Hi, i'm a normal player of league with some experience with ADCarry. ONE month before the release of Jhin i create (and improved) the - from my point of view - the perfect build for this cool champ! Oh, just one more thing before start: i'm not english, so don't mind if you see some errors, if you have problems to understand say it to me in the comment below!

The first thing you obviusly saw was that 4 glyph of attack speed. The runes you're seeing are the ones i use with all my adcarries, 'cause are simply perfect. They're a little risky for that missing magic resist but trust me, you always need to take some risk as an adcarry, support need to work save us! Eheh...

Than, Masteries:
Fury for that 4% ATKSpeed you want!
Double Edged Sword or Feast at your choice.
Vampirism 'cause yes, c'mon take that 2% lifesteal!
Bounty Hunter is better than Oppressor because after 3 champs you kill you have 3% bonus damages, and so, more damages.
Battering Blows are you seriously want to ask why?
I'm preatty sure that Warlord's Bloodlust and Fervor of Battle are the better choices! The first one for the fourth always-crit shot of Jhin and for the high crit chance i built through the games on him, or if you want MORE damages on hit the second one, because you always start a fight with W and Q if you're not sniping far away, so you instantly stack 4 stacks of FOB. More Damagy.
Savagery for helping farm.
Secret Stash Like a potion, but better!
Merciless those 5% bonus damages when enemies are under 40% of maximum health are great for a sniper like you!
Dangerous Game It can simply saves you from a tick of ignite after a heavy duel or fight.

I've seen some.. ahm... bad builds on game, from my point of view they're particulary wrong.
But we don't want to act like those false artist of death of them, don't we?

FIRST OF ALL A TIP:

Jhin is a mid-late ADCarry! He's like vayne and twitch in some ways, you can do some engages early but CAREFULLY! I advice you to focus on farm during early to reach the golds for BOTRK and Berserker.

START:

So, for begin the classic start of the Doran's Blade + biscuit combo, it's perfect. Some HP, AD and LS, what's better for sustain?

Now the problems comes: i seen some first items on him really.. odd. Before you ask, no, Rapid Firecannon is not good as first item.

CORE:

Let's start like a real mid-late ADCarry: rush Blade of the Ruined King and Berserker's Greaves the fast you can. I will explain why BOTRK later, in the chapter of "Let's have some Mathemathic Moments"
Than you need and high attack speed + crit chance item. I ALWAYS build Phantom Dancer. It gives you 45% ATKSpeed, 30% crit chance, 5%(+7%) movement speed, those stats are pure PERFECTION for you! You can build Statikk Shiv if you're a purist but keep in mind: those 10% of atkSpeed less on Jhin are 2.5% less of AD.

MID-LATE ITEMS:

Passed core items its time for ignorant damages (MOTTO.. MOTTO MOTTO CHIKARA DA!!! -cit.): Essence Reaver is a fantastic item on Jhin, 'cause you spend a lot of mana for be usefull in fight and you can simply stay there like a Jinx without mana, she's an hyper carry, you're a buster, things are different. So rush it and than buy Trinity Force and Infinity Edge.

Now the boring stuff comes.

tl;dr

more ATKSpeed + more Crit Chance = too much AD(640+).

So sum up the stats we're interested of that we have from the basic build i wrote:

Base AD of Jhin at 18(only one stat we're interested of him):

113

Stats From Runes + Masteries:

Stats from items:

Total AD: 113 + 8.55 + 180 = 301.55
Total Bonus ATKSpeed: 20 + 130 = 150%
Total Bonus Crit Chance: 90%

Now that we have the stats we needed we can use them for our math.

First of all, Jhin have 40% AD Bonus at level 18, than he have +4% per 10% crit chance and +2.5% per 10% bonus attack speed.
Now we'll convert ATKSpeed and CCh in the percentuals we need:

So the calculation is:

301.55 + 40%(120,62) + 37.5%(113,08) + 36%(108,56) = 643,81

643,81 AD.
If under effect of unique passive Spellblade of trinity: 643.81x2= 1287,62 in one hit.
Still not convinced? Let's add damage from crit (they're reduced by 25% but we have Infinity Edge so we deal 187,5% as crit) 1287,62 x 187,5% = 2414,29.
AND if you're not convinced though you still need to add 25% of the target missing health if the bullet is the fourth.

The only problem of this build is that you don't build any kind of armor pen, except for the 7% you recive from masteries, so watch out versus target with too much armor (they need anyway at least 300 armor for resist at your 4th shot without taking serious damages).

Hope that this build will work with you too. I ALWAYS end in positive with this build and the other Jhins i fought (built in disgusting ways) always took kicks from me.

Last thing, yes, this build is viable top and mid too!