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Let me be clear if you do the math on Ahri Everfrost ALWAYS does more damage then Luden as you have 20% extra AP ratio on Everfrost. The only situation when Luden might be better is if you can proc it twice in a prolongued duel, but for what Ahri does most of the games which are picks and burst Everfrost is far superior in both damage and utility.
Besides the Active you don't benefit as much from a Penetration build, full AP is usually better, as you have a total of 348% AP (/w Everfrost and Electrocute) while hitting your whole kit, and and the 10 AP mythic passive while slightly inferior is comparable to the Penetration from Luden due to Shadowflame making it possible to reach 38 Mpen without Luden/Proto.
Moreover Shadowflame is better then Horizon focus as 2nd or 3rd item, but worse as 5th