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

A few patches ago, he made a video showing what would be the mathematically correct build for Kayle. To do that, he wrote a script that calculated the optimal build. I was fascinated by his work, so I reached out to him and asked for permission to use the foundation of what he had already created and continue working on finding the mathematically correct build for Kayle.

He gave me permission and allowed me to use his code and everything else. I actually ran the calculations a few patches ago, but I didn't keep the results updated.

Until now.

With the recent changes to Runaan's Hurricane and Yun Tal Wildarrows, I decided to run the calculations again and see what the optimal build looks like right now.

But this time, I wanted to go a little further.

I rewrote the script to search through ALL items in Riot's database using the Data Dragon API. I also set it up to automatically query the database and load the most recent item data from each patch. In other words, with this new version of the script, there is no longer any need to manually update the stats of each item.

Just run the script and enjoy the new build.

Well... not quite.

With this many items, the script had to calculate approximately 2.8 billion combinations.

Yes, 2.8 billion.

And that took an entire day to process on an R7 5800X.

But we have a result:

Available items: 204
5-item builds: 2,802,350,040

Starting optimization...
2,802,300,000 / 2,802,350,040 (100.0%)
Optimization completed.

BEST BUILD — PRIMARY DPS
Hexoptics C44
Infinity Edge
Stormrazor
Guinsoo's Rageblade
Kraken Slayer

Primary DPS: 2,281
Secondary DPS: 330
Score (1 + 2×): 2,941

BEST BUILD — SECONDARY DPS
Infinity Edge
Runaan's Hurricane
Rabadon's Deathcap
Nashor's Tooth
Shadowflame

Primary DPS: 1,656
Secondary DPS: 1,870
Score (1 + 2×): 5,182

I plan to improve this post over the next few days, add some images, and release the code for anyone who wants to test it themselves.

For now, I'll just share the items.

IMPORTANT: Even though this is the "mathematically perfect" build, it does not necessarily mean it will be the best build throughout an actual competitive game. The power spikes are very different from those of a pure AP build.

My goal here is almost entirely scientific. So please don't criticize the build simply because it is different from the way you normally play Kayle.

The point is to find the mathematically optimal result based on the parameters being tested — not necessarily the most practical build for every game.