I'm currently bouncing between D2 and Masters (https://lolchess.gg/profile/na/banlandoruspls). It’s a long post because I want to be as transparent about the analysis as possible, so I’ve bolded the most important parts. I've attached my code here, but do note that I plan on cleaning it up to keep it maintainable and easy to develop for future TFT analysis of other champs. This code is kinda scrappy in the meantime, but hopefully understandable.

Brawler/Blaster is commonly seen as a top 4 comp, but with the recent nerfs to Dark Star and Star Guardians, we could potentially see it rise to become one of the best comps this B patch. However, even in high elo streams, a lot of people aren’t sure what the best items are for Jinx- is it double giant slayer? Giant slayer last whisper? What about infinity edge? There’s a lot of questions to ask, and I hope to answer them all through a very detailed mathematical simulation.

First of all, do not build red buff on Jinx. Any of your blasters can apply the exact same burn onto the enemy, there’s literally 0 point to put this item on Jinx considering it doesn’t even give her any offensive stats. Yes, red buff is absolutely essential on blasters, but don’t put it on Jinx.

As for the candidates of item builds, I had to limit my choices to the following: GS/GS/GA, GS/LW/GA, IE/IE/GA, IE/LW/GA, and LW/GS/GA. I ended up choosing GA as a defacto third defensive item, I don’t think the 15 AD makes a huge difference for the results and one should feel free to use Trap Claw, QSS, or whatever defensive item might be best for your game. Still, I don’t think it’s immediately obvious to anyone which build will end up being the best among these 5.

As for how I did the simulation- I was inspired by /u/MismatchedSock and his Jhin analysis for IE vs LW, and I very roughly had a similar setup, but with a lot more challenges. Unlike Jhin, Jinx has varying attack speed not only from the different builds that I wanted to do, but also from her passive after one takedown. Furthermore, I also took into consideration the blaster 4 bonus. Finally, Giant Slayer depends on the enemy current health- I have to model the enemy’s health AND armor.

So basically, for each build, I simulated Jinx taking down enemies of X health and Y armor, where X ranges from 500 to 2500 health (1* units to 2* Cho’gath with Brawler 4) and Y ranges from 0 to 360 (which is Vanguard 4 armor items), 1000 times. Based on all those trials, I can calculate the average amount of time in seconds it takes (which is necessary because of the varying attack speeds) for her to get the kill. I can then keep track of which build got the takedown the fastest for each type of enemy. I also simulated whether the enemy had bramble vest or not.

The following graph is a heatmap of the results for Jinx before her passive attack speed bonus, against enemies with no bramble vest. In order to read the plot, simply find the (armor, health) coordinate of the opponent you care about, and the color of at that coordinate indicates the build that took that opponent down the fastest.

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https://preview.redd.it/8xr5vmygkeu41.png?width=441&format=png&auto=webp&s=814ac1411b3f833a62e3932acf09232b13083565

How do we interpret this result? Here are some of my insights:

• Against anything less tanky than a 2* unit with Vanguard 2, double IE is good, followed by IE/GS
• Against 3* units with little armor or 2* brawlers with Brawler 4 bonus, double GS is best, followed by IE/GS
• Against 2* vanguards with Vanguard 4, IE/LW is best
• Against 3* vanguards with vanguard 4, LW/GS is best

In other words, your itemization on Jinx heavily depends on the lobby! For example, let’s say you see several vanguard sniper players. You should strongly be considering IE/LW/GA. However, GS/GS/GA is better for the brawler/blaster mirror match. But against arguably weaker frontline comps (4 Chrono Kayle), I would probably advise IE/GS/GA. The only thing I probably wouldn’t do is double IE, because it doesn’t scale well into the late game.

I will say, keep in mind that Jinx’s first takedown is usually whoever Blitz hooks (because you should position your Jinx to be right next to your Blitzcrank)- I think therefore it’s within reason to assume that a fair number of your first takedowns will be 2*, non tanky units that people tend to throw away in the corner.

The following plot shows which builds do well for her second takedown, with the increased attack speed.

https://preview.redd.it/2s4032pikeu41.png?width=441&format=png&auto=webp&s=27b00362c186d4f0d8cf0c9f9641a51675c92c78

After you gain the attack speed bonus from passive, it seems clear to me that two builds stand above the others: GS/GS/GA against non-vanguard players and LW/GS/GA against vanguard players.

Finally, the next two heatmaps are Jinx against bramble opponents.

https://preview.redd.it/o86vazndkeu41.png?width=441&format=png&auto=webp&s=0fd1c45bdbba81d2d8228be60b23c2f641918f6a

https://preview.redd.it/f0bnz0zekeu41.png?width=441&format=png&auto=webp&s=91c791b7ba784bd74c34b8189c0f3b3ed92afec2

Clearly, for anything that equips bramble vest and is not Vanguard, GS/GS/GA is optimal, and IE/LW/GA is optimal against Vanguards with bramble.

Edit: Just noticed that the first plot starts from 0 armor (which can't happen with Bramble, you have minimum 50 base armor). So actually, IE/LW/GA is best for pretty much any case with Bramble.

TL;DR Based on all the analysis above, my personal two builds that I would recommend are GS/GS/GA (if there are not many vanguard players) and IE/LW/GA (if there are several vanguard players or bramble players). The second build in particular I feel is overlooked by most players.