Why don't we use this scoring system: 2 points for a win, 1 point for a draw, 0 point for a lose? In chess tournaments, when you win you get 1 point, when you draw you get 0.5 point, when you lose you get 0 point.

So we have to use two additional symbols to represent the score of a player: the radix point and the digit "5".
Or sometimes we use three additional symbols: " 1 / 2 ".

My question is: why don't we just multiply everything by 2?
When you win you would get 2 points, when you draw you would get 1 point, when you lose you would get 0 point.

This would simply have the benefit of economizing symbols and making the scores shorter. No more ".5" or "1/2".
Because it's a long-established convention and changing it at this point would be much more trouble than it's worth.

In the words of Gerald Weinberg 


  Things are the way they are because they got that way