Cheatsheet is hard to understand, guide lacks details and is incomplete.
I'm still wondering if this guide has potential or not.

You have Math prove or it is just a supposition?

Uhhhh AP ezreal is played in diamond, and I agree that they aren't completely serious about it but ap ezreal is viable enough to be played in anything other than professional gaming. And no, orianna is not better in EVERY way. Ezreal does more damage, and has a better escape.

He deals plenty of damage but a normal AP build for Ezreal brings no utility to a team, hence why we don't see much of it.

However there is a great alternative for players who enjoy playing Ezreal and want to go Mid but don't want to bring their team down.

There is an AD Mid Utility build for Ezreal that works wonders and solves all of the problems that afflict AP Ezreal. I have been experimenting with it ever since they switched Muramana's passive from magic damage to physical damage. Set up typical AD Ezreal runes (AD / Life Steal Quints, AD Marks, Armor Seals, MR Glyphs). All you have to do is rush Manamune which allows you to farm incredibly easy in Mid Lane, provides AD for last hitting and mana for spamming Mystic Shot to farm / push / harass. Arcane Shift keeps you safe from ganks and your long farm-range via Mystic Shot also compliments this safety. Max Mystic Shot 1st, Arcane Shift 2nd ( Muramana will apply its on-hit damage on Arcane Shift), and Essence Flux last. You should be able to evolve Manamune into Muramana before 24 minutes, as Manamune stacks on ability use AND auto-attack unlike Tear of the Goddess which only stacks on ability use. You get Iceborn Gauntlet ASAP as well. If you need MR you can buy an early Negatron Cloak before resuming normal build (this can build into Banshee's Veil later). This is where the build begins to differ from the normal Ezreal "blue build". Buy Black Cleaver. You are not the primary AD Carry on your team. You are an AD Mid. Iceborn Gauntlet will help you peel for your ADC and help you kite / chase the enemy front line. Black Cleaver's armor shred stacks apply on Mystic Shot (2 stacks if Muramana is on), your Auto Attack, and on Arcane Shift when you have Muramana toggled on. This will allow you to shred the armor of the enemy front line so that your ADC can melt them. You also have a wonderful Attack Speed Buff on Essence Flux to give to your ADC. Make sure to use it to buff your ADC rather than hitting enemies with it because your AS doesn't matter. I normally round the build out with a Last Whisper and a Banshee's Veil but sometimes I will buy a Frozen Heart if the enemy team consists of AS oriented divers like Nocturne.

This build allows you to manipulate Iceborn Gauntlet to peel and guarantee that your ADC remains untouched in fights, allows you to buff your ADC's AS with Essence Flux, and shred the enemy's armor with Black Cleaver. This build also does IMMENSE DAMAGE and I usually end up having higher "damage dealt to champs" on the end game graph than my ADC does, despite the fact that I am peeling for them and buffing them. The mana you get from Banshee's, Iceborn, Muramana, and occasionally FH makes your Muramana's passive do insane damage. It also cures AP Ezreal's problem of having a bad laning phase. AD Ezreal has an easy time mid. He farms / pushes well and is relevant in early skirmishes much quicker than AP Ezreal.

Though, I love playing AP Ezreal just for ***** and giggles so I can snipe people and yell BOOM HEADSHOT when I get a kill across the map. The AD Mid build overall works the best though and brings the most damage / utility to Ez as a Mid Laner. Oh and YES it does work.

In true, like Satella say, an AP Ezreal is not unique in anything, an Orianna, like satella says too, do all he do better and something more, like farm easy. Its not about it is bad or it don't do his job, it is about reason. AP Ezreal have no reason to exist. But I think it is valid on normal games (supposed to be just for fun) if you don't have/don't like play another hero that do he does better. On pro leagues he may not appear. Sad but true.

If there's a champion who does everything better, why would you pick the inferior one? Not only are you decreasing the chance that you'll win the game, but you also handicap 4 other people on your team by doing it.

Ezreal does more damage than either lux or orianna if he has the same items, just gonna point that out. And not just a little more damage, a pretty significant amount.

Why do people play league of legends? If your playing just to pick the best champions and do only that, then your doing it wrong. Ap ezreal is insanely fun as a whole. He isn't viable in competitive play simply because he wouldn't get past the laning phase. At any elo below challenger he's fine. Diamonds play ap ezreal too.

What? Are you drunk?

Aseafy: Or, you can simply play champions like Lux/ Orianna and deal huge damage in a bigger AoE while being able to CC the enemy team. AP Ezreal doesn't offer anything spectacular to make him a compelling pick in any serious competitive play.

Want damage? Play Fizz and get 210% AP ratio on his Q, in addition to 175% AP scaling reliable AoE damage combined with a slow and knockup. Did I mention his laning phase is awesome and he is just as mobile as Ezreal?

Dude. He uses his q, gets lich bane proc. Q hits, and then procs lichbane. His q pretty much has a 1:1 ratio when it hits.

And ezreals main reliable damage is NOT his ultimate, you guys have obviously never played with a good ap ezreal. I'm not trying to say this guide is the best, but ap ezreal isn't as bad as you guys say. He arcane shift and w deal huge damage (the same as lux's skills pretty much).

Spellsword Mastery Point adds the other +.05 to make it a 1.0 AP ratio on Q. What do you mean it needs another skill to activate spellblade? Lich Bane works the same as Tforce or Iceborn on Mystic Shot, in that it activates and simultaneously procs the on hit effect. The ratios and raw damage are there for late game he just lacks CC, utility, and early game roaming pressure. He's also generally squishy and relies on kiting.

What the heck are you talking about? His Q has 0.2 AP. Sure, it can proc Lich Bane totalling 0.95 AP, but that's not spammable, it needs another skill to activate the spellblade.

He has 0 CC and his main source of reliable damage is his ultimate. Most of his teamfight damage comes from his ultimate. His Q is single target and his W is tiny.

His ganks suck, too. Champions like Orianna and Cassiopeia are basically better than Ezreal at every single stage of the game for everything except mobility. Most mid champions are either good at being roaming assassins or CC machines. Ezreal does neither. I can possibly see this working in specific team comps, but it's not gonna happen in solo queue where many people pick whatever and give 0 ****s about team comp despite the fact that they should know better.