Posted 06-14-2012 at 08:47 PM byKuroNeko Updated 08-03-2012 at 06:03 PM byKuroNeko
We've all heard it before. "Crits don't stack noob." But it's only partially true. If your hero has more than one crit, the crits will "partially" stack, as the last acquired crit will override the other when they both proc, so you waste a portion of the dps.
I've done this before, but I think the item stats have changed since then. Anyway.
>> Note: most of this post is math, so skip to the bottom half of the spoilers if you trust me and just want to know the results
It's sort of like stacking spell resistance.
Hero: 25% --> 25% resist
Hero w/ Hood: 25% + 30% --> 52.5% resist
Hood lets a normal hero resist 27.5% more of incoming spell dmg.
Conclusion: Magina gets (a lot) less bang for his buck buying hood than a normal hero does. Let's see if the same applies to Mortred.
(overall he would be better off buying raw hp than spell resist against nukers, which is why vanguard is effective on him)
I'm going to start off with some estimation, disregarding the +15% AS from mkb. It shouldn't matter a whole lot anyway for now since Mort has truckloads of agi (2nd highest agi growth next to Terrorblade) and an ability that adds 100% AS, right? Well, I'll come back to this later. This is just to get some ballpark numbers for what these items are really giving you.
Buriza: +81 dmg, 25% for 250% dmg
Mkb: +88 dmg, 35% for 100 dmg
Melee bashes deal magical damage, so this means that Mkb adds 88 physical damage along with 100 magical damage on 35% of attacks, or an average of 35 magical on every attack. So we are left with the following:
Damage from a critical attack is calculated by the damage gained (difference between the crit damage and your usual attack) and the probability of landing the crit.
A usual attack deals 100%. If a critical has a 30% chance to deal 175% (the stats of Lycan's shapeshift crit btw), then the difference is 75%.
Therefore, 30%*75% = 22.5% or a +22.5% damage increase. Calculate other crits the same way.
Like I said earlier, if you proc 2 crits on the same attack, the last acquired critical will take precedence. For skills, "acquisition" is determined by when you added the first point into it. Now, unless you're one crazy mofo CSer and somehow manage to rice a Buriza before hitting lvl6, then in the event of a double crit, Buriza will be overriding Coup.
Therefore, with both:
> 25% of attacks deal 250% dmg
> 11.25% attacks deal 250/325/400%
> (3/4)*15% chance for 250/325/400% dmg since coup will fail to proc on 25% of attacks
> 36.25% chance to crit some way or another (just fyi)
> Buriza provides +32.5% dmg
> Coup normally provides +22.5/33.75/45% dmg, but here it provides 3/4 of that, or
> 16.875% // 25.3125% // 33.75% dmg
Add the two together, and this is a net gain of 49.375% // 57.8125% // 66.25% dmg.
Rounded, about 49.4% / 58.8% / 66.3%.
Now for the meaty stuff, the actual damage calculations. Since we're ignoring the 15% attack speed from MKB for now, it's simply a matter of adding up damage. I'm going to call this DPA, or damage per attack, since we're talking about average damage and probabilities and whatnot. I don't think that you're going to get Buriza before lvl 2 coup at least, so I won't calculate it. See spoilers above if you're wondering where I'm getting my numbers, otherwise read on if you're the TL;DR type.
Assumptions: for now, I am assuming that PA is naked with no items, that the target has no armor, and P.S. I am ignoring Mkb's 15% attack speed bonus.
Mort starts with an average of 47 dmg. She gains she gains 3.15 agility (+3.15 dmg) every level (lvl).
This gets a little more complicated when Mort starts leveling Attribute Bonus... so I'm going to ignore that for now, too. >,>
Alright, so a naked buriza Mortred will dish out more damage per attack than a naked Mkb Mortred. Big deal, right? To be fair, I'll calculate the dps of both the build types using a few common items, this time counting in the 15% attack speed from Mkb. I'll be using a lvl16 Mortred, with HotD, str power treads, a magic wand, all skills maxed, with 1 level in stats.
If you don't already know how attack speed works, read up!
( 1 + IAS ) / BAT = Attacks Per Game Second
BAT / ( 1 + IAS ) = Game Seconds Per Attack
Attack speed has the lower limit of -80% and the upper limit of 400% for DotA (-80 < ias < 400). Let's plug in some numbers.
0% means (1/1) the attacks. (0.00+1)
100% means (2/1) the attacks. (1.00+1)
200% means (3/1) the attacks. (2.00+1)
300% means (4/1) the attacks, (3.00+1) and
400% means (5/1) the attacks. (4.00+1)
Just like for spell resistance, you're getting less and less bang for your buck if you keep slapping on attack speed items; you're getting the same amount of attacks per second per %IAS, but the improvement gets less meaningful each time.
Oh, and -80% means 1/5 the attacks. Useful if you're playing enchantress.
Now that we have attack speed out of the way, we'll be using the formula DPS = (attacks per second)*(avg damage per attack)
HotD gives +20 dmg, stats from wand give +3 dmg, attribute bonus gives +2 dmg, so I'll be adding in +25 dmg to my original formula
Damage Per Attack
DPA(b, c3, items) = 1.66250(128+3.15L+25)
DPA(b, c3, items) = 212.8 + 5.236875L + 41.5625 ... Mort is lvl 16, so L = 16
DPA(b, c3, items) = 212.8 + 5.236875(16) + 41.5625
DPA(b, c3, items) = 212.8 + 83.79 + 41.5625
DPA(b, c3, items) = 338.1525
As for attacks, we have a lvl16 Mort at 3.15 agi per level, 23 base agi, +2 agi from attributes, +3 from wand, and 25% as from treads.
Therefore the dps of this build is (293.83 + (26.25))*1.284705882352941 or 377.4851294117647+(33.7235294117647) damage per second.
Which is about [411.2 dps] or 377.5 + 33.7 dps
[414.5 dps] > [411.2 dps]!
It's not much, but it's there. Level up any more, put any more pts into attribute bonus, buy any more dps... and buriza will only lead further and further.
And honestly look how close the DPS's are. And yet people think that Buriza is a piece of shit compared to Mkb... and this is why, my friends, why doing the math is so important.
1) Mkb will be dealing relatively more damage from its bash the more armor the attack target has. However, also keep in mind that adding on any damage items e.g. bfury, deso, an aura, even damage from a bkb will only increase the discrepancy between Buriza dps and Mkb dps.
2) Whether or not you still want Mkb is up to you. True Strike is a good ability, and so are mini-bashes. But say you don't need mini bashes. Or true strike. And you think that you'll be farming quite a lot this game, possibly enough for a 2nd top tier damage item. Then consider Buriza.
3) After doing the math earlier (like last year) I realized that Buriza WITH Mkb can be pretty effective actually, minibashing AND critting with almost every attack. Consider this option.
4) Sadly, in the middle of the last calculations I realized that my graph functions count lvl = 1 as adding agility, gain*lvl, instead of gain*(lvl-1). This throws off the data by 3.15 agi. I couldn't really go back and redo everything, so just keep in mind that the calculations are a little over 3 dps off. Shrug.
If you've read this far, props to you and thanks for reading (or at least skimming). Spread the word. Peace.