My current favorite champion to achieve the highest rate of solo carry is Kha'Zix.
Firstly I believe that Jungle is the most impactful role in soloQ and therefor the role to main if you want to increase your potential to carry.
Then Kha is excellent at taking out key target before a fight or at the beginning of the fight. The jump reset allow you to get out of sticky situations after your assassination and allowing you to tempo a little bit before going back in to clean the team fight.
Kha is also amazing to secure objectives.
This just my opinion,based on my matches in silver PH server, this based on 9.6 patch and you may want to read the patch notes for more details
Firstly I believe that Jungle is the most impactful role in soloQ and therefor the role to main if you want to increase your potential to carry.
Then Kha is excellent at taking out key target before a fight or at the beginning of the fight. The jump reset allow you to get out of sticky situations after your assassination and allowing you to tempo a little bit before going back in to clean the team fight.
Kha is also amazing to secure objectives.
It got me to diamond within a week on NA