Thanks I've included that.
Also realised that the formatting is buggered for the mathsey bits. I'll try and fix soon.
If i'm going for a second crit, I normally go demon edge first, idk if it's better mathematically but it made sense to me without theorying it
It depends on how much gold I have(Usually as Sven). If it is going well I buy a strait Demon's edge or if it is going less well, I get a crystalis.
@Guiri Hm. I didn't think about second crits. Because of the way the chance stacks I'm not sure which is more effective.
I might have a look tonight.
Neither am I, and I'm not a big math fan, that's why I just hedge my bets and *normally* go DE first, unless I'm struggling to farm.
I also find that the DE has more utility, I could swap to a divine if needed :D
Dude. I mean, DUUUUDE. This shit is calculated in ~4 actions, not in a freaking wall of smthng.
btw, for not being completelly off topic.
Daedalus gives more dps than MKB when your damage is 40 or more. But, there are few nuances...
I can't follow your math at all. You end results are fine but those equations! Try this:
cystalis adds 20% chance to do 175% dmg. If it were 100% then 20% chance is straight up 20% more dmg but the increase is only 75% on that 20% chance so 75% of 20% = 15% increase.
Increase chance X increase percent = increase
0.2 X 0.75 = 0.15 or 15%
Now for the other equation:
Demon edge = crystalis
d + 46 = 1.15 (d + 30) Multiply out the right hand side
d + 46 = 1.15d + 34.5 subtract d from both sides
46 = 0.15d + 34.5 subtract 34.5 from both sides
11.5 = 0.15d divide both sides by 0.15
76.667 = d
Here is something many people acually would be interested in.
What is more efficient?
1 deadalous
or
2 critsticks
Yeah... it's been literally 10 years since I've done even nearly that amount of maths :p
Kicking myself for not remembering I could remove 1 d from the right side by doing 1.15d -> 0.15d
Maybe that whole school thing was quite important.
Next step. Learn to English propa!
That's hard to quantify because daedulus is one slot while crystalis is two. It's like saying what's more efficent, 10 branches for 500g or an ult orb for 2100g? Obviously the branches are much cheaper but you don't have that inventory.
But if you want to know which gives more dmg increase?
Daedulus increase is 25% proc for 2.4x dmg or 140% over base
.25 x 1.4 = .35 or 35% increase in dmg from the crits
Total dmg added is 35% of your base plus 109 which is the 81 with an added 35%
Two crystaliss is just doubling the amount from before so 30% increase to base plus 69 dmg but there's a small chance to double crit. I think the math is:
.2 * .2 * 1.5 = .06 or 6% more dmg. That's 20% chance times 20% chance or 4% chance to double proc and you get 75 + 75% more dmg or 150% dmg.
I don't know if that's all correct but it's pretty close, total with two crystalis should then be 36% of base plus 81.6. So actually daedulus is more dmg cus 1% increase in base to make up 27.4 dmg you'd need to be doing like 2000 base. But efficency? The two crystalis cost 1250 less gold.
I guess if you have slots going two crystalis first and then upgrading one into daed might not be a bad idea.
Edit: Actually I overestimated the crystalis double crit because you were going to crit on one anyway so the amount added is a little over half that. It's probably between 3.5% and 4% increase, not the full 6%. I think that math is more complicated. Either way, daed > two crystalis but costs a lot more.
When I get back from work (unless someone beats me to it) I'll check the double Daedauls vs 2 x Crystalys and What's better to pick up first when going for a second round of crits.
I'll try to hide the eyesore that was my maths this time though 
Crystalys first /thread
By the time you formed up a crystalys you would have more than 76 base damage.
Dem double crits...
Double Crystalis gives 8% less overall damage increase and 33,15 less flat damage (including crit modificator) compared to one Daedalus.
Also, when you are going for a second Daedalus, starting with Crystalis is preferable in almost every possible situation.
Turns out that going for Daedalus instead of 2x Crystalys not only gives your more damage but is also more cost effective as you will be paying for about 3-5 gold per point of damage less.
small crit is more efficient for sure.
u get demon edge first if you are losing and you want to have the option of rapier open, plus you are getting pushed so getting the ss component asap means u can complete the daed in base.
ppl rly needs fuckin math for this?... what the fuck?? you would get birth killed if nazis were ruling the world .
this has been theorycrafted in dotatalk.com and other websites before, I suggest using google.
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Was bored last night so decided to work out the exact point where getting a Crystalys first is more beneficial than Demon Edge while building a Daedalus. I'm sure all the experienced players already know this but this but may help lower / middle level players with their purchase choices.
aanndd the magic number is [color=green]76.66[/color]
What does this actually mean?
Basically if you are hitting for more than 76.66 getting the Crystalys first will give you more average damage per hit than a Demon Edge so should be picked up first.
If you are hitting for less than 76.66 getting the Demon Edge first will give you more average dps.
What does this mean practically?
Realistically I can't imagine a situation where you would be aiming to get crits on a hero hitting for less than 76 and the Crystalys is cheaper so the "cost per damage" point is actually even lower than 76. On top of all of that it's also much easier to build the separate pieces of a Crystalys than a straight Demon Edge. So Crystalys all the way!
TLDR; It's almost always beneficial to pick up the Crystalys before the Demon Edge (from a purely mathematical stand point anyway)
Maths below for any geeks interested to know how I worked it out (and point out any fuck ups in my maths)
[code]
Crystalis Extra Dmg
-------------------
t = total damage
d = base damage
e = extra damage from crits
t = d + e
t - d = e
e = ( d x ( 75 ÷ 100 ) x ( 20 ÷ 100 ) )
e =( d x ( 3 ÷ 4 ) x ( 1 ÷ 5 ) )
e = ( d x ( 3 ÷ 20 ) )
e = d(0.15)
e = d(0.15)
Crystalis = +15% avg damage
Demon Edge vs Crystalys
----------------------
d = damage before Demon Edge or Crystalys
Demon Edge Damage = Crystalys Damage
d + 46 = 1.15 ( d + 30 )
d + 46 = ( d + 30 ) + 15 x ( ( d + 30 ) ÷ 100 )
d + 46 = ( d + 30 ) + ( 15d ÷ 100 ) + 4.5
d + 46 - 4.5 = ( d + 30 ) + ( 15d ÷ 100 )
d + 41.5 = ( d + 30 ) + ( 15d ÷ 100 )
100d + 4150 = 100 x ( d + 30 ) + 15d
100d + 4150 = 100d + 3000 + 15d
100d + 4150 - (100d + 3000 + 15d) = 0
100d + 4150 - 100d - 3000 - 15d = 0
4150 - 3000 -15d = 0
4150 - 3000 = 15d
1150 = 15d
76.66 = d
If you have less than 76.66 dmg Demon Edge is more avgerage damage
If you have more than 76.66 dmg Crystalys is more average damage
[/code]
edit: Fixed le maths formatting