This build has been undergoing changes and adaptations as the game updates, and the new season is no different. The old version of this build used Holefear's results as the final composition. I talked to him and decided to continue the work he started. I recreated the build calculation script and updated all the changes, that is, I added the new items and the NERFS TO KAYLE >:(
With this I had very different results and I was very happy with that. For those who have followed my builds for a longer time, you will remember that for a long time I put together hybrid builds, and the results for patch 26.1b are a build almost very similar to the one I have already indicated in previous patches, but with the nerfs to Kayle's AD damage, this build tends to be more AP in the end.

For those interested in studying the code, adding information, or correcting any errors, I'm making the repository available:
Kayle: Build Mathematicaly Corret

For core items, we have Nashor's Tooth and Kraken Slayer. These two items have great synergy and scale well with Kayle's damage. This combination also addresses a major nerf we received, which was the removal of attack speed based on AP. With these two items, in addition to high damage, we'll have a lot of attack speed.
In the third item, we have two options: one more focused on 1v1 fights and the other more focused on team fights. Guinsoo's Rageblade will continue the hybrid build pattern, giving us AD, AP, and AS. Runaan's Hurricane is an option for team fights because of its passive. In my tests, Guinsoo's Rageblade performs better, but I see that Runaan's Hurricane might be the better choice against predominantly melee teams.
Finally, we have a lot of AP damage with magic penetration. Our two final items will be Shadow Flame and Rabadon's Deathcap. Since Kayle had nerfs to her AD damage, this late-game AP burst performs better than AD+Crit damage, even with the increased critical damage this season.

For our rune choice, we'll take advantage of our high attack speed. So, for our primary runes, we'll go with Lethal Tempo. And for our secondary runes, we'll go with Bone Plating and Excessive Growth. There are two reasons for these secondary runes. First, our hybrid damage build on Wrath benefits from runes like Crescent Storm, as it will give us AP or AD. And the second reason is that I focus on playing Top, and these runes provide more security for fights and ganks.