Why would I pick Jax
When I could pick Irelia or Riven
When I could pick Irelia or Riven
because he has more eyes
Because your team is low on magic damage.

Because he is the champ.
Because he is the champ
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Because I haven't done my placements yet and animation cancelling is Freelo? idk, you tell me. I haven't played her since S2.
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"Hey man, I'm diamond! That means I'm always better than the rest of you no matter what!" :D
Yeah, because there's no way anyone is not climbing because there are things they'd rather do with their time, right? It's cool that he enjoys his climb, but the man can't take a joke.
Yes animation cancelling is a huge advantage though I will agree.
Because, Jax's late game is scarier than both of theirs and will win 1 v 1 against either of them post 6. Also
and Jax is only 1350 IP so he's easy to buy.
If you're team is physical-heavy Jax is a pretty solid mixed-damage type to throw a monkey-wrench in hostile itemization.
As mixed damage - Jax is also a much better pick vs. a few top-lane picks that really want to stack armor.
into
would not be a good idea.
Vs. split-pushers that are going to be trying 1v1 tactics: Jax is pretty much the best 1v1 champion in the game, and will cause serious issues to anyone AA reliant enough to deal respectable damage vs. towers.
If you're team is thinking about doing a 1v2 lane swap to allow a marksman like Vayne a solid start - you're obliterating Riven's chief strength and likely causing a domino effect that will kill her remaining strengths, where Jax is a little more level based and will be a monster given enough time. Riven's team-fight presence by comparison is almost completely reliant on getting a lead, where Jax can still be useful if he's even or slightly behind. 100% evasion and 25% AoE reduction doesn't change based on itemization, Riven's HP shield does.
If your team wants to focus on picks, split-pushing, or otherwise skirmishing strategies involving several small-fights over large, team-fight battles: Jax is absurdly good at those.
There's plenty of strategic reasons to pick Jax over Riven or Irelia.
The strengths Riven and Irelia have is they're just more reliable in blind-pick games where they're strengths play better to default strategies. Don't confuse that with always being better 100% of the time, it's not at all the same thing.
I wouldn't pick Jax into Malph either, Malph cuts his DPS pretty hard. But that's a side point, and your point is great.
Jax is a ball of stats. Of course he's not going to be worth picking if other ball of stats are better than him. In a couple of months he'll likely be a bigger ball of stats than Irelia and you'll get to play him again - yay.
Because he's one of those champions Gameplay & Balance just loves no matter what.
A lot of those eggplants I run into on the rift also are not lacking in self esteem I can tell you that...
I used Jax to kick butt a few seconds ago. He's freelo
because u r not a filthy human beigns?