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’m sorry, but can you share your math?
I will start with, the only good comparison is Shadowflame. Voidstaff and Rabadon have a different purpose, stats and cost.
That being said, HF deals more damage than SF only in 4 cases - against high HP and low MR targets, low HP and MR targets, and very high HP and very high MR targets, or if you have enough Penetration to deal true damage without the HF passive.
Since you are building Flat Penetration to burst squishies, you want the maximum damage on low to mid HP and low to mid MR targets, and while the margin is… kinda small, it is 100% in favour of SF. Furthermore, Flat pen works exponentially well the more Flat Pen you have. so having just more flat pen from SF is just better for the playstyle.
If you are against tanks, you may prefer HF, but tank-busting is not the job of a mage.