If I could Re-work Urgot, this is how I would do it.
I didn't use any real numbers for damage and or CC other than time based numbers in this because I'm not the best at math and feel I would not do well in proper balancing so instead I used descriptions in the same style as you would find on the client and decided to leave it to your imagination.
let me know your thoughts.
Passive: Grotesque Vital Fluids Upon death, Urgots grotesque body overflows with corrosive fluids for 1 second, he will then explode, leaving a lingering corrosive gas in a small area for 5 seconds that slows and damages enemies based on his level every second they remain in the gas until it dissipates.
Q- Acid Hunter Missile ACTIVE: Urgot fires a missile in a line towards the cursor, dealing physical damage to the first enemy hit, leaving a corrosive charge for 5 seconds dealing physical damage over time.
W- Terror Capacitor ACTIVE: Urgot charges up his capacitor to gain a shield that reduces Damage taken by a base percentage, plus a percentage of his maximum health, for up to 4 seconds. while the shield lasts, Urgot gaines flat movement speed and ignores unit collision.
E- Swap Ray ACTIVE: Fires a slow moving Skillshot based beam that decreases in size the farther it travels. If the beam hits a champion they will be charged, and after a .5 second refresh, Urgot my press E again to swap places with the afflicted champion while within a certain distance, if the enemy champion is too far away, then after 3 seconds the charge will detonate, dealing magic damage and applying a mild slow effect for 1.5 seconds. can be blocked by minions and neutral monsters, but he won't swap with them.
R- Noxian Overdrive ACTIVE: for the next 7 seconds, Urgot goes into Noxian Overdrive, empowering his abilities. While in this state, Acid Hunter Missiles lock onto targets that are hovered over your mouse cursor within a medium radius, and gain Splash damage, dealing initial damage to surrounding targets and adding reduced corrosive charge to surrounding targets within a small radius. initial target will still take full corrosive damage. Terror Capacitors shield will persist for the full duration of Noxian Overdrive and is empowered, dealing minor magic damage within a small radius around Urgot, allies also gain a small percentage of Urgots bonus Armor and Magic Resist while the ult persists. Swap Ray will ignore unit collision, and the slow is applied instantly on hit, or after the swap is complete.
I decided his Q should be a little more threatening as i felt it didn't do a whole lot as a harras tool being able to be blocked by minions, so i gave it a corrosive buff to compensate for it, now it is a lot more powerful while still avoidable through kitting and staying behind your minions.
As for his W, I wanted to boost urgots identity as an ADC tank, with emphasis on tanking potential, by adding damage reduction through a percentage instead of a flat number, and by adding health scaling instead of AP scaling, i feel this opens up more item options for more pure tanking builds such as randuins, warmogs, and banshee's veil.
His E is a modified version of his old ult, it no longer gives armor or suppresses them, but gives urgot an annoying form of CC. I added the ability to be able to swap on will so Urgot could avoid baiting situations making it a worthwhile tool to use and with his new tanking prowess, gives his a great initiation tool to single out carries and throwing himself into the enemy teams with encourage them to waste damage and spells while his teammates finish off the carry. The drawback, the further the beam goes, the harder it is to land, the small refresh time window gives the enemy time to flash, dash, and run out of range before the recast.
As for his Ult, I wanted to do something that not only increased his threat as a carry, but would still be viable for tanky builds. I felt that making his Q based more on AD scaling on his Q would be enough to be a high damage carry, in ult form so I simply recycled his homing and added splash of his old E ability to make it more of a game changer like most ults. I added the Armor and MR buff to allies to further synergies potential tank builds on urgot. if urgot builds like a carry, the ult increases carry potential while adding little defence. if urgot builds tanky, the ult will increase tanking potential while still giving a little extra damage.
How did I do?