Which burst mage scales best in the game?

I would think Veigar due to Phenomenal Evil Power.

Viegar has likely the highest burst, lux has the utility and range.

I'd suggest Vel'Koz (as a vel main) since he has a decent burst combo.

His passive deals true damage and his ulti deals true damage when his passive is proced, making him capable of melting squishees and tanks alike. Although you'll need to aim well cuz they are all skillshots and time them well so you can hit as multiple champs as possible.

Although keep in mind he is squishee and immobile. But you can always build these items for a little tankiness and you can also build for the mobility, but you have to stack it up so it can make you go super fast.

Since you asked which one scales best, like bruh, Veigar is legit the AP variant of Nasus.

I mean veigar indefinitely scales and I wouldnt really call tf a burst mage... hes more of his own type.

Depends. Veigar scales the best late game while Zoe scales the best mid game for example.

"AP scaling" mean one of two things: 1.) the flat amount of damage added per AP, and 2.) the ratio of adding AP compared to the base damage of a spell.

We'll also discount and who have infinite damage scaling

There's also the cooldown of spells to account for. I'll assume "burst" is dealt over 3 seconds, though at this point in the game that's damn near the length of an entire team fight.

I'll mostly be focusing on the cooldowns and raw damage added, and assume 40% CDR since every champion scales faster with 1066 gold of CDR than with AP.

with Charm amp, 307.6% AP scaling assuming everything hits the same target 2Qs, 1W, and 3s of Tibbers = 340% AP scaling 5 seconds of Q exposure (1 Q then another after 2.1s), 5 seconds of W exposure, 6 enhanced Es in 3 seconds, and R: 625% AP

is likely far and away the winner, as most others you listed have total scaling around 200% AP. I'll just cover the other answers people are giving in the thread.

: Q1 and 2, enhanced E, and 3 seconds of R: 265% AP scaling 3 soldier engage, 1.375 attacks per second = 2 autos, E passthrough, and R: 310%. If we extend the burst window out to allow an additional 3-soldier auto, it goes up to 400%. highest damage combo: Q W E Q E Q = 345% AP scaling, 23% bonus mana scaling. Hard to quantify whether this is more or less than Cass's damage output, but it's worth noting reaching 40% CDR with mana AP items is harder than focusing on just CDR and AP With 3 seconds of R exposure and both hits of death ray: 365% AP scaling 2 Es, Q, W, 1.5 seconds of R exposure, and 3 passive procs: 415% AP scaling

And to answer your specific question below:

Empowered Q and fully charged E both amped by R, and R's detonation damage: 280% AP R, 5 isolated Qs, and 3s of E: 435% AP; if the Q target isn't isolated, drops to 285% 3 autos, 2 Qs, W, E and R: 313% AP scaling

Ryze touched me with his 2 mana items. i almost died.

True Burst Mage = Veigar scales the best.

Out of the entire Mage roster the best scaling Mages are