Jayce got 2 abilities, that deal magic damage. His E, which hits for insane 20% of targets HP and his W, which is lighting aura around him. That aura is only skill, which scales with AP out of 7 abilities Jayce posses. Still I think it's worth building around. Because Singed exists.
Let's look at the numbers between Singed and Jayce
Singed wins there by hard. 25% of mana into HP is amazing. Singed will out-health Jayce any time.
- Jayce's W has 4 second duration, 6 second cooldown and 95+0.25 AP, costs 10 "mana-per-second"
- Singed's Q has no cd, "infinite" duration 70+0.3 AP, costs 13 mana-per-second
Cooldown part can be solved by CDR, if you want perma-W, since with 34% CDR, it has 4 sec cooldown.
After solving simple equation (95+0.25x=70+0.3x) I have found Singed needs >500 AP to get more damage from his Q and Jayce with same AP with W.
Trade-off might be that you will get 2 more ticks outside of gas with Singed (there should probably be done math about how big of an edge Singed gets thanks to this), but Jayce's W has much wider and better positioned aura of effect, where you will hit more enemies and a lot easier. And chasing is much less awkward with Jayce than with Singed, since you have your aura in front of you too.
- Jayce's E does 160+20% of enemy health damage, stuns for 1 second and knocks them in front of you, 40 mana, 10 cd
- Singed's E does 300+1.0 AP, fling over the head, 140 mana, 10 cd
Neither Jayce nor Singed get a lot of AP, so I doubt Fling outdamages Jayce's E. Especially with some MPen, 20% down from a tanky character is painful.
Its now all about if you prefer fling over the head or fling forward. Personally I was always terrible with Fling on Singed so I enjoy Jayce more. Especially with his Q.
III. AOE SLOW
- Singed got 75% slow on 14 sec cd, no damage, 110 mana, huge range
- Jayce got 50% slow on 8 sec cd, 200 damage, 60 mana
This is the tiebreaker for me. Having gap-closer/slow is just awesome, and gives yet another damage edge over Singed.
- Singed gets 65 ap, mres, armor and movement for 5 seconds
- Jayce gets 35 mres and armor at all times while in Hammer mode
Singed is definitly stronger during those 5 seconds, but only by 65 ap, 30 mres and 30 armor. Movement speed is not a problem for Jayce, he gets 40 on every transform and additional 50% boost from Speed Gate, which is available much more often. Also shot in ranged mode reduces Armor and Mres (yay!) and first hit in Hammer mode does bonus magical damage (yay, 3rd magical damage source!)
One last tiny point: Jayce can be long-range and farm from a distance, which gives him instantly edge in line. You can even start with a doran blade or two and then continue with AP build, similar to Kennen. Especially since W on early levels is not nearly as reliable as Singed's Q on early levels.
As attachement, I tried this in Dominion and it worked quite good (those 2 normal games are with AD build).