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Hey platinumdragon, your scoring idea is quite interesting. I came up with a similar one once: b has to exceed w by 14 (for 19x19 board, 2xkomi in general) points to win, w has to exceed b by 1 point to win, anything in between is a draw (japanese scoring). I'm only 15, so people didn't respect it much and said it was too drawish, but what do you think of it? BTW, your "line of territory" and "line of influence" sum up to be the "fair komi" for any particular board (2nd line of territory plus 3rd line of influence equals 5 komi on 9x9, 3rd line of territory plus 4th line of influence equals 7 komi on 19x19, etc) in case you didn't know (japanese scoring). This has the rare exceptions: too small board (like 5x5), and infinitely big board (which isn't worth playing on anyway). ~srn347
The concept of draw is to prove that one player is better. If a player could not accept for a draw to exist, then they lack to skills to prove they are better than other players. Draw says that the player needs to improve more.
For the territory influence thing, it's the mathematics behind the board. Count the points from outside in until you reach half the board points. This line becomes the territory line. Defend this line and outward will guarantee a victory because it will assure that you will get at least half of the board. The point of the game is to get a little over half the board. That's why the territory line and the influence line is determine by the size of the board. It's only a coincident, or there may be a mathematical relation between komi and the size of the board. For certain, I will say that the largest board of a particular territory line will have it's komi the sum of the territory line and influence line. Such as 15x15 does not have komi of 7 because it's not the largest board of its kind. However, 19x19 is the largest 3rd territory line board.