How I would rework draven
I see that there are basically two options. Keep everything the same but boost him so that he gets some viability. This is the simplest rout and the only way to do it simple is to give him 150 range on his autos. Yea. I50. More than caitlyn. I say its the most simple, but really you need to increase adc attack range across the board so its got some hidden complexity..
The second way is to still give him increased range, but not as much and you change the way his axes fall and the way his w works. His w makes him like a hypercarry. It doesnt need to do that. His w needs to be a level 2 powerspike and not a late game dps steroid on top of his ad steroid (which is largely irrelevant btw. 200 bonus dmg per every other auto is garbage, no matter what anyone thinks).
If you look at draven's carry potential thru the game, he looks like a weird hypercarry. Hes got a trough between 20 and 35 min and then his win rate picks back up. This is because he obviously has snowball potential (mostly due to the duo lane, but also bc his passive and kit) but the spike in his carry potential after 35 minutes is because of his attack speed scaling which is some of the best in the game. Unless i remember wrongly, his base attack speed is among the highest in the game and his attack speed scales better with level than most. Combining this with his w, which he can use 100% of the time, and draven easily comes near the 2.5 AS cap late game. Thats what allows him to act sort of like a hypercarry.
I would change the w to be an auto attack reset like sivir's, the move speed and unit collision buff he currently gets (bet you didnt know he ignores unit collision on w), and nothing more. If you balance him so that 30% attack speed runes and the w spell allow both axes to exist in the air at the same time, then thats a really good lvl 2 for draven. He can toss both axes at you and position them to fall at the same spot at the same time since they will both be in the air at the same time. Then get his w reset. The key is that the attack reset allows two axe particles to exist in the air at the same time. That way, when he clicks off the glyphs should be overlapping when they appear on the ground. Im debating as to if the two autos should sort of just count as one auto for the purposes of rapid fire cannon. I think that they should both get the range from RFC. The enemy back line can just be zoned from him since the lack of AS steroid means that a strong front line will be able to deal with him.
This w change removes dravens late game potential to a large degree, which is problematic for his balance. He needs to start falling off after three items. It also gives him a lvl 2 powerspike worth respecting. Im not saying his current lvl 2 isnt worth respecting, but its more likely that you will overestimate that powerspike than anything else.
Another change I would make is to the way his axes fall. I would give players more controle over their placement. Id take away the random side to side displacement that occurs when you try to be stationary and I would take away the fixed distance aspect of the glyphs OR I would change the shape of his glyphs. If allowing players to precicely choose where the axes fall does not work out, then I would make the glyphs longer so that he has some flexibility as to where he can stand to catch the axe. Maybe an oval shape, with the long axis in the direction he throws the axe. That would help him juke and it would help him catch axes on the run. Keeping the overall area of the glyphs the same is not really important, but if you wanted to you could make the oval sort of skinny so that he has less leeway to catch the axe in the other direction. Lastly, I would make the axes fall at a rate that scales with his attack speed. Should fall at a rate of AS*2. And thats all I would change with regard to his axes.
Stand aside is fine as is, but with the w changes above you would expect people to start maxing it second which is good for draven overall.
His ult is something I would like to change. If his ult just boosted his auto attack range by 50 percent and worked sort of like kogs then I would like that.
I hate his passive. Id like to see something like a thick skin passive on him. Like tham kench grey health, but no shield. The gold passive is just fucking terrible. Its exciting to cash it in, but adds no gameplay and often has no impact. If I get a kill and back for a BF sword and boots, instead of a BF sword and one pot, thats unlikely to add anything significant to the next fight and you cant play around it like you can with jinx's sweet passive. I think grey hp would be really good for an early game adc and not broken at all late game, as long as you cant reactivate it for the shield. But hell, id take just about anything over dravens current passive. 10% lifesteal would be just dandy in comparison. I think some form of sustain would be best for him.