Jayce is probably my favorite example of a "sleeper hit." When he came out, I bought his bundle outright, because I knew he was very strong champ, and he'd continue to be that way. I was already playing him top to deal with solo queue Darius or Yorick or Garen (RARGHN), and then suddenly he just exploded all over the place. He has no ultimate, but his lane is almost unbeatable with how hard he pokes, how well he can harass, and how much burst he has with his full combo. He isn't exactly overpowered since his Gate and Thundering Blow nerf, but he is a pain to deal with.
|Range and melee||No real ultimate|
|Heavy poke||Doesn't sustain well|
|Gate is utility||Fragile in cannon stance|
|Free mana returns||No range in Hammer|
|Fun as all hell||Cannon range is low|
|Versatile||Can't do one job well in teamfights|
|Lots of combos|
|Fits jungler, mid, or top|
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To understand why Jayce really isn't that awful, you have to realize what you give up for teamfights when you pick him for a top- or mid-lane champ. Nidalee is the obvious comparison, another top-laner with a transform ultimate, but she didn't get her ult at level one, and their kits approach two completely different directions. She's a mess, since items dictate what she does, yet both of her kits require different items. Jayce is not like that.
When you stick him at top, you're giving up a lot of things top laners can offer you. Ultimates are that big, powerful thing that gives your champ something amazing to do. Let's just look at someone like Cho'Gath, who has his scary true damage bite that gives him HP when he kills with it. Or Olaf, who can tear a bee-line right for your carry. Shen, who is still a top-ban for his ult. Jax, with his free resistances and third-strike damage. Riven, with her Wind Slash and bonus damage on auto attacks. Malphite's ADC-destroying initiation. Yorick, who can give someone a second life to pull their abilities. Darius, who is Darius.
With Jayce, you miss out on all of that, in exchange for a versatile bard who is a jack-of-all-trades. He can poke, he can teamfight, he can damage, and he can tank, but not all at once, and not in large areas. He will always be a huge nightmare in lane, but his usefulness runs out when that lane ends and teamfights break out. In teamfights, he can do a lot of damage, but lacks area control in the ways he has it in lane. In that way, he's a lot like Teemo.
Now, granted, he's basically a won lane, but so was Yorick, and Yorick has a better lategame than Jayce does. Jayce is all a matter of winning his lane so hard whoever he's fighting doesn't even get an item. And that's really why he gets banned. But he's beatable.
The real struggle of laning phase (any lane, with any champion) is staying relevant to mid- and late-game, which usually involves just destroying your opponent. The benefits of constant kills and farm, as well as being more powerful than your enemy in teamfights, gets you ahead more than anything else. But this isn't always the case – this is why a Vayne or an Ezreal can come to lategame with 350 CS and very few kills and still melt everyone on the team.
One Man Arsenal
So, what does this have to do with Jayce? Well you can handle him one of two ways – you can defeat him like Teemo if you know what you're doing. Pick a high-burst damage character who can duel decently well, like Wukong or Renekton, and just hang back until you get the abilities you need just from experience (level 3 for Renekton usually works, Wu needs to wait for his ult). Then, force him to transform from Hammer to Cannon (not wait until he's in the stance, wait till he changes to the stance), and dump everything on him.
The burst from Renek's three-strike stun and combo is enough to drop him. Jayce has no innate sustain, remember, so take advantage of this if you can, complimenting some innate sustain like Renekton's Q. Though he's a pain to deal with, his transformation cooldown is critical to beating him. When he changes, he just locked out half his kit, so take advantage of it. If he changes to Cannon, he's squishy and can't disengage. If he changes to Hammer, he's a tough fighter with a lot of damage, but he's vulnerable to harass, and can only burn his engage/disengage to fight you. He's got six seconds to think about the mistake he made, so take advantage.
Or, alternatively, do what I do, and just don't fight him. Whenever I see Jayce, you know what I do? Bankplank. Pick Gangplank, and do my best Nasus impression. I buy a Philo Stone, Heart of Gold, and an Avarice Blade, and I farm (especially my Q) for half the game. Whenever he harasses, I just snag the creeps I can and hang back. If he attacks me, I back off and wait for the creeps to swing towards me.
It's not the guaranteed way – and honestly, I prefer if you could crush him, since it removes midgame completely – but it's for-sure the safest. The dude is a jack of all trades, but Gangplank does his job better lategame. He's hits harder, tanks better, and doesn't have to lock out his skills to do either. He can even CC better, with his passive slow/Phage slow, Morale, and ult to lock down priority targets in teamfights.
Plus plus, look at it this way – Jayce will fight you and get one or two kills around midgame, so (spitballing some numbers) that'll put him at about 100 cs by say 20 minutes. Let's say he's at about 5k gold, probably more. In our theorycrafted situation, Gangplank will farm about 350 on his Q, might get an assist or two from ult support or top lane ganks, so that's about 50-150 gold, depending on the lanes. About this time, the GP/5 items are starting to repay themselves, so that's about 500-600 per item. So let's say he's at around 6-7k earned? Minus the purchase of the GP/10 items, of course.
You might not have as much use midgame if you bought a Phage and Wriggles, but come lategame you can sell the Philo and Avarice and buy a Triforce outright, and it comes all without that messy “fighting Jayce” thing.
But okay, enough about that. I think this is how people feel about Teemo. It's more important to know how to beat him than it is to play him. And it's because he's honestly not that hard to play.
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Since he gets his Transform at level 1, that's your main advantage, and you need to push it. Swap to Cannon first thing, and go to lane and lay the pressure on. Keep auto-attack harassing the best you can, and if they duck into the brush, jab at them with Power Slam combo (Blast + Gate). Don't get too spam-happy, though, as the Gate's casting costs are higher than it used to be.
Whenever engaging for more than harass, keep in mind the basic combos for Jayce, and fiddle with permutations from there. Power Slam is Gate and Blast, which augments the damage, and To The Skies followed by Thundering Blow is a strong melee combo. Add whatever strikes your fancy from there – turn on Hyper Charge, transform, then follow up with the melee combo. Alternatively, You can also Power Slam before that, then run through the gate to pursue for the melee combo. Or Power Slam, Hyper Charge, run through the gate, transform for bonus damage on next hit, To The Skies, three max-speed attacks at boosted damage (Hyper Charge carries over to Hammer), then Thundering Blow.
As with Gangplank, paths diverge, but either way you want a Triforce. It just has too much of what he wants; fast cooldowns means lots of Sheen procs, a passive slow, bonus attack speed, crit chance, a bigger mana pool, and movement speed. From here, decide what's important to the team – are you the primary initiator, or just a damage dealer? For the former, tank items like Frozen Heart (CDR does wonders) or Randuin's Omen, Banshee Veil, and Guardian Angel. Otherwise, Bloodthirster, Last Whisper, and possibly a Stark's Fervor or Maw, depending on what you're going for. Mix and match depending on what the team needs.
And really, that's all there is to it. Jayce is pretty simple (albeit very very fun) to play, and build, and he's extremely versatile. It's all a matter of crushing your laning phase. But really, you didn't come here to learn how to play him – you want to know how to stop him. And as I said, there's very little ways to beat him that aren't risky. Hopefully, the Season 3 changes will make him more of a fragile lane, because that's what he needs to be less frustrating.