I did some math to find out which AP items were the best if you wanted as much damage as possible. I only did the math for Void staff, Horizon Focus, Shadowflame and Rabadon (considering you already have Luden and sorcerer boots).
In the end Horizon Focus is always higher if you can proc its effect. So I’m wondering why every Lux player for example aren’t buying it second item.
I think a lot of people dont run the numbers, but instead look at the general idea behind an item. Horizon has CDR while shadowflame has Pen. You’d assume off of that that Shadowflame damage > Horizon, but you’re right about it dealing more (as long as you can proc it). You can also proc it by slowing people which everyone and their mother can do so it should indeed have a higher pick rate than shadow flame. As a Shaco main, the reveal is almost more annoying than the actual damage. Champions like Shaco, Akali, Talon can’t get in safely for what feels an eternity just because Lux max range Eed you once right as dragon starts getting low.