From my own experinece as a player (I started when I was 12 years old, and got tennis scholarship in U.S.A.) and my experience as a coach(I was with one person from the time she was 6 year old to WTA ranking) to try to make as a professional tennis player would not be smart move on your part.
I would state just few reasons why:
- professional tennis is highly competitive sport
- at 13 you already missed the best phases of development for certain physical capabilities
- it takes 10 years (10000 hours) of training to get to the point where one can say if there is chance to become professional
- tennis is very unjust sport.Only players within first 100 ATP/WTA can make living playing tennis
- to start you have to have everything of high quality what is very expensive
The chance to succed in tennis when you start at right time(first 100 in the world) is very small.Your chance at 13 to do this is non existant.Everybody who says opposite is oversimplifying complexity of one to become professional tennis player.So, I would suggest that you learn tennis to be able to play as recreational player, and use your energy, drive, and time for some other goal which you have realistic chance to achieve it.
I must mention one episode from my coaching life.In 1995 I started to coach a 10 year old girl who started to play tennis when she was 9.She already competed in the tournaments 10 and under.I noticed her talent, but because of the late start she was not equal to her age peers.Althought, she was making fast progress when I found out that at the same she was playing badminton (she started to play badminton when she was 6 years old), and doing fine, I recommended her parents to stop playing tennis, and concentrate on badminton.They did. I was proud of myself as I made her very good tennis player.8 years later, I read in the newspaper that she made national team in badminton.
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In Depth Description of Bringing a Child Up a Competitive Ladder with Advices and Recommendations