Not sure how crit works

I play Carries every now and then, mostly Anti-Mage, and I notice a lot that whenever I do play a carry, I usually buy a Crystalis and then leave that alone to get my other items, mostly because I have no idea how crits work. I know that they make you do more damage, but it's not like a DD Rune that is just your damage x2, it's usually in percentages, as with Phantom Assassin's ulti, or Crystalis and Daedalus, and I'm not very good at telling how much this is boosting my damage at all.

Could anyone give me a simplified version if how much these things boost your damage? Like, does PA's ulti increase her attack damage by say, 4x?

PA's level 3 crit is 450% crit so it does 4.5 times your damage, juggernaut has a 200% crit so does 2 times his attack damage.

Btw dont buy crit first, it isnt very good early game and slows down your farm becouse you could be getting attack speed or lifesteal.

You'd just multiply the bonus by the chance to see what the average increase is. So reliably speaking PA's ult increases her attack damage output to (4.5 * .15 = .67) 167% with a level 3 Coup de Grace.

If you mean how much it increases your damage on average (rather than just when it Procs), Multiply your Damage by the Crit, then by the Chance to Proc, then just add you Damage again (since you'll always get a regular attack anyway) e.g...

Coup de Grace when Maxed has a 15% chance to do 450% Damage. At level 16, with Phase Boots, Drum of Endurance and Maelstrom, Phantom Assassin's Attack Damage is 105 + 48 for a total of 153. Since Crits take both into account your Average Damage

153 + (153 * 4.5 * 0.15)
153 + 103
256 Damage

So if you look at it another way, a Crystalis gives you an extra 35% Damage on average (after adding the 30 Bonus Damage), and a Daedalus gives you an extra 60% damage on average (after adding the 81 Bonus Damage)

P.S. Double Damage actually only Doubles your Base Damage, so if you have 123 + 24 Damage a DD Rune would give you 123 + 147 (123 Base, then 24 + 123 Bonus Damage)

P.P.S. This ^

360%=3.6x
200%=2x
What means that Phanton Assassin ulti hit deals 4.5x the damage (450%)
Remember: If a Hero buys both a Crystalys and a Daedalus, on every hit the Hero has a 20% chance of proccing a critical attack from Daedalus, a 15% chance from Crystalys, and a 5% chance of proccing both. Unlike the independent stacking, Daedalus overrides the Crystalys in the last case, because it has a higher critical damage multiplier and only one critical can proc on one hit.

See it like this: THere is a % of chance you will do a crit a % of dmg you will do whenever you hit a crit. For instance Chaos Knight has 10% chance to do a critical which is 1/10 ^^