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Welcome fellow Jax fans! Jax, being the league's resident arms-master, has many choices of armaments for himself. This item listing is intended to help people make decisions about which items to buy for Jax while taking his passive into account.
For section II.A, I list all possible starting items, not just ones relevant to his passive. For section II.B, I list only items affected by his passive, including some items not commonly used (or recommended by me) for Jax. I do leave out some items that I perceive as unfathomable, but can add them if requested to.
I. Mechanics and Assumptions
A quick overview of skills with ap ratios included:
Equipment Mastery (passive) - Jax gains 4 hp per point of dmg received from items. Jax gains 2 hp per point of ap received from items.
Leap Strike Jax leaps at a target dealing an additional 50/75/100/125/150 (+ 1*ap) magic dmg
Empower Jax charges his weapon to cause 40/60/80/100/120 (+ .2*dmg + .2*ap) dmg to all nearby enemies
Counter Strike After a dodge, Jax can stun surrounding enemies for 1 sec and deals 80/100/120/140/160 (+ .8*ap) magic dmg. Also passively increases dodge chance by 10/12/14/16/18%
Relentless Assault Every 3rd hit on the same target causes an additional 140/170/210 (+ 1*ap) bonus magic dmg. Also passively increases attack speed by 6/10/14% stacking 10 times.
SOON TO COME: SECTION ON DODGE MECHANICS
A) Potential Starting Items *(Elixir values set to lvl 1)*
Doran's Blade - 435g
144 hp (120 hp + 24 hp from passive), 6 dmg, 4% lifesteal
Doran's Ring - 435g
140 hp (120 hp + 20 hp from passive), 10 ap, 5 mp5
Doran's Shield - 435g
120 hp, 8 armor, 8 hp/5
Long Sword - 415g
10 dmg, 40 hp from passive
Amplifying Tome - 435g
20 ap, 40 hp from passive
Elixir of Fortitude - 300g
310 hp (230 hp + 80hp from passive), 20 dmg
Elixir of Brilliance - 300g
31 ap, 62 hp from passive, 10% reduced cooldowns
Guinsoo's Rageblade (0 stacks) - 2235g
35 dmg, 45 ap, 230 hp (140 hp from passive + 90 hp from passive)
Guinsoo's Rageblade (8 stacks) - 2235g
35 dmg, 93 ap (45 ap + 48 ap from 8 stacks of 6 ap), 32% attack speed (8 stacks of 4% attack speed), 326 hp (140 hp from passive + 186 hp from passive)
NOTE: HP from Guinsoo's Rageblade remains static and is based off of the highest number of stacks obtained.
297 hp (225 hp + 72 hp from passive), 18 dmg, 25% chance to slow target by 30% for 2.5 secs
Frozen Mallet 3270g
780 hp (700 hp + 80 hp from passive), 20 dmg, auto attacks slow target by ??% for 2.5 secs
Rylai's Crystal Scepter 3205g
660 hp (500 hp + 160 hp from passive), 80 ap, Leap Strike and Relentless Assult slow by 35% for 2 secs; Empower and Counter Strike aoe slow by 15% for 2 secs
Mejai's Soulstealer 1235g
20 ap, 40 hp from passive, 8 ap and 16 hp from passive per stack
@ 20 stacks: 180 ap, 360 hp from passive
Sword of the Occult 1369g
10 dmg, 40 hp from passive, 5 dmg and 20 hp from passive per stack
@ 20 stacks: 110 dmg and 440 hp from passive
250 mana, 25 ap, 50 hp from passive, after spell cast next auto attack has 80% increased base dmg on a 3 sec cooldown
350 mana, 80 ap, 160 hp from passive, 30 magic resist, 7% movement speed, after spell cast next auto attack has 100% ap as dmg on a 3 sec cooldown
Trinity Force 3995g
20 dmg, 30 ap, 25% attack speed, 12% crit chance, 12% movement speed, 440 hp (300 hp + 80 hp from passive + 60 hp from passive), 300 mana, 25% chance to slow target by 35% for 2.5 secs, after spell cast next auto attack has 130% increased base dmg on a 3 sec cooldown
Void Staff 2295g
70 ap, 140 hp from passive, 40% spell penetration
Madred's Bloodrazor 3900g
30 dmg, 120 hp from passive, 40% attack speed, 25 armor, 4% of target's max hp per hit as magic dmg
Infinity Edge 4080g
80 dmg, 320 hp from passive, 20% crit chance, 250% crit dmg instead of 200% crit dmg
Zhonya's Ring 3580g
120 ap, 240 hp from passive, increases ap by 25%, active 2 secs stasis
NOTE: Need confirmation if passive 25% ap increase also increases hp.
Black Cleaver 3065g
75 dmg, 300 hp from passive, 12 armor reduced from each hit stacking 5 times
60 dmg, 240 hp from passive, 15% lifesteal, 1 dmg and 4 hp from passive, .25% lifesteal per kill
@ fully stacked (60 creep kills): 100 dmg, 400 hp from passive, 25% lifesteal
Last Whsiper 1965g
20 dmg, 80 hp from passive, 40% attack speed, 40% armor penetration
Rod of Ages 3035g
480 hp (380 hp + 100 hp from passive), 425 mana, 50 ap, 22 hp (18 hp + 4 hp from passive) 20 mana and 2 ap every minute.
@ fully stacked (15 mins): 810 hp (650 hp + 160 hp from passive), 725 mana, 80 ap
The Brutalizer 1337g
25 dmg, 100 hp from passive, 10 reduced cooldown, 15 armor penetration
Nashtor's Tooth - 2745g
30% attack speed, 55 ap, 110 hp from passive, 12 mp5, 25% reduced cooldowns
Abyssal Scepter 2650g
70 ap, 140 hp from passive, 57 magic resist, - 20 enemy magic resist [aura]
42 dmg, 168 hp from passive, 15 hp/5, 4 mp5, small splash dmg
Atma's Impaler 2405g
45 armor, 18% crit chance, 2% max hp as dmg and 4 times that dmg as hp
NOTE: Need confirmation on looping mechanics of Atma's Imapler passive. Does it loop infinitely until values are too small to be significant? Or does it only loop once?
Elixir of Fortitude @ lvl 18 300g
480 hp (400 hp + 80 hp from passive), 20 dmg
Elixir of Brilliance @ lvl 18 300g
65 ap, 130 hp from passive, 10% reduced cooldowns
SOON TO COME: TRUE AMOUNT OF DODGE OBTAINED FROM NINJA TABI AND PHANTOM DANCER AFTER DIMINISHING RETURNS.
Feel free to post corrections, suggestions, issues with formatting, your own personal item build, or any other comments! Thanks!