One of the problems is that because of the way damage in League of Legends works nowadays (Which I don't think is necessarily a bad thing) Every mage is a burst mage.
The Wiki says "Burst Mages aim to single out vulnerable targets by locking them down and following up with a devastating barrage of damage from range. Burst Mages struggle heavily against beefier targets who can shrug off their initial spike of damage." But that pretty much Defines all but a couple of mages.
The only Mages who don't basically die if they don't one combo you are like Cassiopeia, Rumble, Asol, Vlad, and Aniva. Every other mage, if the enemy gets to them and they don't kill them in 1 combo. They just die.
Like for example. They list Viktor as a battlemage. That's some bullshit. He is just a low range burst mage. His E has a nice AOE, but in reality, unless people are stacking up you will only hit 1-2 people with it, and 90% of his damage is loaded into a Lich Bane Q Nuke. Also Generally a Viktor will Blow his full combo one 1 target to eradicate them from the game. Also, he has very low survivability because his CC only works if they are immobile, and don't kill him within 1.5s
Basically what I'm saying is that the categorization of "Burst Mage" is fairly irrelevant since every Mage in the game operates on an "I Instakill 1 target and if they don't die I die." Playstyle. Every Mage minus a few exceptions is a burst mage in modern League of Legends. Now it wasn't always this way. There was a time when Viktor was a control mage. He had like 1/2 the damage he has now, and it was loaded 90% into his E. Not to mention since damage was lower his W was actually a pretty useful ability. But times have changed and burst mage is kind of an irrelevant categorization.
