Von Ulric Jessop 

1. Points distribution 
Points distribution is modified to remove the fixed 50 leading points. Ratio of leading points to time points boosted to compensate and distance points curve slightly adjusted. With 50% pilots the points distribution is almost exactly the same as the existing system.
The exact distribution formulae are as follows:
	•	goal_ratio = pilots_in_goal / scoring_pilots 
	•	dist_pts = 1000 * (0.9 - 1.67 * goal_ratio + 1.71 * goal_ratio^2 - 0.59 * goal_ratio^3)
	•	lead_pts = (1000 - dist_pts) / 3.8
	•	time pts = 1000 - (dist_pts + lead_pts) 
I've attached a plot of the new points distribution (solid) versus the old (dashed). Note that with no-one in goal, I intend to award 100 leading points instead of the 25 according to the formula. If anyone objects to this in particular, let me know. 
2. Modification of Leading Points formula
Use of integral of leading weight curve to compute area under the curve from trackpoint to trackpoint, and also to compute missing area. This will only affect people who do not reach ESS, and gives them much fairer leading points.
The leading area is the sum of all areas between adjacent trackpoints plus missing area caused by the pilot not reaching ESS.
The leading weight is the function w(d) = (1 - 10^(9 * d - 9))^5 * (1 - 10^(-3 * d))^2, where d is the remaining distance to ESS / SS distance 
The old method of computing the area between two trackpoints P0 and P1 was simply (t0 + t1) / 2 * (d1 - d0) * w(d), where tn is the time since the earliest start, and dn is the distance remaining to ESS, of trackpoint Pn. The missing area was max_time * dM * w(dM), where PM was the last trackpoint in the flight. The use of the average time of the two trackpoints was for compatibility with old GAP versions and is probably outdated. It would probably be better to just use t1. 
The new method uses the integral of w(d), W(d0, d1) which is the area under w(d) between d=d0 and d=d1.
So now the area between two trackpoints P0 and P1 is simply W(d0, d1) * d0 * t1 (not using the average time), and the missing area is W(d0, 0) * d0 * max_time.
There is virtually no difference between the two methods for the area between two trackpoints. However, the old method of computing missing area makes the leading area almost totally dependent on the distance from ESS, while the new method is much fairer. In tasks with no-one in goal, the leading points will be much more related to leading, and less to the distance flown.