I just wanted to put this out for all you guys trying to carry yourselves (out of Bronze especially). If you don't mind playing ADC and can actually last hit (this is very important) then this is where you need to look.

Attack speed is quite important for Ezreal. It allows for his full potential as a champion to be unlocked. So starting at the offensive tree, you definitely want to start with fury and get 4/4 on it and also in tier 1 you want to get 1/1 in butcher, this will help your CS. Then you want to drop to tier 2 and get 3/3 in brute force. Now some people like to put 1/1 in feast, however it is not necessary for this build. So we move on to tier 3 where you will get 1/1 in martial mastery, and 3/3 in executioner. In tier 4 you will get 3/3 in warlord, and 1/1 in dangerous game. In tier 5 you will get 1/1 in frenzy this will allow you to have even more attack speed making you an even more formidable opponent, and 3/3 in devastating strikes. To finally end in havoc. Moving to the defensive tree you want to get 2/2 in block, and 2/2 in enchanted armor. Then drop to tier 2 and get 1/1 in unyielding and 3/3 in veteran scars. Finally in tier 3 you get 1/1 in juggernaut.

All that needs to be said is that I know many people go max mystic shot first then essence flux, but with this build not complimenting AP at all its more beneficial to max arcane shift second and essence flux last since you only really need it for CD reduction and some harass. Also arcane shift has better damage starting and scaling to level as well as having its CD reduced for quicker escapes.

Flash is pretty much a given you either have this or you will have a rough time if you get caught either with your escape down or by a gap closer. As far as barrier goes it's a good spell to have for those dark moments. If you support is not running heal I would advise you to take it over barrier. Also if you feel rather confident with your support and your own ability you can also substitute barrier for ignite.

GET GOOD AT LAST HITS! I cannot stress this enough as an ADC this is very important to you and so is in lane management. You don't want to spam you mystic shot to farm just try to land as many auto attack last hits as possible and mystic shot when needed. Hitting full health minions or the big minion will help you see how much damage you are doing so you can estimate your last hitting better.