Nashors Tooth is the best attack speed item you can build on Jax
Let's face it folks, Riot caters to ADC/Mage players who hate having their asses handed to them by a snowballed Jax, and our champ is shit.
Jax has had a sub 48% winrate in top lane for the last year or so, and he's currently at the bottom of the list with the new rageblade changes aside from Vlad who was EVISCERATED by Riot.
Jax needs an Attack Speed item and the new Rageblade is shit. It gives you 8% AS per auto so it takes longer to stack up and it does less magic damage. You will never proc it in a teamfight until the fights practically over and in lane the build path is so expensive/terrible that you will be annihilated before you ever get to use it (situationally).
BoRK has had its onhit effect nerfed to 6% HP on hit so it is also dog#$%@. Seriously try rushing this item folks. It used to be Jax's core item in that it let him duel tanks but as of now you're wasting your money on an item that hits tanks with a wet noodle and has a decent sticking power active. The fact that Hextech Gunblade does far more damage to all types of champs tanks/carries and gives you more sustain makes BoRK fundamentally useless.
So Gunblade is core on Jax, only because BoRK is so garbage, but we still need an attack speed item.
Trinity Force you say? HAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHahahahahahaha...
No. It gives Jax 0 AP, 25 AD, 15% Attack Speed, and 5% movespeed. All for 3800 Gold. What a deal. At least you have 20% crit chance now and you get 10% CDR! Seriously, this item is overpriced garbage. Riot made it an ADC item, not a bruiser item (like Rageblade). Sucks to suck, but you're only building a trinity force as a luxury item.
Wit's End is nice, but Jax wants more than just Attack SPeed and an on hit.
Which brings us to, NASHOR'S TOOTH.
The stats that this item gives are just MASSIVE on paper, and unlike Recurve bow, Stinger is a MASSIVE powerspike to sit on in lane. The more Attack Speed Jax has, the faster he stacks his passive and the more ult procs he gets on his enemies. Stinger gives Jax 50% AS which is massive since it is more AS you get than from a fully stacked rageblade and you ALWAYS have it.
There is a minor lull in the buildpath when you are waiting to complete nashors as Amp Tome/Codex aren't much of a powerspike, but the completed item all of a sudden grants Jax a whopping 80 AP and 20% CDR, and scaling magic damage on all of his Auto Attacks. Nashors Tooth gives you more attack speed, AP, and onhit damage than a fully stacked Rageblade and you get it all without having to stack it. You lose out on the conditional AD granted by Rageblade, but this is more than made up for the fact that you deal a lot more magic damage, you have 20% CDR for low CD leapstrikes/empowers/counterstrikes, and most importantly that you are always a huge threat and not half a champion until you have stacked 6 auto attacks.
I highly recommend trying this build out into matchups where you get to AA a lot. matches like trynd/riven/olaf/irelia/tanks, etc. Vs squishy champs, I would recommend a hextech gunblade rush which got buffed thanks to the instant hit active.
Nashors Tooth empowers all of jax's magic damage on hits and causes his abilites to hit like a truck.
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