Here's the way I think you get to the tennis scoring system, which may not be accurate:

First, you start by scoring based on a clock face - in 15s, aiming to hit 60 (four 15s). So a quarter of a circle per point, and a full circle to win.

But, then you have the rule where someone must not hit 4 scores (60 points) to win but must have have 4 scores AND be up by 2 scores, not just 1. So for example, if both players are at 45 points, one of them needs a net of 2 more scores to win. To make this work and keep 60 as the number to win, you need to squeeze two more scores in between 45 and 60. So instead of 15s, you go by 10s. Of course two tens below 60 is 40 instead of 45, so you adjust the 45 down to 40. Thus the possible scores go 0,15,30,40,50,60.

Except once both players have at least 3 scores (40 points), all that matters is who is ahead, since they both qualify to win as soon as they are two scores ahead. Therefore there really is no 50, as you either go from 40 to win, or you both hit 40 and then the scores don't matter and you just talk about who has the advantage (one score ahead). So you have 0,15,30,40,Win