Tristana: Thoughts and Ideas
Three majour flaws about Tristana:
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She is a very clunky feeling champion.
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Two of her abilities literally just should be implemented into her base stats, this also makes her have two abilities that are not very interesting.
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Tristana doesn't actually have an identity; hyper marksman is not one because we have plenty of those already and the others have their own niche to them. Jinx is the resetting crazy person - with lots of guns, Twitch is Spray and Pray teamfighting madness, Kog'Maw throws up on your face - also a void puppy, Sivir makes your team move fast with Ricochet's artificial long range, etc. Tristana right now has just steroids and is clunky to balance out those steroids - also I do not want Tristana's identity to solely be on the fact that she scales (or have this identity at all) so a redesign would be the best for her for the long term.
Reminder: Numbers are the easiest things to change and tune.
Basic Attack Range: 575 units [up and down from 550-669] Attack Animation: Should be cleaned up and quickened to feel less clunky, and feel more responsive Movement: 330 units per second [up from 325] Attack Speed: 0.677 +4% per level [up from 0.656 +1.5% per level]
Rapid Fire (Passive): Whenever Tristana casts on ability her next basic attack within 2 seconds fires 4 shots at 30% damage each, only the first shot applies on-hit effects. If this attack critically strikes then the shots do not deal increased damage and instead more shots are fired [8 for normal crits; 10 with Infinity Edge crits].
Demolition (Q): Cooldown; 10/9.5/9/8.5/8 seconds; Cost: 50 Mana; Range: 900 units Passive: Tristana's executes cause the dying enemy to explode sending off shrapnel around it dealing 30/50/70/90/110(+20%AP) magic damage to nearby enemies.
Active: Tristana fires a shot in the target direction dealing 10/15/20/25/30(+100%AD) physical damage to struck enemies, including structures, and applying Demolition's passive around every enemy struck.
Rocket Jump (W): Cooldown: 18/16/14/12/10 seconds; Cost: 60 Mana; Range: 900 / 350 units Active: Tristana blasts the ground at her feet and goes flying off to the target location, slowing enemies down by 90% for 1.5/1.75/2/2.25/2.5 seconds upon impact. Tristana can basic attack and cast her other abilities during Rocket Jump.
If Tristana lands on an Explosive Charge then it detonates for doubles its damage and refunds Rocket Jump's cooldown and mana cost.
Passive: Kills or assists against enemy champions, structures, or epic monsters will refund Rocket Jump's cooldown.
Explosive Charge (E): Cooldown: 12/11/10/9/8 seconds [after detonation]; Cost: 40 Mana; Range: 600 / 350/700 units 1st Cast: Tristana places a charge on the target enemy, can be placed onto enemy structures greatly increasing the explosion radius. The charge falls off the target and becomes disarmed if Tristana does not attack the target for 4 seconds.
Every attack and shot from Tristana charges this charge causing it to deal 10/15/20/25/30(+10%AD)(+15%AP) physical damage when it explodes, stacking infinitely.
2nd Cast: Tristana detonates the charge. If the target dies then the charge also detonates.
Kamikaze Bomb (R): Cooldown: 120/100/80 seconds; Cost: 100 Mana; Range: 900 / 600 units 1st Cast: Tristana places a large bomb on the target champion or at the target location for the next 5 seconds.
2nd Cast: Tristana detonates the bomb knocking back struck nearby enemies and herself away. If Tristana gets 10 attacks and shots against the bomb then it will explode immediately and deal 300/400/500(+100%AP) magic damage to struck enemies, can damage enemy structures.
If Kamikaze Bomb is on an allied champion or Tristana then it cannot be attacked and deals 250/325/400(+80%AP) magic damage while knocking back struck enemies when detonated.

(yes Trist has one, but based on this you aren't using it to gapclose), invisibility
as well as the movespeed from Lethality items and Youmuu's and Edge of Night shields.