a certain amount of gold, and with Midas that creep gives 190. The gold benefit of Midas is 190 minus whatever that certain amount was. That's the point of the math below. 2. Cost should be for the entire item, not just the recipe. One doesn't buy casual Gloves of Haste; one buys gloves to turn them into something better, so the cost of the gloves should be included. 3. Midas is used the moment it's off cooldown, every time it's off cooldown. 4. Experience bonus is not taken into account. The exp bonus is obviously valuable, but it's impossible to define exp in terms of gold since they're two very different things. So from a strict gold-payback perspective, exp has to be ignored. 5. Time savings in farming (and the extra gold and experience that comes with this) is not taken into account. Time savings comes from the attack speed boost and from being able to insta-kill a creep every 100 seconds. 6. The potential benefit one would have gained from buying something else instead of Midas is not taken into account. 7. The average gold reward from killing a given creep is used, not the range. 12+ uses makes for a large enough sample size to ignore the range. 8. The only relevant creeps are melee creeps, camp creeps that give the most experience (one of which also gives the most gold), and camp creeps that give the least gold. This establishes the min and max number of Midas uses, with an additional data point for lane creeps. Note that ranged creeps should never be Midas-ed because they give more gold and less experience than melee creeps.

Assumptions 3-6 are big. Depending on the hero and how the game progresses, Midas can pay for itself slightly faster or significantly slower than is calculated below (and it can cause a disadvantage in midgame teamfights, and so on). The math is an important starting point, but it's only a starting point.

Here's the math in four steps:

n1: Creep gold: -melee: 38-48 (43 avg) -Kobold: 7-9 (8 avg)* -avg for all lesser small-camp creeps: 21.33** -Satyr Tormentor: 97-111 (104 avg)*** -avg for all 119-exp creeps: 78.6**** Notes: *Camp creep that gives the least gold. **Includes Kobold, Hill Troll Berserker, and so on... the creep in each camp that gives the least gold. Hill Troll Berserker is used twice in this calculation since it appears in two camps. Assumes that each camp has the same probability of appearing. ***Camp creep that gives the most gold. Also note that Liquipedia has 91-111 (104 avg), and I don't know which is correct. Thankfully, no matter which average is used, the number of Midas uses ends up being the same. ****One appears in each large camp. Assumes that each camp has the same probability of appearing.

n2: Additional gold per Midas usage (190-n1): -melee: 152 -Kobold: 182 -lesser small-camp creeps (avg): 168.67 -Satyr Tormentor: 86 -119-exp creeps (avg): 111.4

n3: Uses needed to reach 2050 gold (2050/n2): -melee: 14 -Kobold: 12 -lesser small-camp creeps (avg): 13 -Satyr Tormentor: 24 -119-exp creeps (avg): 19

n4: time needed to reach 2050 gold ((n3-1)*100) (then divided by 60 to give minutes): -melee: 21:40 -Kobold: 18:20 -lesser small-camp creeps (avg): 20:00 -Satyr Tormentor: 38:20 -119-exp creeps (avg): 30:00 Note that it's n3-1 and not just n3 because there isn't any cooldown before the first use. Put another way: after 100 seconds the Midas should have been used twice, not just once.

In addition to Kobolds, 12 uses also applies to Kobold Tunnelers, Satyr Banishers, and Skeleton Warriors because they give less than 190-(2050/12) gold. But this is such a small group that 13 uses is the practical minimum. Also, because this is only one less than what's needed for melee creeps, and because people usually either use Midas against lane creeps or to maximize experience on large creeps, there isn't any need to put this on the main wiki page. If people want to investigate it further then the math will be here on the discussion page.

Lastly, while Midas can be sold, and this halves the required uses/time, this only happens in practice if the sixth slot is needed. By that time, it's late game and Midas has obviously more than paid for itself. So there's no need to include this on the wiki page.

See top for summary.

Hydoc (talk) 00:00, 25 May 2014 (UTC)