You can't ever kill Alistar. He'll bounce you around like a tennis ball and there's really nothing you can do about it. He outdamages you early on simply because you'll never be able to stick onto him. The later it gets, the more hellish it becomes. Luckily this pick is only really prevalent as a challenger counterpick.
Gragas
You'll be punished for taking any cs, you cannot Q + E him; he'll counter it with a simple E. Gragas' only weakness early is his lack of mana if he doesn't start tear or build Lost Chapter, meaning he'll eventually run out of mana. Late game and after these purchases you can only really hope he whiffs and wastes E in order to even deal any damage to Gragas.
Akali
Only playable level 1. Abuse her weaker level 1 if you can, snowball from the small lead you gain then. Don't trade if she has W, only farm and take what you can get. Playable lane to a certain degree before she gets 6, after 6 it's torture. Splitpushing strat works very well into Akali. She can't kill you as easily with a Maw + Hullbreaker combo.
K'Sante
K'Sante is usually piloted by bad players, so you'll have an easy time without actually needing any help in this lane. However, be wary of a few things. Don't get hit by his Q when going for minions, expect a W by K'Sante if you press E near him. He'll first try to jump out with E, and if you follow him he'll W. Dodge the W. Lastly, you one shot him if he ever decides to ult in a situation where you aren't 10 HP.
Malphite
Malphite can be abused early, if he has grasp. With arcane comet, he's very hard to beat. Don't get chunked while grabbing cs, only go for those he doesn't punish while staying in EXP range. You can't win any fights if he has E, so don't fight post level 3 if he has E up. Fighting's not recommended without sheen or Divine, so get a DS or Cull and scale.
Anivia
Even though it's uncommon to find Anivia top, you can't really do much against her. Scale, don't tank too much damage and only trade if she wastes Q. So long she holds her stun, you cant fight.
Camille
While the general consensus around this lane is that Camille gets dogged on, it's not that easy. Don't fight Camille near a wall and don't get chunked by her W. The lane is somewhat tough to play, however the late game is in the bag. Sterak's recommended.
Cho'Gath
Definitely playable. Cheese in the furthest bush top lane relative to the enemies' tower, wait for him to arrive and ambush him. Abuse your broken level 1 at the first 3 melee minions. dodge Q if he unlocked that. Besides the level 1, you can trade when you get sheen or if he walks up to you. Auto win after Divine/Trinity + Vamp Scepter
Darius
Jax favored MU. This lane depends on both players' E ability. Dodge Q with your own Q and dodge his W with your E if possible. Remember to not be grabbed while in E, as he can deny your stun and run you down. Aside from that, you win this lane pretty hard. You win without E mattering all too much after Divine.
Aatrox
Skill matchup, slightly Jax favored. It's all about how you go about dodging Aatrox's Q's. Always fight if his Q is down. Dodge Q1 by side-stepping and Q2 by leaping onto Aatrox, though be careful to not get hit by W/Q3 afterwards. You can Q out of the W in case you get hit. Level 1 cheese in the toplane bush that's near the enemy top tower.
Dr. Mundo
Only match up where BotRK is recommended at all. Dodge cleavers and run ignite if you need it, however you most likely dont. This champ is dog****, you'd have to try to lose this one.
Akshan
Can't lose. Bodyblock his E, that's about it. If he walks up to you to trade ever, leap and E. Akshan should NEVER be able to run you down.
Tryndamere
When fighting Tryndamere, hold E until he presses E and follow him with your Q. If he never E's, you'll lose the trade by simply auto attacks. Eventually you'll be forced to jump out/walk away after a certain amount of hits. Don't all-in a full hp tryndamere with R, you will die if you have no significant advantage. Short trades with W and E while using Q if needed to run if possible are recommended. Late game tryndamere becomes harder and how to play into him fully depends on his build and your armor count. The more armor you have, the easier time you'll have.
Cassiopeia
Pretty bad match up, depending on her skillshot hitting abilities and your feetwork. You can cheese her weak level 1. You lose any trade she hits Q in. Anticipate an R when you press E, so try and dodge it whenever you do use E post-6. Wit's End recommended 2nd.
Garen
Beat him up early game and keep the lead you gained from that. The only thing to watch out for is to not stand in his E, excluding level 1. Level 1 you may attack him to your heart's content with your E as you win it incredibly hard, even while tanking every E tick. After that, fighting him is always possible until he presses E. Dodge his Q with your E. You cannot evade Garen R with your E, so don't try to.
Fiora
Skill matchup. Anti-heal can be bought or take ignite. TLDR: Don't get hit by her W while not letting her proc any vitals.
Her Q can be dodged with your E. Any trade you take with Fiora heavily depends on her W usage and your E timing. Mix up your E detonation time everytime you fight her, so that it becomes an unpredictable game of "When will Jax recast E?". Sidestep the W as a whole too. If she parries the stun, but you dodge the parry, the trade is equal. DONT GET HIT BY HER PARRY EVEN IF IT DOESN'T STUN! the attack speed slow makes it so you cannot win any trades if she hits it. Lastly, stand against a wall when she presses r, that way 1 vital is impossible to be procced and she can subsequently not proc her R healing.
Gangplank
Rarely do you find any good GP players. When you notice the GP sucks, this matchup is free. Now assuming that the GP knows how to play league, it's quite a handful to deal with. First off, GP has mana issues early on. Try to abuse that by tanking Q's with doran's shield and eventually fighting him once he's on low mana. Remember that you can Q on GP's barrels. You can reduce his barrel damage with your E by 25% and you can dodge his Q while preventing his Auto burn from proccing. You can ONLY fight gp if he has no barrels set up in lane or has none ready to be placed. Otherwise, farm. Becomes harder once he gets sheen, then becomes a significantly easier match up post-6, but becomes hard once again after the GP gets Essence Reaver.
Gnar
You outscale Gnar, play to outscale him. Once you do, you can use the splitpush build. Gnar will never be able to stop you on his own, unless he uses his Mega Gnar form which he needs to be useful in teamfights.
Gwen
Easy lane. Just know that all your pressure lies in your E, so don't completely waste it as that is her only opportunity of ever fighting you. Antiheal isn't mandatory versus Gwen.
Heimerdinger
Even though heimer is oppressive and annoying, you virtually cannot lose after a magic mantle and sheen, even while tanking every ability in the book (though try not to get hit by his E, even if it doesn't matter in the long run). Give up the cs you cannot take and outscale him rapidly.
Illaoi
No real Jax specific sauce to be spilled here. Antiheal is a MUST, paired with DS and Black Cleaver. Dodge E + all tentacles, run if she ults and dodge her W with E. You can react to the latter part. Hullbreaker is a great option, as this champion plays like Yorick; she doesn't leave sidelane, so you will be prompted to keep matching her. If you're the only hope of winning the game, force another teammate that is weaker than you, yet strong enough to match Illaoi so you can join the fray and carry yourself to victory.
Karma
Don't bother fighting. Scale and play splitpush Jax, she'll never stop you on her own. Then again, it's a Karma so she'll likely be duoing someone or stick to another teammate.
Yorick
Only "Even" due to his annoying perma splitpush playstyle. Dodge the E and you're fine. Q is blockable with E and lastly, jump out of the cage. Don't **** with Yorick if he has all his ghouls and maiden up. His maiden increases his 1v1 potential massively. Try to deal with the maiden before looking at Yorick. Hullbreaker helps a ton.
Jayce
Fully depends on the Jayce player. You can only fight Jayce if he has no E (hammer form) push back. A bad Jayce will walk into your Q range. If he does while his E is on cooldown, you have a kill window. Use it. Splitpush build works immaculately as you can dive this boy from full hp with 2 items, regardless of his E.
Kayle
Don't get frozen on when she becomes level 6 and don't fight level 1 if she has ignite or resolve. If she gets Rylai's the match up becomes slightly harder, but the Kayle has to play it perfectly in order to win. You have much more room for error, while still countering her at her prime level 16.
Kennen
Only farming & scaling as the lane is doomed anyways. Opt into a splitpush build, Kennen cannot stop you even if you're 0/10.
Kled
Respect Kled's strong early game and you'll beat him 100% of the time. Kled's strenghts lie in his remounting ability. Don't use E on a mounted kled if you are all-ining him. Keep the E for when he dismounts, so he can never remount. Only try and trade with a Kled early on if he misses his Q. Eventually it won't matter if he hits it or doesn't.
Irelia
Can't really lose unless she's irelking. Fight her level 1 before the creeps get low enough for her to Q onto them to get resets. Don't press Q until she dashes away. Remember that Q should be used as an effective gap closer, not a damaging tool. Walk up - E + autos - Q if she tries to leap away. You don't need BotRK to match Irelia. When fighting Irelia with BotRK, remember that this item only deals damage if the target has high current hp, meaning that you should only E when all-ining Irelia after you get below roughly 40% current hp. You're bound to lose lots of hp at the start of a fight with Irelia.
Lulu
Same as Karma, except you can actually fight Lulu whenever you please. Splitpushing build for the same reasons.
Mordekaiser
Fight after he uses Q and E. Bonus points if you dodge them. Back off whenever he presses W. Do this on repeat and you win. DONT GO BLADE OF THE RUINED KING INTO MORDEKAISER!!!!
Nasus
The usual. Deny him cs, dive if you can, back off if he uses W and don't get chunked by his E. Nowadays, Nasus players max E and take Mana + Ability haste boots before divine sunderer, so it's really important you don't get hit by all of his E's. Freezing is your way of winning this lane instantly.
Olaf
Not the hardest of lanes, not the easiest. Try not to get chunked by his Q. You have a window to fight if he ever misses Q and can't pick it back up. NEVER ENGAGE WITH Q. Always use Q to back off or finish him off. You can try and bait his ultimate by pressing E post-6 and leaping away in succession (assuming his Q is on cooldown!) Antiheal recommended + BC.
Ornn
Only a pain in the very early stages of the game. Buy DS into BC with mercs. Don't get hit by his Q, W and brittle auto's. They can be blocked with E. Juke his R with Q or stun him with E right before he can recast R. If you do not grief the very early stages of the lane, you should be completely fine. Match up becomes and stays free after Divine.
Pantheon
Really bad lane. Try to not tilt and dont get chunked by his Q. You can't ever fight Pantheon if he has a brain. Assuming he doesn't, your windows are if he long range Q's
or wastes W/Missclicks a minion. You only ever so slightly outscale Pantheon; he's really not a weak champion later on anymore despite what people say. This matchup is significantly easier if he goes Goredrinker instead of Eclipse, as you will actually outscale him much harder if he does go that item.
Poppy
You need Black Cleaver, Divine Sunderer and Bramble Vest to deal with Poppy. She out-trades you in lane and can't be traded with solely because of her W. Don't stand near walls so you don't get pinned to them. Be wary of flash + E. Never use Q on her if she has her W up. She will always be able to react to it and cancel your jump instantly. This is primarily why the matchup stinks. You'll never solokill a good Poppy, so play for your team or splitpush accordingly to the situation.
Quinn
Same as Jayce. She has to waste her knockback AND be in range for your Q. Can't play otherwise. Don't leap in with your E, she'll simply knock you back and make you miss E. You outscale Quinn very hard, so use that as a way to win.
Rammus
Don't auto in his W state + Perma shove every wave = gg
Singed
If he proxies, farm up. Nothing else you can do. If he lanes, quick trades with single W taps. Don't go for any trades if you get outspaced. Only Q after he flings you away; you have a very small window to instantly jump back onto him after his fling to stick onto him. Unkillable after he gets Rylai's.
Renekton
Dodge W with E (reactable), then follow his E with a well timed Q + E2.
Don't fight into a Renekton with 50+ fury. After the removal of the mythic iteration of prowler's, he can't even opt for a one-shot build. You outscale incredibly hard, so don't grief lane too hard.
Rengar
Don't fight level 1. Give up the cs on level 1 and even xp if needed.
Don't fight if he has empowered ability ready (he won't Q, he'll most likely W or even E)
Some form of armor is heavily recommended. You can only fight if he's not in a bush and doesn't have an empowered ability ready. You outscale.
Riven
Only hard early on. Riven will win every trade with Auto - W - E away. Don't leap onto her either, she'll E - W in quick succession. You can take fights later on at 2+ items or if you can tell that the Riven is bad/messed up a certain trading pattern/has everything on cooldown, somehow.
Rumble
60% winrate champ if only OTPS played him
Ryze
Rare to see so i don't know much, but I do know that it's painful
Sejuani
If she takes Ignite + tp, respect her potential kill pressure. Don't trade with E, she can always leap away. If she is in melee range, cast E and hold it until she leaps away. Follow her with Q and detonate the E. If she has no Ignite, she has no kill pressure.
Sett
Don't fight full grit Sett.
Don't fight a Lethal Tempo + Ignite Sett at all.
When those 2 conditions are met, play in short trades. Fight until sett's grit is high. Once it is, leap away asap and don't get pulled back in or get hit by his W
Shen
A good shen will never die to you 1v1. Never stand in the direction that Shen will taunt away into. If you do this and press E in the fight, You'll be taunted while he runs, making you unable to leap in time, miss your E and lose the trade. Kill him if he ever taunts onto you for whatever reason (assuming you're not getting ganked or low af). Short trades with W are the way to win this lane. You outscale and win every fight post Divine Sunderer.
Sion
Don't get Q'd and don't fight in his wave. In lane you'll win every trade, but try to dodge his E + Q combo. DS - BC build and you'll always win. Hullbreaker buy if he perma sidelanes. 1 of 2 match-ups where BotRK is an okay buy.
Tahm Kench
Dodge his Q
Don't perform any trades if he has Q up.
If you dodge his Q, short trades are possible, but it's much better to focus solely on farm as he heals damage back up with Doran's Shield, E Passive and resolve. Easier matchup after Divine + Black Cleaver.
Teemo
Always fight after he uses Q. If you jump on him while blinded, don't waste your time auto-attacking. Make sure your E will hit the Teemo and chunk him hard after the blind wears out. Don't walk into mushrooms and don't get chunked in lane. Free win after mercuries/legend: tenacity is stacked or first item completed. Besides the first 2 points, there's nothing to watch out for. If you do not have any form of tenacity, Teemo can Q you, stand still and become invisible. Rarely ever happens due to Q damage, but be careful anyway.
Urgot
Borderline major difficulty. Inconsistent matchup. Don't fight level 1, you lose it. Dodge his E and do not fight in general if he has E up, unless you're confident you can avoid it. Urgot's utility is higher than you later on, so this is an icky matchup. This applies throughout the entire game.
Vladimir
Start Q and beat him up, he won't expect it. Although winrates say otherwise, you can definitely win this match up with ease. Don't ever E when he has pool, unless he's at full hp. Pool does max hp damage in order to cast it, so he'll lose lots of hp for trying to cast W. Don't ever let him proc his empowered Q on you. Freezing helps deny the vladimir cs.
Antiheal is a must. Ghost optional, makes life easier.
Volibear
Dodge Q and/or W with E, stun, leave with Q if you need to dodge his E and repeat. His W Mark will not stay if you dodge his W with your E, although he still heals hp back. PTA/Conq/Grasp will not be procced, however. Antiheal can be bought, but it's not necessary. Tank/Bruiser voli can nearly never kill you. AP Voli should be more carefully dealt with, but is also easier to kill at the same time. Just respect the AP bear moreso than you would respect a bruiser bear.
Warwick
Q and R are dodgeable with E. Bring antiheal in some way, shape or form and it becomes an even lighter breeze of a lane. Simply respect his healing and you should be fine; this is Warwick's worst match-up after all and with good reason.
Wukong
Short trades. Dodge Q with E and only fight if he engages onto you. Early on, trade exchanges with W are possible, until he levels up Q. His range will beat yours significantly and you won't be able to exchange auto's anymore.
Ulting his clone and the real Wukong grants double resistances due to it counting wukong's clone as a 2nd champion, so that's your window to get the most out of your ult.
Yasuo
You beat him level 1.
You beat him level 2.
You beat him level 3.
You beat him level 6. So on and so forth. :) Only tips to give is that
you should hold Q for when he dashes away in an attempt to avoid your E and that you can dodge yasuo & yone's Q1, Q2 and Q3 with E.
Yone
A bit harder than Yasuo due to Yone being the superior champion, however the same things apply.
Jarvan IV
Any champion that can engage on/dive the backline gives you free reign on who you want to focus. This way you're also not the person who people will usually watch out for primarily.
Zac
Any champion that can engage on/dive the backline gives you free reign on who you want to focus. This way you're also not the person who people will usually watch out for primarily.
Sejuani
Any champion that can engage on/dive the backline gives you free reign on who you want to focus. This way you're also not the person who people will usually watch out for primarily.
Diana
Any champion that can engage on/dive the backline gives you free reign on who you want to focus. This way you're also not the person who people will usually watch out for primarily.
Hecarim
Any champion that can engage on/dive the backline gives you free reign on who you want to focus. This way you're also not the person who people will usually watch out for primarily.
Amumu
Any champion that can engage on/dive the backline gives you free reign on who you want to focus. This way you're also not the person who people will usually watch out for primarily.
Karma
Any enchanter works well with Jax, simply making running down everyone you meet an easier task. Engage supports are also good for the reasons mentioned before.
Lulu
Any enchanter works well with Jax, simply making running down everyone you meet an easier task.
Yuumi
Any enchanter works well with Jax, simply making running down everyone you meet an easier task.
Soraka
Any enchanter works well with Jax, simply making running down everyone you meet an easier task.
Synergies
IdealStrongOkLowNone
Jarvan IV
Any champion that can engage on/dive the backline gives you free reign on who you want to focus. This way you're also not the person who people will usually watch out for primarily.
Zac
Any champion that can engage on/dive the backline gives you free reign on who you want to focus. This way you're also not the person who people will usually watch out for primarily.
Sejuani
Any champion that can engage on/dive the backline gives you free reign on who you want to focus. This way you're also not the person who people will usually watch out for primarily.
Diana
Any champion that can engage on/dive the backline gives you free reign on who you want to focus. This way you're also not the person who people will usually watch out for primarily.
Hecarim
Any champion that can engage on/dive the backline gives you free reign on who you want to focus. This way you're also not the person who people will usually watch out for primarily.
Amumu
Any champion that can engage on/dive the backline gives you free reign on who you want to focus. This way you're also not the person who people will usually watch out for primarily.
Karma
Any enchanter works well with Jax, simply making running down everyone you meet an easier task. Engage supports are also good for the reasons mentioned before.
Lulu
Any enchanter works well with Jax, simply making running down everyone you meet an easier task.
Yuumi
Any enchanter works well with Jax, simply making running down everyone you meet an easier task.
Soraka
Any enchanter works well with Jax, simply making running down everyone you meet an easier task.
Jax his basic attacks generate a stack of on-attack for 2.5 seconds, refreshing on subsequent attacks and stacking up to 8 times. Stacks expire by one every 0.25 seconds when the duration ends. For each stack, Jax gains bonus attack speed. Stacking this ability before a fight could be detrimental to winning it.
Jax dashes to the target unit's location. This ability can be cast on wards, allied or enemy minions/champions, Jarvan IV's Flag, Rek'sai's Tunnel, Thresh's Lantern, ...
If the target is an enemy and they are in range, upon arrival, Jax deals physical damage. W can be merged with Q to deal extra damage upon arrival.
Jax empowers his next basic attack or Leap Strike against an enemy within 10 seconds to deal bonus magic damage. If Empower is used on a basic attack, it will gain 50 bonus range. This ability is an auto attack reset, meaning it can be cast instantly after dealing damage with a basic attack while cancelling the timer to auto attack again.
Jax enters Evasion for 2 seconds: a defensive stance that causes him to dodge all incoming non-Turret basic attacks and take 25% reduced damage from all area of effect abilities from champions.
Counter Strike can be recast after 1 second and does so automatically after the duration.
RECAST: Jax deals magic damage to nearby enemies, with the total damage increased by 20% for each attack dodged, up to a 100% increase, and stuns them for 1 second.
PASSIVE: Jax his basic attacks generate a stack of Grandmaster-At-Arms on-hit for 2.5 seconds, refreshing on subsequent hits and stacking up to 2 times. At 2 stacks, his next basic attack is empowered to consume them all to deal bonus magic damage. While Grandmaster-At-Arms is active, the empowered attack triggers at 1 stack instead.
ACTIVE: Jax swings his lantern around, dealing magic damage to nearby enemies. If this hits a champion, he gains bonus armor, increased for each champion hit beyond the first and bonus magic resistance equal to 60% of that amount as well as 10% increased size for 8 seconds.
PROS & CONS
PROS
+ Great duelist + Great at extended fights + Good at short trades + Great splitpusher + Great waveclear + Great scaling + Great level 1 + Low cooldowns + Built-in damage, mobility and tankiness
CONS
- Mana hungry into tanky enemies - Sub-par early between levels 2-5 (including those levels) - Heavily match-up dependant. Jax cannot function well without sufficient match-up knowledge. - Gets dogged on if it falls behind even slightly. This goes for any juggernaut, so it also applies to Jax. - Macro-reliant champion. This means that fights are moreso in the enemies' control, due to that champion most likely having more mechanics and tricks to work with. You rely on having a better gameplan and thought process to win the game.
ITEMS
Divine Sunderer
This item is your bread and butter. It gives you sustain, %max hp damage, armor pen, hp, damage AND haste. Basically everything you could ever ask for. This greatly strengthens Jax his short trade AND extended trade potential due to the empowered Sheen effect, making it so you could effectively heal from fighting enemies. This is the mythic you will be going most games and is your biggest spike.
Trinity Force
As of Patch 13.14, the item got nerfed and isn't as good as it used to be. However, it has become better at short trades and only becomes worse in very long fights that take 9+ auto's. You can still run this item into squishy enemies and for splitpushing, as the tower damage is still better compared to Divine Sunderer
Black Cleaver
Black Cleaver has been an excellent choice for a second item and still is, but I recommend to opt for Spear of Shojin 2nd instead now. Upon further reviewing and testing, Black Cleaver should only be built into significant armor (think of tanks in general) or if your team is full AD.
Side note: Empower does not stack Black Cleaver and Jax deals hybrid (ad and ap) damage, meaning that this items' effectiveness actually drops relative to Spear of Shojin! This item is still great and is fine to be built 2nd, but the general item is not this one anymore.
Blade of the Ruined King
DO NOT BUILD THIS ITEM. You are better off getting yourself either a Black Cleaver, Wit's End or defensive item like Maw of Malmortius. The reason being is that this item only deals damage to a HIGH CURRENT HP TARGET, weakens you in teamfights relative to the other options mentioned and is countered by sufficient armor, contrary to popular belief. The item deals significantly less damage the lower the target gets and deals less-than-optimal damage into high armor enemies that like items such as Frostfire Gauntlet and Jak'Sho and even a component like Bramble Vest. This is subsequently an inconsistent damage source. It is only recommended into Dr. Mundo and Sion, as these 2 champions want to stack hp by going Heartsteel; the stat that Blade of the Ruined King counters. If Sion is not building Heartsteel, you do not go BotRK. This item is a former shell of itself and is not what it used to be, therefore I highly recommend you to opt for a different item.
Wit's End
A very nice item on Jax. This item synergises well with his Auto-Attacking nature. It's a solid item to go 2nd if you need the magic resist now, or 3rd afterBlack Cleaver. The 2 items have good synergy. Not much else to say about this item. Build it if your opponent is an AP Champion like Mordekaiser or Gwen. Delay Wit's End by buying Black Cleaver if the Armor Shred is more important, like into Ornn and perhaps Mordekaiser again.
Spear of Shojin
Great item with insane passives and stats. You should be going this item 2nd in most of your games as it offers everything you need. The components are mostly cheap and great as well. This item gives the most ability haste that an item can give, gives 15 more AD than Black Cleaver and also has a movement speed passive. This item has basically no downsides other than it being relatively expensive (+200g over Black Cleaver) and it offering no resistances, however the upsides heavily outweigh the downsides.
Maw of Malmortius
A very nice defensive option into burst mages, such as LeBlanc, Syndra and Ahri. The appeal of this item obviously lies in the magic damage shield, while giving a nice amount of AD too. Build this item into AP Assassins like Fizz (excluding Evelynn, she pierces through it) and any other solo AP carries. This item will save your life often, despite it being a former shell of what it used to be having it's omnivamp removed.
Sterak's Gage
Lifeline item nr. 2. It offers a nice amount of AD depending on level and is one of the only sources of Tenacity in the game. This item should only be built over Maw if the enemy doesn't consist of any alarming amount of AP damage. In other words, build this item into full AD or heavily lacking AP team compositions. ONLY build this item as a 3rd, 4th or 5th option, never 2nd as it's power scales with level (this is why it's a good item for splitpushing).
Ravenous Hydra
The 85 AD item. This item goes very well with Trinity Force and is quite underrated. You want to build this item when you're in need of sustain or are splitpushing, which you most likely are when building Trinity. It is not recommended to pair this item withDivine Sunderer, as the healing is slightly overkill. In the case where you have Divine, you're better off sitting on a Vamp Scepter and building a different item or finishing it into a Blade of the Ruined King in those rare games.
Titanic Hydra
Ravenous Hydra's counterpart. The damage on this item scales with bonus hp, so you should opt for this over Ravenous Hydra if you're leaning towards a tankier build that includes lots of bonus HP, such as Force of Nature and Black Cleaver. Works exceptionally well as a 4th/5th item and shouldn't be built before that. Works equally well into melee and ranged champions.
Hullbreaker
Everyone's favorite splitpushing item. The item speaks for itself on when to build it; take it if you're aiming for turrets this game or are stuck in a sidelane due to having to match a Yorick or an Illaoi. Splitpushing aside, this item also has great stats; you can definitely teamfight with it, though to make use of the passive you'd have to be alone.
Force of Nature
Now, while this item has been "gutted", it's still a good option into AP champions that repeatedly spam magic damage on low cooldown or have lots of CC. This item gives 90 MR When fully stacked. The downside of this item is that you will lack damage and that it takes longer to stack, so you should definitely build an item with damage after or before building this item. Prime examples of champions that you should take this item into include Fiddlesticks, Cassiopeia, Nautilus and Teemo.
Abyssal Mask
This item is overpowered beyond belief. You get 60 MR (95 near 5 enemies), 300 Bonus HP and 10 Haste while reducing the enemies' MR when near themFOR 2400G. Usually, you'd only go this item in very niche instances where you had a fed AP carry that you'd peel. Now, it should be built in games where you need the MR right now due to it's absurdly cheap cost, incredible stats and indirect damage increase for you and your allies. The latter part is a small bonus though, you don't buy it for that.
Frozen Heart
While not the best option, it's definitely not bad. Jax like this item due to the high armor and amount of mana that it gives. After the mana cost nerf on Grandmaster-At-Arms, this item has become better to build as you now do suffer from more mana issues. It used to be a core item due to the cost being only 2500G some time ago, however now the cost has been nerfed and you'll lack damage if you go FH. I'd recommend going this item into tankier opponents, high AD opponents or an attack speed oriented team, such as Jarvan IV and AD Twitch.
Randuin's Omen
Not much to say about this item as it speaks for itelf. Take it into dangerous AD enemies that rely on crit damage, such as Jhin, Tristana and Gangplank. Don't forget to use the active!
Guardian Angel
Item that enhances carry potential. When you're the hero of the game and you cannot afford dying even once moving forward, this item is recommended. Don't care too much about the Armor stat, you buy it for the Revive passive.
Anathema's Chains
Absolutely goated item that should be bought WAY more. It reduces a single target's tenacity and reduces their damage dealt to you by 30%! It is the best item in the game at keeping a single carry in check. Buy it into every single Evelynn and in games where the carry is the only person of that damage type. If the entire enemy is AP, but the only AD person is fed, you buy Anathema's and vice versa. Take it 3rd or beyond.
Zhonya's Hourglass
Build this item when your team has no engage and if you're being hard focused. This item is kind of sub-optimal to build due to its components being lackluster for Jax. It would be much better for you to buy a different item if you're not in need of the stopwatch active, simply put.
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