Jax Build Guide by PH45
[10.21] PH45's In-depth guide to Jax, the Grandmaster!By PH45 | Updated on October 16, 2020
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Choose Champion Build:
Runes: Read the notes
+10% Attack Speed
+9 Adaptive (5.4 AD or 9 AP)
+10% Attack Speed
+9 Adaptive (5.4 AD or 9 AP)
Ability Order Max vs melees and usual matchups
Threats & Synergies
When facing Cho'Gath in lane, pay attention to his position when he uses Vorpal Spikes. Don't get hit by the spikes to avoid the slow and if he fights you with them make sure to dodge the damage with your Counter Strike. Key here is to dodge his Rupture and just all in him after that since he loses to you after that unless you are miles behind him (which shouldn't happen). Just be careful if you are low HP as he can quickly delete you with his Feast. Overall one of the easier matchups for Jax.
While playing against Illaoi it's important to dodge her Test of Spirit. After she misses that you are free to trade with her as she misses a good portion of her damage when she can't utilize the spirit from it. If she ults and you know you can't finish her at that moment Q away as she heals for a good amount when she deals damage in her ult. If you are having trouble with her healing buy a Bramble Vest or a Executioner's Calling.
The reworked Aatrox is a lane bully, especially to melees. He works as juggernaut now and he is actually pretty oppressive vs melees. Important thing in this matchup is to dodge his key points of his Q. It is also important to walk out of his W from the side before it retracts you to the middle as it basically guarantees him a key area hit on his Q if you stay in the area. Trade while he uses the first 2 procs and then quickly jump out before the 3rd one lands. Tabi and bramble are good items to get but mobility helps out a lot and most often after getting Phage your kill pressure on him rises a lot. Late game you outscale. If he misses his Infernal Chains you can try to all in him. Just dance around his Q procs as they chunk you a lot.
The reworked Akali can prove to be quite annoying but she got pretty gutted so she isn't that often seen anymore. Fight her when her shroud is down but care about her burst. Also try to not eat her Q for free since she will chunk you down fast with those + her empowered auto afterwards. She can also be tricky to kill due to her multiple dashes. Most of the time I just buy a Tiamat in this matchup, try to shove in and potentially roam or just keep her under tower since the kill pressure on her isn't that high unless she takes dumb fights with you.
Can be a difficult lane. Important thing is to block his W with your E and don't let him get his passive to 5 stacks on you. If you can't run out of his Q circle Q on him so you will be in the inner ring, denying him his heal. You outscale him quite well so just don't let him get ahead and you should win him. Early tabis also help quite a lot in this matchup. All in if he misses E, just be careful since most Darius's run Ghost so they will have kiting potential with it.
Avoid his cleavers as they slow you quite a bit aswell as deal hefty amount of damage. You have low kill pressure on him once he get's a few items. Blade of the ruined king is decent against him, but that item overall isn't that worth in the grand scheme of things. Again, Excecutioner's Calling is a great choice against a healing champion like Mundo.
Fiora is an annoying but fun matchup. Be careful when using your E since if she ripostes it you will pretty much die to her as she stuns you with it as well as cripples you.. It is best for you to try and upkeep your E for the maximum duration as most Fioras will try to predict you to use your E's stun earlier than the end of the duration. If the vital is in a bad spot walk out of her vision so the vital reappears in a different spot. If she ults and you can't kill her quickly ward jump out since she deals true damage aswell as heals herself for quite a bit. Tabis are good in this matchup aswell. Good thing to remember while she has ulted you is to hug a wall with one vital so she can't proc it, meaning she won't get her healing area.
Really passive lane for most part as GP tends to play pretty safe early on. His Q poke can be annoying so you can start Dorans shield + pot if you want to negate some of that poke. Try to bait out his oranges and when it's on cooldown then all in him. While fighting him prioritize destroying his barrels as otherwise he will slow you and chunk you hard with them.
Garen is a pretty bad matchup right now due to how Riot made him extremely dominant already early. Most Garen's just run Ignite and play to win the lane during early. The key in this matchup right now is to not fight him while his E is up. You can also just dodge his Q with your E. Most Garens build squishy so later the game goes you do outscale and Garens weaknesses still take their place but getting there can be hard. Most of the time if the Garen is playing agro the best bet is to play safe until your jungler paths top and you are SURE you can kill him, otherwise wait for scaling unless you are confident on your own skill.
You can't really kill him easily as he will just jump away if you engage on him. He will just poke you with his Q and his W's damage. Get tabis and after he uses his jump then engage on him while it's on cooldown.
Really annoying since if you try to jump on him he will just E on you and negate your jump aswell as stun you briefly so he can proc his TDL and run away. Just farm and try not to fall for his bait's as he can set up for ganks quite well with his E and ult.
Dodge her stun blade and be careful of her Q'ing around. Otherwise just smack her like any other melee matchup.
One of the toughest matchups for Jax. He will poke you out of lane in the early levels of the game and if you try to all in him he will just E you out of your stun range if you jump on him and even if you don't you dont necessarily have the time to jump on him. Build tabis and ask your jungler for ganks if you think you can kill him. Farm as much as you can as this is a lane that is very difficult to win until later points of the game.
This matchup changed with the Pantheon rework, although it still remains Pantheon sided for the lane phase. His Q poke is less reliable now and his passive no longer blocks autos, but his Q goes through minions and deals AoE damage. Be careful about his empowered W as that can hurt quite a bit when he combos in his other abilities. When he uses his E, Q behind him to be able to deal damage to him. You still outscale him so you should be fine if you don't int the lane.
Shouldn't be too big of an issue but he has quite a bit of damage early on so don't underestimate him. His all in is very strong so if he jumps on you with his ult just jump out of it with wardhop or onto a minion.
He is really annoying and slippery. Will poke you early a lot so getting some sustain is a good idea. If you try to jump on him he will just stun you and E away. If his E is on cooldown and you are confident he can't kill you all in him then. Care for jungle ganks as his ult sets up ganks quite well.
Dodge his W's procs with E and you should do good. Avoid getting hit by his Q and you should win all ins against him. Careful however since he gets courage quickly when hes attacking a champion so back off if you are low hp since he get's quite a lot of hp back just by attacking you a couple of times.
Annoying to lane against pre-6 but after that you can get some damage onto her with your Q + 3rd auto proc off your R. Most of the time if you jump on her she will just W you onto place and E or run away. Careful of her ult as she can get quite a bit of damage onto you while you are ccd.
Maybe one of the most annoying lanes you can face. He is weak in early levels so try to force him out early. If you try to trade with him after 3 he will just E and you probably can't finish one auto attack off before he runs out of range. He stacks armor too so your autoattacks won't do much damage to him. If he E's just jump away with Q so you wont take more damage from him. Beware at 6 since his ult is really strong cc that can enable the enemy jungler to get a free kill on you if you aren't careful.
Can be semi-difficult to kill as he has built in sustain and he can just Q you if you try to jump on him. After 6 and with a couple items he shouldn't be a problem to you though. Bork is good buy against him.
Try to make use of his weak early game. All in him at level 1 with e and force him away. If you play smart you can win this matchup but later on his W's attack speed and movespeed slow will make it hard for you to kill him. Ask your jungler for a gank if he pushes as he has no escapes besides his summoners.
CC monster. You will have a hard time killing him if he plays the lane right. After a couple items you can kill him but it is incredibly easy for him to setup ganks with his cc full kit.
Don't let him get too many E's on to you as it deals true damage. He has quite a good sustain with his W so careful for that. He also gets more attackspeed the lower his HP gets so be careful of that.
Her W will deny your jump so try to bait it out and jump on her when it's ended. She will get quite tanky and still deal good amount of damage so she might be hard to deal with especially early with her shield and stun. Try not to stand near walls as she can stun you with her E if she gets you against the wall.
Annoying poke and will just E away if you jump on her. You can't do much unless she misplays so sustain and farm what you can and wait for your jungler. Later on you can burst her down but early you should not have too big of a chance on killing her.
Lane bully, nothing else. Be careful at early levels since if he has fury built up his w and q deal a lot of damage. Block his W with E and you should win every trade. After 6 you should have quite an easy time against him with poking him with your ult + W proc. Tabis recommended in this matchup.
Abuse her cooldowns. She can burst you quite quickly. At level 6 if you are low be careful as she can quickly catch up to you and just ult you to death. Very slippery so hard to kill early.
He can just force you out of lane with his flamespitter and harpoons. Get some magic resist and after 6 you can just auto minions twice, then Q onto rumble and auto + W for a lot of burst damage. Merc treads are a solid in this matchup.
Can be difficult to kill since he can block autoattacks aswell. Gets quite tanky but he shouldnt have kill pressure on you unless he sets up an gank with his E. He will roam after 6 with his ult so be prepare to teleport where he is going or to stop it with your stun.
You can try to fight him level 1 by stacking your attack speed and Qing on him. Can be really annoying until about level 11 when you have some items you can actually kill him despite him being Teemo. Usually Teemos want to cheese so they run ignite so be careful as his poison + ignite can kill you really easily in early levels. Get some magic resists, Adaptive Help is a super good item vs Teemo. Later on you will be much more useful than Teemo as Teemo is mainly a lane bully champ rather than late game teamfighter.
Block his Q with your E and be careful when he ults you as it removes some of your resists and drains your hp over time. Don't give him lead in lane and you should win him. If he gets ahead he will become too tanky for you to deal with until later on if you can catch up.
Don't get cheesed early by his RNG crits. Save your Q for re-engaging him after he spins away. You outscale him, especially after you get Tabis and 40% CDR. Also building Randuins is a great choice against him as that cuts down his damage a lot.
Sustain is good in this lane, get some mr and vamp scepter and just farm up and you can kill him later on. You have to bait his pool though or he will just dodge your stun with it. While laning try to avoid getting hit by his strong Q poke since it deals quite hefty amount of damage. Stay behind minions so his E can't hit you.
Feel like new Volibear is just kinda meh atm. Buy healing reduction since in extended fights his W will heal him. Block his Q with your E and don't stand in his E area and you should win the lane. Bork rush is fine but Trinity force build works too.
Very slippery so you should not try to fight him too much early. After level 6 you should be able to outrade him with your Q + passive R proc. Tabis are good against him aswell.
Can be annoying, don't chase him unless you are confident you can kill him. Some run ignite on Singed so be careful of that as he deals surprising amounts of damage with or without it. Adaptive Helm is a great item against him.
Dodge his Q and you should be fine. Gets pretty tanky so might be hard to kill until you get some items. After he dies run away as his passive form deals quite a lot of damage.
Get early mercury treads and try not to get rooted by his W. After level 6 you should be able to beat him in trades if you don't get hit by his W. He has good sustain though so prepare to get forced out of lane, jungler ganks are pretty important in this lane as it can be difficult to beat him 1v1.
Play careful as he has quite a bit of burst damage. Block his Q with your E and wait to stun him after he comes out of his stealth. At level 6 he will probably try to all in you so care for that. Tabis are important in this lane. Also keep in mind he can recast his ultimate for a second knockup so he can keep you CC'd for longer, which can setup ganks quite easily.
Seen rarely in top lane. Can be tricky to deal with since she can push you away with her E if you try to jump on her or stun her. Best advice is to get tabis and after she has used her E then Q on her and chip her bit by bit. Careful at level 6 as she can stealth and move away from your stun and just throw you to a nearby wall and stun you.
Get's quite tanky and has somewhat of an advantage in lane with his forging items. After a certain point you won't probably be able to kill him since he get's tanky but you can try to shove him under his tower. Make sure to save your E for his W+auto combo.
Relies on autoattacking a lot, so you should be fine if you manage to block her Q, especially the true damage one. She can be difficult to gank if she has her E up since she can just hop over walls with it so if your jungler is coming for a gank try to bait her into using it.
Deals a good amount of damage early and can be hard to duel early as well due to his passive negating your W damage. Get merc treads and farm up and fight him if he misses his Q and W.
Reworked Kayle doesn't have a huge threat level due to her really weak early game. Care for her empowered E auto and try to not trade when she has lowered your resistances with her Q. Smash her early so she won't get to her powerful late-game state since at that point you are pretty screwed.
Mordekaiser is pretty strong right now in the meta, but Jax can deal with him semi-well if you know what you are doing. Don't get chunked by his Q too much. Keep in mind his shield stored on his second bar when engaging. Main thing is to dodge the E so you can stay on top of him for the trade. You probably want to try and chunk him and back off bit by bit early since his passive is really strong.
Early game might be tricky due to his bulkiness and huge damage on W. Dodge his Q with your E and path behind him while he casts W to avoid the true damage and beat him down after that. Just be careful that he doesn't ult you under tower post-6. You outscale him late game, though his W damage will still be very high once his grit builds up so be vary of that.
Runes: Basic PTA
+10% Attack Speed
+9 Adaptive (5.4 AD or 9 AP)
+10% Attack Speed
+9 Adaptive (5.4 AD or 9 AP)
+10% Attack Speed
+9 Adaptive (5.4 AD or 9 AP)
Champion Build Guide
Hello, I'm PH45, and this is my Jax Guide.
My real name is Patrik, but you can call me either way. I am a long time League of Legends player (started back in Season 1). I'm a top lane main, and I picked up Jax as my main champion back in Season 5 and have played him mostly ever since. I've been Diamond since Season 7. I have about 2 million mastery points on Jax when adding up all of my accounts, so needless to say I have played him quite a bit.
My currently played EUW accounts
I also got multiple other accounts but right now I'm mainly playing on the account I listed above.
Check out my YouTube channel where I occasionally post League related videos!
Now on to Jax. Jax is a bruiser style champion, who can really be very diverse with his builds and playstyles. You can play him as a splitpusher and duel almost anyone late game, or you can build him more tanky and peel for your carries, or just go all out and build him as a burster (although not recommended most of the time). Jax is a great champion to pickup as he isn't necessarily the most complex champion mechanics wise, but rather requires matchup knowledge. Knowing where to be and what to do at the right time as Jax is the key to utilizing him to his fullest potential.
Flash: Best summoner spell in the game. Some like Ghost but I much more prefer Flash for capability of getting over walls or quickly getting in range with Leap Strike.
Ignite: I wouldn't really bother taking Ignite on Jax. Sure it can help you score early kills but the spell scales so badly compared to Teleport it's just not worth it. Especially if you lose lane hard it will feel extremely bad to have this summoner spell when you could've just had Teleport to help you out in a losing matchup/bad lane phase.
Teleport: Teleport is the second choice in 99% of cases in top lane for Jax. Most of the time it enables you to splitpush and teleport to teamfights if you aren't near the fight when it breaks out. It can also help you in tough matchups where you have to back a lot early but main focus with Teleport is to have map pressure instead of getting back to lane to catch that one wave. Just be careful when using it since you can't cancel the teleport anymore so choose wisely when to use it. Though now it grants 30-50% movement speed on arrival which can help while doing ganks with it.
Smite is mandatory for jungling so if you are jungling take it. Often I like to take Skirmisher's Sabre when I'm jungling as Jax for the added dueling power, although Stalker's Blade isn't bad either especially if you need the slow for certain kind of targets.
+ Excellent duelist
+ Can fight almost anyone late game
+ Extremely strong late game
+ Great splitpusher
+ Has a built-in escape with ward + Q
+ Has an auto-attack reset
+ Gets naturally tanky in fights when using R as it gives you a good amount of resists
Jax is a very strong fighter once he picks up a couple items, and in late game he can be a monster in the right hands.
- Can be shut down with CC
- Hard to get back in the game if behind
- Requires matchup knowledge
- Has some difficult matchups
- Can sometimes struggle with teamfights
Falling behind as Jax can be very punishing. It is really hard to get back to the game if you fall behind a lot and especially then if the enemy team keeps denying you XP and CS.
|Precision is arguably the best choice for Jax. It gives him a lot of things he wants like free damage, healing and also tenacity which is really important on a melee champion like Jax.|
As the keystone of choice I have picked Conqueror. Damaging abilities and attacks grant 1.7-4.2 adaptive force for 8 seconds and it stacks up to 12 times. At max stacks you'll heal for 15% of post-migitation damage. This means you'll heal less the more resistances your opponents have. For jungling Press the Attack is the superior choice (although Conqueror is okey in jg now). In top lane Conqueror is the better keystone right now.
Press the Attack gives you more damage towards the target you have attacked with 3 consecutive basic attacks and it also increases damage to them from all sources for 6 seconds. Jax can pretty reliably proc Press the Attack and gets great benefit from using it, but I think Conqueror is the better keystone on top lane right now, Press the Attack is better suited for jungling.
|Next one on the list is Triumph. Short and sweet, it can save you in a clutch situation or just grant you some HP back in a intense teamfight.|
|Next are the Legend tier runes, from which all are fine really, although I think Legend: Tenacity and Legend: Bloodline outweigh Legend: Alacrity. Legend: Tenacity helps a lot vs high CC comps, or even vs lower CC comps it can still be really valuable. You should alter your choice depending on your matchup and enemy comp. If your opponents have a lot of CC or lockdown then Legend: Tenacity should be an obvious choice. If however the enemy team has little-to-no CC then Legend: Bloodline is a great choice due to the sustain it offers, especially since my builds usually don't include lifesteal.|
|Lastly from the Precision tree we have either Coup de Grace or Last Stand. I like Last Stand on Jax since you'll be in the middle of the fight most of the time so you'll take damage anyways and deal more damage with it. With Coup de Grace your targets melt faster when you get them below 40% HP, which Jax can do relatively easily when snowballing. Both are fine but personally at this moment, I prefer Last Stand.|
|Inspiration is still fine, it has choices between offering a bit of CDR for summoners, items and spells or you can go for some sustaining, and also some free gold basically.|
|Magical Footwear is nice as it lets you sink gold into other items rather than boots. It takes 12 minutes to arrive though if you don't get any kp during early game so it can be quite harsh to take if you have a rough time in lane.|
|Biscuit Delivery is also a viable option to take on Jax, combined with Time Warp Tonic. It helps you in harder matchups and lanes where you need to sustain more, since Jax doesn't have the best early game and it's pretty easily exploitable especially the higher you go on the ladder.|
|Time Warp Tonic is nice for lane phase, your early trading benefits from the movespeed boost while active and also the instant heal for half of the potions healing can catch your opponent off guard. Other choice is Cosmic Insight This helps to give you lower cooldowns, although to utilize this fully you'd want to get 40% CDR from items. This essentially means Trinity Force and the either two 10% CDR items or one 20%.|
As for the stats you choose the attack speed one is really helpful, but the other 2 you should decide based on the opposing team, I usually end up grabbing the adaptive force + armor but vs AP lanes taking MR will be beneficial.
|If you want to go for more defensive runes then take the Resolve tree.|
|For the first rune I would probably Bone Plating. It helps you in lane with your trades. After it procs it reduces the damage your opponents next 3 attacks/abilities deal to you by 30-60 depending on your level.|
|Second rune choice is Demolish. It allows you to push towers down even faster, especially now that turret plating is added to the game this will help you take down those plates faster than ever.|
Here as well the stats you choose should be decided depending on opponents. The attack speed one is really helpful, but the other 2 are more depending on do you need resistances/extra HP. Adaptive Force also feels solid for going agro early
|Sorcery offers tools to scale into late game and also some laning help with Nullifying Orb.|
|You can take Nullifying Orb for heavy AP lanes like Swain, Kennen, Heimerdinger etc as it helps you a lot since it's like a mini Hexdrinker. Nimbus Cloak is an interesting choice. You get movement speed after casting a summoner spell, so your Teleport ganks will be much more threatening.|
|Transcendence is a nice choice for the CDR. Especially now that Spear of Shojin is gone, this is one way to get more CDR to hit the magical 40% CDR threshold.|
Relentless Assault (Passive): Jax gains bonus attack speed for 2.5 seconds every time he lands a basic attack, stacking up to 8 times. This falls off one stack at a time. To utilize this passive in lane auto attack minions as much as you can before engaging the enemy so you have more attack speed to fight with.
Leap Strike (Q): Jax leaps to targeted enemy while dealing physical damage to the target. It can also be used to jump on wards, plants, Thresh lanterns etc. If you use your W before using Q the W's damage will be applied on top of your Q's damage.
Empower (W): Jax's next basic attack or Leap Strike within 10 seconds deals bonus magic damage. It is also an autoattack reset so after your auto attack has landed activate this for and immediate autoattack. It also adds 50 extra range on the empowered auto, which can make it easier to hit for a quick poke or trade.
Counter Strike (E): When activated the first time Jax will block all incoming auto attacks for 2 seconds aswell as will take 25% reduced damage from all area of effect abilities. At the end of the duration or when reactivated Jax stuns nearby enemies for 1 second and deals physical damage to them, increased by 20% for each attack dodged, up to a 100% increase. This is the key to winning melee matchups at level 1. Just auto minions for your passive and then auto the enemy while near his minion wave so your E's damage increases.
Grandmaster's Might (R): It's passive enables Jax to deal bonus magic damage on every third basic attack within 2.5 seconds of each other. When activated Jax gains bonus armor and bonus magic resistance for 8 seconds. Once you hit level 6 in lane auto minions twice and then Q onto your enemy and autoattack and follow with immediate W for a good amount of burst.
|You want to be taking points on Grandmaster's Might whenever possible. Out of the basic skills you want to max Empower first for maximum DPS. After that you max Counter Strike, having it up more means you'll be both more defensive and threatening at the same time since this ability is what makes Jax so annoying. Lastly you max Leap Strike.|
This item is extremely efficient when looking at it's stats. It gives Jax HP which is always good especially early on, some damage and most importantly it improves Jax's wave clear immensively. Titanic Hydra also gives Jax an extra auto reset for more burst.
Maybe the most important item for Jax. It gives Jax everything he can want. It has nice boost on his attack speed, some damage, movement speed, but most importantly it gives him the Sheen proc that makes Jax deal so much damage in short bursts.
This item gives lots of healing and some nice burst to kill squishies aswell as let you live longer in fights since it heals you for 15% of all damage you deal.
Blade of the Ruined King
This item has been bad for quite a while, but it recently got buffed to 12% of current health for melee users (as physical damage) which might make it viable for some games since it makes dealing with juggernauts and tanks who have a lot of HP much easier. Armor will still deny value from this item but champions like Sett might not always have a lot of armor so this might be a good option into champions like him.
This item works extremely well with Hextech Gunblade as it improves it's already good healing. It was kind of nerfed in the patch 9.10 but I still think it's relatively good. It is also good against AP poke lanes since the repice item Spectre's Cowl grants you more regeneration after you have been damaged by enemy champion. It also gives nice amount of MR.
The build path got updated again and now it's again a sensible way to build it. I usually pick up Warden's Mail first and then build it onwards from there. Helps extremely well in auto-attack oriented matchups and later on it's slowing effect is nice in teamfights and it also slows enemies attack speed when they hit you so it lessens the enemy DPS.
Good for autoattack reliant matchups and also vs fed ADC's etc. Most of the time I go these boots unless the enemy comp has heavy CC which can be an issue. Late game it isn't as noticeable but it's still quite good.
Pretty self-explanatory, get this if the enemy laner or the whole enemy comp has a lot of CC as it can shut you down pretty well.
The item got a slight change, now builds out of a B. F. Sword and a Cloth Armor, it can be somewhat awkward to build as Jax doesn't need the huge AD you get from B. F. Sword but it's a efficient buy if you are getting focused a lot or you are the frontline of your team. If you have extra gold in late game and this items passive is down sell it and switch it for something else as the pure stats aren't worthwhile the wait.
I don't build this item too often, but when I do damn does it feel good to jump in to the fight and just tanking damage for a long time. Stone Skin passive gives you +40 armor and mr if there are 3 or more opponents near you, so you will just have a lot of extra resistance then, then when you activate it you get extra hp also. You will lose 60% of your damage for 4 seconds but thats a worthy trade off imo, as if you build this item and you go in to a big fight you aren't looking to oneshot anyone at that time, rather soak up damage and after withering the opponents then killing them. Very good buy if your team lacks frontline or you just need to survive longer in fights.
This item seems to be really good in some cases now. If the opposing team has lot's of healing champions or just a fed AD champ with lifesteal this is the perfect item.
Thornmail applies Grievous wounds for 3 seconds which helps killing those pesky healing champs much easier. Also it has the cold steel passive which is nice.
Death's Dance heals for 15% of ALL damage dealt, and as we know Jax knows how to deal damage. The item also recently got a change where it now has 30 armor and magic resistance, which are always good stats to have. The DoT bleed passive is also nice which allows you to have more time in fights healing up, essentially it acts like a damage reduction.
I really like this item on Jax. It gives you some protection against burst, but also still gives you a bit more damage. So for the cost you get some AD, HP shield and +30% tenacity, which is a good stat on Jax. Only thing you need to keep in mind is that the shield doesn't pop every time, so this item is good if you are getting bursted a lot in fights and you need to also negate some CC when chasing down your opponents. This item isn't a must buy every game but it got a lot better than before.
Back when this offered Spear of Shojin's passive, this item was a very desired choice on Jax. After it's change it hasn't been picked up that much anymore and for good reasons. However, this item is still pretty okey for Jax in terms that with this and Trinity Force combined, you'll complete your 40% CDR, which is a big help for Jax since lower cooldowns = more DPS and more Counter Strikes. Also the AD you get from it adds up nicely and the random crit here and there can make a difference in some cases where your opponent might not expect it.
His passive gives him more attack speed and he can take turrets down pretty fast after he get's Sheen. You just auto-attack and right as the attack has landed you use Empower for the auto attack reset and at the same time you get a Sheen proc. Also having Titanic Hydra helps splitpushing as your waveclear improves and it also gives you an autoattack reset.
Jax is also a strong splitpusher since he can duel pretty much anyone in the later points of the game and if you are ahead splitpushing is a great way of giving the enemy team pressure around the map.
Also thanks to his mobility with Leap Strike, Jax can escape sticky situations with his ward hop mechanic which makes him somewhat slippery as he can jump over walls.
When to splitpush?
When splitpushing you are essentially leaving your team 4v5, so your team needs to be aware of what you are doing. The idea of splitpushing is to either attract attention to you, so the opponents send 1-2 or more champions to deal with you which leaves your team free to take objectives with the overpower they have. The other case is that the enemy leave you unnoticed and try to take down your team, in which case your team needs to be aware of the risk and back off before it's too late. When this happens you push the lane you are splitting as hard as you can as you can get surprisingly fast multiple towers down from a lane.
When splitpushing vision is a really important thing. Try to have vision around the area you are pushing so you know when to back off if the opponents try to gank you from the fog of war. Also keep an eye on the minimap to see how many of your opponents are visible, and where they are. Think of who you can solokill and who you can't, who you can possibly 1v2 etc.
If you have Teleport while splitpushing you can also consider Teleporting into teamfights. If your team can hold on the fight while your TP is channeling you can win the teamfight with the element of surprise if the opponents first thought it will be a 5v4 fight for them. Before you tp consider which option gives your team the most advantage. If the fight is already lost pretty hard, push as much as you can and back, remember to keep vision on objectives like Baron Nashor and Dragon depending on the lane you are pushing since if the opponents kill your team they are likely to do one of these objectives if possible.
When you reach 6 a common thing to do is auto minions twice, then Leap Strike on to your opponent, auto them and immediatly follow with Empower. This combo will do good amount of damage as your Grandmaster's Might 3rd proc + Empower do quite a lot of damage in a short burst.
You can also cancel your autoattack animation with your Counter Strike. When you have activated Counter Strike and you have autoattacked, right as the damage from your autoattack lands re-activate Counter Strike and this will cancel the rest of your autoattack. This is very useful if you want to do a fast combo with your W and Titanic Hydra for example.
Ward hopping and trinket choice
Sometimes after top laners and others switch to either Farsight Alteration or Oracle Lens but not on Jax. On Jax you keep Warding Totem so you can ward hop and potentially escape from tough spots. It's extremely useful when splitpushing and there are multiple enemies coming at you you just wardhop over a wall.
You should also note you can use your Leap Strike on things like Jarvan IV flag, Thresh lantern and so on.
Jax is extremely good champion at taking advantage of an lead and carrying your team to victory! He can be difficult to play against comps with lot's of heavy CC but even that can't stop the Grandmaster in some cases.
Any feedback on this guide is highly appreciated, I will be updating this constantly whenever there is something to update or new ways of playing Jax are discovered
Have a great time splitpushing and smashing enemies as Jax!
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Thank you to @Jovy for the awesome banners made for this guide!
Also some of the code used in the making of this guide is from http://www.mobafire.com/league-of-legends/build/making-a-guide-101506#chapter11 @jhoijhoi