Searching through all item combinations

PsychoKitten: thanks for introducing the first real interesting thread in this forum for months. What you did is extreme theory crafting, but it's as relevant and interesting on itself because of that. It doesn't make sense to question why you don't take this or that into account, nor to say "in a real life scenario" blabla. Your model says that already. It's a model with many, many limitations, so that must be taken into account and read as such. But that's what you do, and kudos to you (I especially liked the notes you did on the end of the thread, such as the observations about items like Butterfly and Heart of Tarrasque).

It also doesn't make sense to say stuff like positioning and surviving items is all that matters when you're supporting, for instance, because that's not true (I could ellaborate into why but I have given up on doing that kind of thing here because it causes lenghty discussions that usually end up somehow badly). And yes, the people that mostly comment nowadays are core players, as you so smartly remarked. Don't let yourself be fooled :P

So the questions that I find most important here: the way you built this model, could you build others that compare heroes with other inputs such as the said magical spells properties or other things?

Anyhows, once again, thanks, and do not feel discouraged to keep sharing this kind of info with us here as you keep your research. We really appreciate it.

Psychokitten said it's all about academic interest, which I completely agree with. Isn't questioning things, knowing what they apply to and knowing their limitations are the whole point of academic interest? Isn't questioning what people say without them feeling attacked about it the whole point of academic interest? He can clearly hold his own and make his own points as he's done perfectly well in his past posts, so does he really need babysitting to help him with that?

Knowing the best way to build effective HP is perfectly relevant for a whole bunch of heroes that need to tank up, the likes of Bristleback, Death Prophet, Meepo, Leshrac, Axe and a few others. The thing is, supports have a very different way of working, they're balanced around building cheap defensive items and utility items. That's just how the game is balanced, look at any support's inventory in any competitive game.

You can study the best DPS build on carries, which I completely agree is Manta Style+ Daedalus. The only downside is that Bloodthorn kind of screws this analysis because it's easily purgeable unless you use it on top of a stun. You can remove Bloodthorn from the available items completely (in which case Butterfly will pop up), but that's not necessary. A way to make the analysis take this issue into account would be for example to only allow Bloodthorn active on heroes who have a hard disable : those who natively have a stun, and those who have a Scythe of Vyse or Abyssal Blade in their inventory. Others can't use the active (because it gets purged). Because of the DPS values, it's generally enough to kill a hero even during a 2 second stun. If you put in a rule like that, you can make it work. I'd actually be pretty interested in that result.

You can study effective HP, but there are a few limitations here as well. Evasion is easily countered by Monkey King Bar so you have to take into account the case where enemies have MKB as well. Also, there's the issue of the distribution between physical and magic damage. Personally I'd look at these cases :
- Physical EHP (enemies without MKB)
- Physical EHP (enemies with MKB)
- Magical EHP
- Realistic case (50% physical 50% magical damage, enemies with MKB)


You do realize that the whole point of pointing out a limitation is to encourage to recognize it and find ways to work around it, right? So it's actually, in fact, way more constructive to do that than defending something no matter what because of the classic fallacy that confuses criticizing a person and criticizing his ideas...
That's like, the basics of science :)

Thanks for all the feedback, folks, and especially ChiChi, who "got" what the whole project was about. I was kind of expecting to get completely torn apart. I am well aware of the limitations of this approach.



Adding the spell capabilities of all the heroes and coding them into something representative in the model is a lot of work (115 heroes with 4 spells each is 460 spells, and then you have the different spell levels...). I don't think it would be practical. Does anyone know of any compiled hero spell tables?

What I think could be doable to improve the DPS prediction by splitting the damage of each item into more categories (regular, piercing, mana burn, crit, bash etc) and then calculate an effective DPS expressed as HP/second (or time to kill) against different targets (with different armor for example). This would address part of plaq's critique. Then e.g. Desolator would be treated explicitly as an armor reducing item, rather than just giving +43% physical damage, as I have coded it now.

I might be able to look at that in a few weeks.

Hamstertamer's suggestions are also good, of adding more kinds of effective hit point measures, for example a mix of physical/magic. But MKB's bash deals both physical and magic damage, so I don't think you can calculate a special EHP for just MKB without knowing the item composition of the attacker.

Regarding applicability: I realize that some people in the forum play competitively, so naturally, your first approach is to try to find something useful that can be applied in the game...and seeing stuff like Bloodthorn + Divine Rapier popping up does not look serious. :)

For curiosity, I removed Bloodthorn from the search as suggested. The best combo to max DPS then becomes (tested: Mirana, Anti-Mage, Necrophos, Axe)

Power Treads(AGI) + Daedalus + Manta Style + Desolator

DPS is ca 2250 on Anti-Mage and 2000 on Mirana. So Butterfly still doesn't show up for max DPS. For comparison, when I pop in Butterfly instead of Desolator, DPS goes down to 2039 for Anti-Mage, but EHP(physical) goes up a lot (3950 -> 6917).

Again, Butterfly is a defensive item :)

I think you're still biased by the fact that you hardcoded Desolator armor reduction to be a 43% damage increase.

https://hydra-media.cursecdn.com/dota2.gamepedia.com/d/d0/Dota_2_armor_debuff_efficiency.png

It's only a 43% damage increase on a hero who has around 7 armor. Take a 20 armor hero, it's more like a 23% damage increase instead.

I think you could do something like take the average of the curve somehow, like assume the enemy hero is sitting at 15 armor, or 20 armor. Those are pretty realistic values in a typical game when people are 4-slotted.

Thanks, that's a handy plot. I eyeballed 43% from another graph. I agree that +43% is too optimistic. Adjusting Desolator dmg to +25% (armor 18ish) shifts the bias to... another Deadalus! Again, on several heroes.

But to highlight how little difference there are between certain builds:

Anti-Mage lvl 25: Power Treads(AGI) + Daedalus + Manta Style + Desolator => DPS 2250
Anti-Mage lvl 25: Power Treads(AGI) +2x Daedalus + Manta Style => DPS 2228

It is likely within the error margin of the simulation. So just because attack speed items do not show up as optimal choices for DPS does not mean that they are bad choices per se. It could be that they just give 1-2% less DPS. That can still be ok, given other benefits.

Hmm... looking good :)

Maybe you can try heroes with multiple units, then factor in stuff like Necronomicon units and auras like Vlads and stuff! That could be very interesting.

you can't have deso orb on antimage if you ever skill his mana break

Thanks for the answer PsychoKitten! I see what you mean. Keep us updated on your progresses!

Btw, would you mind running that model for me, that is, for Crystal Maiden specifically, or is it roughly the same as the initial model since you also used Necros?

I'm writing this official guide for her and I play her a Lot, so some of the things of you said and the conclusions from the model are helping me rethinking my build :)

I don;t think it generalizes to all heroes. Someone like Lina, Windranger, or Huskar has garbage illusions, but scales more with attack damage.

Lina would probably want something like 3x Daedalus for max damage, Windranger would want Aghanim's Scepter + 2x Daedalus and Huskar insanely low HP and I have no clue what items, as his passive is annoying to calculate things with.