You have a hidden MMR in normal games and also another separate hidden MMR for ranked. MMR goes up as you win and down as you lose. It takes quite a while to get your MMR adjusted to the point where you're being matched with other people who are pretty much all the same skill level. It is possible that your normal MMR is lower than your ranked MMR, which means that you play against easier opponents in normals. Naturally, you do better when your opponents are worse.
In addition, you've only played 19 ranked games in total. Not only does this mean it's really likely that your MMR is off, it's also a mistake to draw a conclusion based on your performance in so few games. You have only one ranked game as Jayce. Give it time for the law of averages to work. Maybe your next game as Jayce will go better, maybe it won't. When you're 3-20 as Jayce then you can say you've done really bad with him.
And finally, just a quick word of advice. In both your normal history and your ranked, I see games where you didn't buy boots. There's no champion or role that doesn't need boots. Even if it's a 20 minute game, you should have boots by then. When you rely on your base movespeed, you give a lot of free kills over to the enemy and you also let a lot of kills get away, all while providing reduced map pressure and missing more farm than you should. Everyone needs boots, pronto.