Explain CTH to me! (in General)

This is a battle of me fighting Karn-Silver Golem.
Play-by-play
Arpen Karn-Silver Golem
Nemia Lor cast Dispel Magic on all enemy Minions (1,512,175)
cast Dispel Magic on all enemy Minions (320,058)
Ranged Combat
Nemia Lor's shot flew past


Nemia Lor's explosive shot hit [188634], [52391], Karn [41218]
absorbs damage [30,000]

R.I.P.

Nemia Lor's shot ricocheted near


Nemia Lor's explosive shot hit [174722], Karn [37584]
absorbs damage [30,000]


Nemia Lor's explosive shot hit [242531], Karn [54806]
absorbs damage [30,000]


Nemia Lor's explosive shot hit [170309], Karn [38731]
absorbs damage [30,000]
's Decay hit Nemia Lor [366,080]



His front minion that I'm hitting all of range has DB's and 20 Dex. I have PTH and 542k Dex.

Shouldn't I be getting a CTH of 160, making missing impossible?

How much pth do you have?

+75

If you take a look you can see that karn's DBs are +154 which means they grant 153 evasion. Evasion cuts into your dex granted cth after it has eliminated all of your pth.

This means that with full dex advantage you end up with 82 cth with no other penalties. In the first few rounds there are also ranged penalties to cth so it is probably closer to 50-60 for those couple rounds. This would be the reason why you are seeing misses.

Oh, I see now. I thought that DB's couldn't cut into Dex-based PTH. They can, but only down to the base hit value of the weapon.

Exactly

I consider our to-hit system as the most convoluted part of the game, so you're not remotely alone in having to ask about it.