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1) The picture showing Empower has incorrect information on it. (Empower scaling is wrong).
2) A couple of things are still out of date (Summoner's Wrath doesn't exist anymore so the explanation for Ignite is out dated. Your Doran's Blade start does not include a Health Potion. Also, the label for Quints of AD is "Greater Quintessence of Strength").
3) You never mention maxing Leap Strike first. Against ranged champions this is a better alternative to maxing Empower. Not only can you trade with ranged champions more often with the shorter cool down, but you can evade ganks easier. Also, maxing Q first and Empower only having 1 point in it, there's no need to use W in your harassment combo which helps with your early game mana issues allowing you to have mana to all in after you jump to and poke the enemy a couple of times. I would max Q over W always except against tanky champions that are going to rush armor because of the mana saving and maneuverability you gain from it. Against armor building champions like Renekton, however, maxing W for more hybrid damage is a better choice because Q is physical damage.
4) I would highly recommend taking "Dangerous Game" in the mastery tree over one point in Sorcery. The extra 5% of health and mana can mean surviving ignite early game or lasting long enough to kill two carries instead of one late game where as the extra 1.25% CDR is going to shave off 0.075 seconds on your Leap Strike cool down, 0.0375 seconds off of Empower, and 0.125 seconds off of Counter Strike. 5% of health early game with 550 base HP is 27.5 HP, if halved by ignite this is 13.75 HP which is one tic of ignite or 1 creep auto. 5% of HP late game with 3.5k HP is 175 HP which is an auto from anyone but the ADC or a tower shot worth of damage.
5) In your laning section you really showed your personal play style (fairly passive but willing to trade and fight if you need to). However, Jax does not have this fragile early game that a lot of people seem to think he does. If you are willing to start Doran's Blade or Shield for combat stats and push the wave a bit, stacking your passive in the process, Jax can out trade most champions early game. The few exceptions being really tanky, manaless champions like Renekton and Shyvana. However, against champions like Warwick, Mundo, Teemo, Vlad, Riven, etc. Jax can win trades early game when played properly and should definitely be the aggressor against range champions and squishy champions. If your play style is passive, then I suggest leaving the laning phase section as it is, but expanding how aggressive you should be in each match-up in the upcoming section. Hopefully this will make you want to try being aggressive early game and will vary your play style a bit. If you're curious on how and when to be aggressive I suggest watching some Wings Of Death VODs on Youtube. He explains his game plan against each champion pretty well and helped me a lot when it came to my early game Jax play.
Overall I still really like your guide. It's great for anyone trying to learn the champion. Just a few small changes that I personally would make but are really up to the player and his style. I hope to see your lane matchup section soon. Keep up the great work.
Fantastic guide. I took a few months off, and when I got back into league my old Jax build didn't work all that well. This guide really helped me get the rust off and pick up my Jax game again.
One question I had, though: what're your thoughts on Black Cleaver vs Youmuu's against armor?
Well I'd say black cleaver is an OK choice because of the stacking, as you should be dealing lots of dmg with AA, but I prefer Youmuu for the straight armor pen and really nice active. That gives you lots of chasing potential.
Overall, I;d say pick up Youmuu if your getting kited hard, and Black cleaver if not so much
One question I had, though: what're your thoughts on Black Cleaver vs Youmuu's against armor?
instant plus 1! great guide, i can tell you put a lot of effort into it :)
haha thanks! have fun on summoner's rift!