The length of the string depends on the top, its gauge (thickness) and the style of throw, but NOT on the height of the player like in yo-yo. That was a mistake on the otherwise great To Be A Player video staring our yophosis.
For the American style of boomerang, tip up, the wrap should reach a height on the side of the top that produces the right lever (with respect to the center of mass) for the top to flip exactly 180 degrees. For example, if the string is too long and gets as high as the center of mass the top will not flip at all. Note that at the start the of the throw the top is spinning slowly and will flip easily. That is the reason the height of the wrap is so important (at least that is my theory.)
You can exchange length with thickness, as a short and thick string will give you the same wrap height than a long and thin string.
Unfortunately, tops can come with the wrong (sometimes very wrong) length of string from the factory. The YYF tops come with too long strings, but you would think most players that buy them are experienced and will realize this.
The Duncan Storm series (Ripcord and Bearing King) came with a string too short and that has frustrated countless players to be. With the short string the lever tends to turn the tip towards the player and the string to unwrap, so you have to throw it smooth and soft. With a longer string you can throw it very hard.
