Yeah, just an interesting little tidbit about good Jax builds. For those who don't know, the reason everyone has been screaming for Jax nerfs lately is his new passive ability -

For every one attack damage from items, Jax gains 4hp, and 2hp for every point of ability power.

Now, a few people realized that of course, Jax's newfound high HP would work naturally well with Atma's Impaler, especially since he relies on doing more damage. With HP easily reaching 3k+ in mid-late game, Jax can turn that into over 60 more damage with less than 2500 gold.

Well, those paying attention when they buy Atma's impaler will notice their HP rise, usually by about 200hp when they buy it.. then a couple seconds later, it rises again by about 20hp or so.. this is due to Jax's passive ability, and the way Atma's Impaler works.

The description on Atma's Impaler can be slightly misleading: "Physical attacks deal an additional 2% of your max health in damage." In actuality, it increases your Attack Damage by 2% of your max health, which of course, means it increases Jax's max HP on top of it - and when his HP raises, it increases his damage a bit more. Infinite loop, except that I doubt the game recognizes numbers below a certain size, not that those numbers would matter in game terms anyways.

Aaanyways, I took the time to calculate the degree to which Jax's passive synergizes with Atma's Impaler.

1 attack = 4HP

4 HP = .08 attack

.08 attack = .24 hp

.24hp = .0048 attack

.0048 attack = .0192 hp

So. With Atma's Impaler, for every 1 attack damage from items, Jax gains:

.0848 attack

.2592 HP

And every 1 AP gives jax .04 additional attack damage from Atma's.

Basically, what this means to you, is on top of the normal bonus every champion gets from atma's impaler, Jax benefits from it with an additional 8.5% damage from items, and obviously 8.5% more HP from damage from items.

Example - one B.F. Sword gives Jax 50AD. Lets just say he happens to have 1800 HP before he buys it.

Jax's passive increases his HP to 2000. Jax buy's Atma's Impaler.

Immediately, Atma's turns his 2000 HP into 40 attack damage. Jax's passive ability turns that 40 attack damage into 160 HP. Atma's turns that into 3.2 more attack damage. Jax turns that into 12.8 HP. Atma turns that into 0.2 damage.

Jax now has 2172.8 HP and 93.4 attack damage, 172.8/43.4 of which came from Atma's Impaler, and 172.8/3.4 of which only Jax would receive.

*Edit* I messed up somewhere above. B.F. Sword gives Jax with Impaler 4.2 extra AD.

If Jax were to buy an additional BF sword after this point, he would gain 54.24 AD, and 216.96 HP; 4.24/16.96 of which are from the synergy.

The best things to exploit this synergy would be things like Health Elixers, the new Sword of the Occult, and Guinsoo's Rageblade (Its almost meant for jax). Also, Baron's buff. Not sure on the exact stats, but I've noticed it give me roughly 800 extra HP (with atma's equipped).

*edit* I wrote this up fairly quickly, if someone notices a math error just lemme know. I already see a discrepancy in the math, but its a small number.