Talk:Item passive stacking

Pseudo-Independent stacking
Im fairly certain that the claim about PRNG stacking being almost additive is false. I understand where the idea came from, but the claim is completely unfounded in any hard evidence.

I did not do the math to disprove this, however I made a simulation where you can plug in how many daedaluses you are using and it simulates whether your right clicks crit or not based on a PRNG roll and the formula for PRNG from the wiki. I cannot link the code since the wiki considers it harmful, let me know how to link it (its in a javascript fiddle).

The resulting chances are very much in line with what you would expect from a true RNG diminishing returns stacking.

The simulated chance to crit - with 1 daedalus is ~ 0.3, with 2 daedalus about 0.5, with 3 about 0.675, with 4 its ~ 0.76, 5 ~ 0.825. Compare this to the true rng diminishing stacking, 1 daedalus - 0.3, 2 daedalus - 0.51, 3 daedalus - 0.657, 4 daedalus ~ 0.751, 5 daedalus ~ 0.832. This claim of additive stacking needs clarification.

Now I dont wanna do a formal proof of why even with PRNG the diminishing returns are the same, but I would start with the fact that the expected chance of a crit occuring on any single attack from one Daedalus is 0.3, even with PRNG. Whats going on behind the scenes, the counter being independent doesnt change this fact. This means that at the limits its still 0.3 for the first to crit, 0.7*0.3 for the second to crit etc, which is the same as if it was true RNG.

Did some more testing ingame, which confirms additive stacking. So it is a thing. However the explanation here on the wiki doesnt really do it justice, it should work that way.

--Kokorok0 (talk) 13:50, 18 January 2017 (UTC)Hi, I was the original author who wrote about the additive stacking of PRD-based items because based on my observations in-game it seemed to work that way. Later on my friend proved to me mathematically that PRD should not differ from true random, so I am aware of your argument here. It is just that the PRD in DOTA seemed bugged seeing that PRD-related item seemed to stack additively in game, so now I'm at a loss as to how to craft this section. It would of course be more accurate to write straightoff that PRD has no significant difference from true random and thus PRD-related skills should not be able to stack additively, but seeing that the stacking is occurring in game, telling people that the stacking works can help them make a judgment for item decisions (usually daedalus).

--Tommassino 15:08 18.1. 2017 Hey, we are currently discussing this with a few more ppl on /r/truedota2 in how_many_daeduli_is_too_much_deaduli. The closest we got so far is that during each attack the PND counter increments for each PND item, then you go through them whether they proc or not and the first one that procs gets its counter reset. This means that if any of the items proc the rest get a 'free' counter increment. This definitely seems like it might not be intended.

--Kokorok0 (talk) 14:50, 18 January 2017 (UTC)I think it is supposed to work that way though? Because the PRD counter of each item is independent, so even if (for example) 1 out of 4 daedalus procced and the other 3 did not proc, the PRD counter for the other 3 should theoretically still increase because they did not proc on that hit. Unless you're saying that if one of the daedalus procced then the system no longer checks for the rest of the daedalus for whether they procced as well, then yeah it should not be intended.

Chance Stacking
I believe there is a mathematical error in the example on 'chance stacking'. When a hero has both Daedalus and Crystalys, you don't get 25% chance for Daedalus, 20% chance for Crystalys and 5% chance to proc both, for what I know.

Instead, you get the following:
 * chance to proc ONLY Daedalus: 25% for Daedalus * 80% for not proccing Crystalys = 20% chance
 * chance to proc ONLY Crystalys: 20% for Crystalys * 75% for not proccing Daedalus = 15% chance
 * chance to proc BOTH:          25% for Daedalus * 20% for Crystalys = 5% chance
 * total chance to get any proc: 20% + 15% + 5% = 40% chance

Now, I'm aware that a mathematical calculation like this will probably only make the article too confusing. So I think it might be better to just change the wording instead.

So instead of:
 * "If a hero buys a Crystalys, and then a Daedalus, on every hit the hero has a 25% chance of receiving the Daedalus critical, a 20% chance of receiving the Crystalys critical, and a 5% chance of receiving both"

...which wrongly implies you have a 50% chance to get any critical, I would put something like this:
 * "If a hero buys a Crystalys, and then a Daedalus, on every hit the hero has a 25% chance of receiving the Daedalus critical and a 20% chance of receiving the Crystalys critical, both of which include an overlapping 5% chance of receiving both, resulting in a total 40% chance to receive any critical."

or this:
 * "If a hero buys a Crystalys, and then a Daedalus, on every hit the hero has a 20% chance of triggering only the Daedalus critical, a 15% chance of triggering only the Crystalys critical, and a 5% chance of triggering both"

A similar error seems to have been made in the calculation with the MKB's:
 * MKB bash chance: 35%

>>lol, why 65%? correct answer should be 0.35*0.35*2 = 24.5%
 * Chance of triggering both bashes: 35% * 35% = 12.25%
 * Chance of triggering only one bash: (35% * 65%)*2 = 45.5%  (instead of 2*35% - 12.25% = 57.75%)

I should note that I haven't tested this data ingame. I'm just assuming it uses the mathematically correct way of combining chances.


 * You are correct. The language should indeed be corrected to reflect the actual probability. -Baloroth 20:52, 30 March 2012 (UTC)

Crit Priority
Apparently, if multiple crits are triggered simultaneously, the game gives priority to the crit with the highest multiplier, not the one that was acquired last: http://dev.dota2.com/showthread.php?t=5071. Someone should adjust the information accordingly. Would be really nice if Valve explained how all these low-level mechanics work themselves but oh well. --Pigbuster 04:45, 5 July 2012 (UTC)
 * . I also update the note on MKB, since that stacks on ranged and melee now just fine. -Baloroth 16:27, 5 July 2012 (UTC)

Evasion
"Only the highest value works per instance."

Evasion stack multiplicatively according to 6.79 changelog.

On other pages it is mentioned that evasion "stacks diminishingly" which is completely wrong. For example 1 Butterfly gives 35% chance to evade, thus 65% chance to be hit. This means a survivability of 1/.65 = 1.538... or 54% increase. Two Butterflies give a total of 57.75% chance to evade, or 42.25% chance to be hit. A naive interpretation would lead one to believe that this is "diminishing returns" since 57.75 < 35 * 2. But running the numbers will indicate the survivability is 1/.4225 = 2.366... or 136% increase in survivability.

But wait, what's 2.366.../1.538... ? Well it's 1.538... exactly the same as the value of a single Butterfly. Evasion does not have diminishing returns, it has multiplicative returns that increase by a linear factor. It's easy to see with an imaginary item with 50% evasion. The first would double your health, the second quadruple, the third would give an x8 multiplier, and the fourth an x16, etc. You can clearly see each additional item multiplies by 2.

Misunderstanding of evasion and armor as being "diminishing" is probably one of the most common mechanical misunderstandings around.

Vanguard
Vanguard now have 100% chance block 32 damage. So "Chance stacking" section should be changed. So do Daedalus.