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Over powered just doing this so it can get published
Assassin's Blessing
Warrior Tabi
Transcendence
Bloodforge
Ichaival
Rage
The Executioner
Heartseeker
Elixir of Speed
Potion of Power
Elixir of Power
Purification Beads
Blink Rune
379 power on 3 hits (ichaival +15 per hit max stack 3 = +45 on the fourth hit) with potion of power 419. 524 with elixir of power. Max attack speed with 2. Crit 45% 1000 depending on protections without potions. Lifesteal 15. Penetration against base pen at 78 protection is 38 pen against 200 protections 82 protections shredded against 400 protections is 154 protections shredded. Early game is good. Mid game is good. Late game over powered. Good in team fights if you have beads and an ult go in kill one person in seconds than ult out of there blink is also useful. Only characters that get to Arachne are Aphrodite with a push away a stun and invulnerable to damage and a heal. Then kumbhakarna you will shred even if he builds all defense but the problem is his 2 stuns and his ult makes it very hard to kill him with an ally besides them no others characters stand a chance.
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In addition, this also isn't a bad build in the fact you're covering other core stats such as penetration (Exe is key for basic attack builds), and when you DO choose to go with a single-crit item build,
That said, build-crafting is more than just about raw stats. It's about understanding the god's kit and which items synergize. For
- Power IS an important stat, don't get me wrong. Her passive gives her 1.5% added power for every 5% of a target's missing health. Higher power, higher % power effect. So you definitely want to build items with decent power.
- At the same time, power isn't the end-all, at least when it comes to ability use. Note that 2 of her regular, non-ult abilities aren't meant to utilize power much.
Cocoon doesn't deal any damage...it's an AS stim and CC ability. 
Web is almost always used not for the damage from the broodlings, but rather for the slow it provides to help you stick to enemies and prevent them from escaping (and the MS boost it gives you during that chase). As such, you typically want to focus on your DPS from basics, though ability-based builds can work.
- Not sure if you know, but
Arachne's attack progression is 0.5 / 1 / 1x. You're welcome to read the following chapter from my items guide which talks about attack progression and Qin's vs. crits, but otherwise, crit calculates off this progression. That first hit of 0.5 means whatever your base damage is ((base attack damage at your level + total power) / mitigations from protections), it's going to do only half that damage. Crit is double your base damage (not including additional % from the 
Deathbringer passive if you build it). But you're not building DB, only Rage, and this is all % crit chance, not a guarantee, so when you DO crit on that first hit, it will only deal the same amount as your normal base damage from your other hits.
- In the end, your better option isn't crit. It's
Qin's Sais. Qin's is an incredibly strong item for basic attack gods that have attacks below a progression of 1...the other big ***sassin user of this item is 
Kali, whose progression is similar to Arachne's, but even more powerful at 1 / 0.5 / 0.5x. Thing is, the Qin's passive bonus damage applies at the same amount on each hit, independent of the lower base damage you deal on quicker hits.
Not sure if this build is designed for Conquest or other modes, as it's not stated, but this build direction isn't optimal for Conquest. She has jungle clear issues, and so a common early-game pickup for her will beYou might see a typical build in the following progression:
If not for Conquest, then you can skip
If you combine Exe and HS's penetration on a squishy god with 70 protection, this would be (70 * 0.64) - 10 = 34.8 physical protection after 3 hits of Exe. They will be mitigating 25.82% of incoming damage from you.
Alternatively, if you got
Some of your calculations are going to be off as you're not factoring in the damage mitigation and other factors. If the build works for you, great, but I'm saying there are reasons she is typically built the way I described, and you might consider trying it out a few times to feel the difference. The build I provided is going to not only destroy squishies effectively, you'll also be a tank killer.
Asi (boots replacement)
Trans
Crusher
Exe
Heartseeker
Qins
Non conquest build, of course.