An idea of a machine gun mage.

I'm just going to say Ryze, because its the easiest for everyone to imagine.

Passive: Each spell cast increases your damage output by x%, starting at 0% scaling up to 120%. Time per stack is 4 seconds. Damage increase on minion spell hit is capped at 50%.

Q (Skillshot): Ryze throws out a orb of energy. Dealing 60/70/80/90/100 + 30% ap magic damage. On Minion hit increase passive by 5%, on champion hit increase passive by 10%. Cooldown: 6/4.75/3.5/2.25/1 Mana cost: 20/25/30/35/40

W (AoE Skillshot): Ryze creates a zone in which all champions are grounded, after .75 second all enemy champions inside are stunned for 1 second. Dealing 80/95/110/125/140 + 20% ap magic damage. On Minion Hit increase passive by 2%. On champion hit (W2) increase passive by 15%. Resets Q. Cooldown: 20/18/16/14/12 Mana cost: 70/80/90/100/110

E (AoE Skillshot): Ryze creates a slow field for 25% of his passive scaling (0% - 30%). When the slow field melts, enemy champions stuck inside the AoE take damage dealing 75/90/105/120/135 + 25% ap magic damage. On Minion Hit increase passive by 3%. On champion hit E1, increase passive by 10%, on champion hit E2 increase passive by 15%. Cooldown: 18/15/12/9/6 Mana cost: 65/75/85/95/105

R (Self Buff): (active) Ryze becomes transcended for 15 seconds. Every time a champion is hit by an ability (non stacking on multi champion hit), reduce cooldowns of all spells by 15%. Capped at 85% on a full cycle. (Passive) Whenever Ryze lands an ability either the initial hit or secondary hit, reduce the cooldown of Q by .5 second (Goes inactive when Active is on).

Extremely strong after laning phase. Extremely weak during laning phase. Best in a teamfight.