Attention - Hotfix: There was an error in the build I previously posted: Rabadon's was increasing AP by 130% instead of the correct 30%. Because of this, the AP build with Terminus appeared to be the right choice. I identified the error and, after correcting it, arrived at this new result.

"Don't worry, I'll scale." You might have seen this intro in one of Hylofear's videos.

A while back, he made a video showing the mathematically correct build for Kayle. To do this, he wrote a script that calculated the ideal build. I was fascinated by his work, so I reached out and asked for permission to use the foundation he had created and continue the search for Kayle's mathematically correct build.

He gave me permission and authorized the use of the code and everything else. But this time, I wanted to go a step further.

I rewrote the entire script to search through ALL items in Riot's database using the Data Dragon API. I also configured it to automatically query the database and load the latest data for each item with every update. Additionally, I separated the sections regarding item passives to gain greater, more reliable control over the results. In other words, with this new version of the script, manually updating each item's stats is no longer necessary.

PROS + Massive Scaling + Mixed Damage + Difference Between Teamfights + Solo HyperCarry Since our final build focuses on attack speed and critical damage, Kayle benefits from extremely aggressive scaling. From level 11 onwards, the waves from her passive Divine Ascent, are modified by critical damage and interact with both of Muramana's passives. Ultimately, this setup takes longer to reach its power spike compared to the standard AP-based build; however, the final damage output is considerably higher, making her solo hypercarry profile even more dominant.

CONS - Weak Laning Phase - Item Dependency - Vulnerability to Ganks - Enemy Focus The downsides of this setup are essentially the same as those of any other Kayle build, but it takes even longer for you to start helping the team; simply playing well, farming safely, and managing the early game isn't enough. You are heavily reliant on the match going long—meaning if your team throws the game early on, you effectively won't get to play at all. With an AP build, you can still contribute a bit earlier, but with a crit build, you need at least 50% crit chance and Infinity Edge to make any real impact.

Precision

I conducted empirical tests for the runes. I went into practice mode and tested every variation. Since the focus is on DPS, the choices are quite limited—basically, it comes down to Lethal Tempo versus Press the Attack. Lethal Tempo yielded slightly better results than Press the Attack, which is why I chose it for this build; however, if you prefer playing with Press the Attack, the final damage difference won't be significant.

Personally, I like playing with Presence of Mind, but since Tear of the Goddess is one of the first items in this build, it doesn't make sense to take another rune for mana regeneration. Kayle's abilities—especially in the early game—have long cooldowns, so you won't be spamming them and running out of mana. Because of this, our options come down to Absorb Life and Triumph. Triumph is great, but since it will take a while for you to secure kills, Absorb Life is the ideal choice—especially considering how weak you are early on, making any health regeneration welcome.

There aren't really any secrets when it comes to Legends; since our focus is DPS, Legend: Alacrity is the obvious choice.

Our last three options are generally very good, and each offers increased damage depending on the situation. Coup de Grace is perhaps the least appealing; since the Starfire Spellblade ability already deals bonus damage based on the target's missing health, the rune would be redundant for executing enemies. Last Stand is practically standard for Kayle, and it makes sense, as it allows you to win almost any matchup at level 1. However, since this build relies on the game going longer, bruisers—and especially tanks—can be a real nuisance to deal with; this is compounded by the fact that our item build lacks penetration (relying solely on the Radiant Blast (Q) ability), which is why I opt for Cut Down to help address that. That said, choosing any of the other options wouldn't necessarily be wrong.

For the secondary tree, I chose Sorcery to boost ability power. However, it is crucial to adjust this secondary setup when facing champions with heavy CC—such as Nasus, Tryndamere, Singed, etc. In those matchups, always take Celerity, Movement Speed, Tenacity, and Boots of Swiftness. With this combination, you’ll have a much smoother time during the laning phase and throughout the game in general.

To wrap up, here is another empirical test. In training mode, I compared two Adaptive Force options against a combination of Adaptive Force and Attack Speed; the option with Attack Speed ​​yielded higher damage. As for the final choice, Health is always good for Kayle, but Tenacity and Slow Resist is very useful in certain matchups.

As for the items—despite them being the most important aspect—there is perhaps the least to explain, since they stem from mathematical results rather than actual gameplay experience. However, I can highlight a few points that make sense and explain why this combination works. Muramana works very well on Kayle because, starting at level 11, her waves of fire apply the item's ability damage bonus, while her basic attack applies the on-hit bonus, resulting in a double application of area-of-effect damage. Additionally, the item provides a significant amount of bonus AD that scales with the champion's maximum mana. Critical Strike Chance are extremely powerful on Kayle because her waves—starting at level 11—also benefit from critical hit modifiers, creating a strong synergy with Muramana. Following this logic, Infinity Edge is a must-have to boost damage, alongside Phantom Dancer for attack speed and Stormrazor to round out the damage and attack speed stats. In matches where selling your boots for an extra item is an option, Yun Tal Wildarrows is the best choice; it not only caps your critical hit chance at 100% but also provides even more damage and attack speed. A possible variation is to swap Phantom Dancer for Runaan's Hurricane. You will deal less single-target damage, but more area-of-effect damage. Boots vary quite a bit. Although Berserker's Greaves are ideal for maximizing DPS, you need to evaluate things on a game-by-game basis. You’ll already have plenty of damage from your other items, so there is room to mix up your choice of boots. Boots of Swiftness ​​are excellent in many situations, but Magic Resist and Armor boots are also useful.

COMMING SOON
I plan to share the code with the community and turn this into a collaborative effort, but since I cannot include a link to that famous repository with an octopus mascot, I am still looking for a way to do so.
For now, I will continue sharing the results.