What would be the most relevant characteristic to have to be extra good player?

There are a number of characteristics that strong players have going for them. Trying to single out just one would be very difficult, IMHO. I used to categorize characteristics as: Psychological, Social, Physiological, Tennis-specific, Financial, Facility, and Luck. Don't forget luck :-)

It seems to be a good thing to have some part of your game that distinguishes you from the average player. Whether that would be a strong serve, an incredible ability to return serves, out-of-this-world foot speed, ability to know how to beat players by knowing what their weaknesses are, left-handedness, strong net play, all of these are possibilities.

The USPTA has a nice set of DVD's that go into the necessary "ingredients" that strong players seem to have in abundance. The package is called "The Six General Performance Components of Tennis." It's available at:

http://usprotennisshop.com/ <-- look for "DVD library" in the lefthand column

You will find a lot of other DVD's there, too.

When you get down to it, lot's of the most talented players never make it on the Tour because they lack commitment, determination and drive and a healthy body that does not injure easily.

If you consider there are many talented people but some are just better - why? The American Jim Courier wasn't the most talented but his drive, commitment and work ethic meant that he was one of the fittest men and could outlast others. He learned and practiced the basic skills as well as always training at maximum pace. I once saw him doing practice sprint runs on a day of 35 celsius degrees in Melbourne during the Australian Open and behind him was a tractor tire that he was dragging.

Roger Federer could not manage the heat very well so he decided to do training camps in Dubai where it gets to 45 celsius+ degrees. Here is the determination and commitment aspect.

If you get to the Open's or any major tournament where the big names are playing, go out to the practice courts and watch the way they practice - you would think they were playing for their lives, and then they shower and go and play their next match - after they've been practicing for 2 hours!

talent is the only differential