Here's a detailed explanation of how times would be converted to points in the system I'm proposing.
The winner of a race gets a predetermined maximum number of points. Every other competitor who finishes that race would be awarded a lesser number of points, based on the percentage by which their finish time exceeds the winner's time. This would be calculated using a simple exponential function so that every additional
X% in time difference behind the winner would earn
half as many points. (I call this
X the "half-points threshold".) After doing a lot of numerical analysis, I'm hovering at 15% as being the best choice for
X, with the range of 10%–20% seeming plausible.
For example, let's say the winner of a marathon finishes in exactly 75 minutes (1:15:00) and is awarded 1000 points. [Using 1000 allows more precision than 100, while avoiding decimal points.] And assume we're using a 15% half-points threshold. Then someone finishing 11.25 minutes later (1:26:15) would be 15% off the winner, and would earn 500 points. Someone finishing another 11.25 minutes later (1:37:30) would be 30% off the winner, and would earn 250 points. And so forth.
Here's a table showing how this would play out for various finish times. (There are three possible point equivalents given for each time; these show the result of using a half-points threshold of 10%, 15%, or 20%.)
1:15:00 = winning time = 1000 : 1000 : 1000 pts
1:15:01 = 0.02% back = 998 : 998 : 999 pts
1:15:02 = 0.04% back = 996 : 997 : 998 pts
1:15:05 = 0.11% back = 992 : 994 : 996 pts
1:15:10 = 0.22% back = 984 : 989 : 992 pts
1:15:15 = 0.33% back = 977 : 984 : 988 pts
1:15:30 = 0.67% back = 954 : 969 : 977 pts
1:15:45 = 1.00% back = 933 : 954 : 965 pts
1:16:00 = 1.33% back = 911 : 940 : 954 pts
1:16:30 = 2.00% back = 870 : 911 : 933 pts
1:17:00 = 2.67% back = 831 : 884 : 911 pts
1:18:00 = 4.00% back = 757 : 831 : 870 pts
1:19:00 = 5.33% back = 690 : 781 : 831 pts
1:20:00 = 6.67% back = 629 : 734 : 793 pts
1:22:00 = 9.33% back = 523 : 649 : 723 pts
1:24:00 = 12.0% back = 435 : 574 : 659 pts
1:26:00 = 14.7% back = 361 : 507 : 601 pts
1:28:00 = 17.3% back = 300 : 448 : 548 pts
1:30:00 = 20.0% back = 250 : 396 : 500 pts
1:35:00 = 26.7% back = 157 : 291 : 396 pts
1:40:00 = 33.3% back = 099 : 214 : 314 pts
1:45:00 = 40.0% back = 062 : 157 : 250 pts
1:50:00 = 46.7% back = 039 : 115 : 198 pts
1:55:00 = 53.3% back = 024 : 085 : 157 pts
2:00:00 = 60.0% back = 015 : 062 : 125 pts
2:10:00 = 73.3% back = 006 : 033 : 078 pts
2:20:00 = 86.7% back = 002 : 018 : 049 pts
2:30:00 = 100% back = 001 : 009 : 031 pts
And here's a chart that shows the same information, from the winning time to +50% back. The 10% curve is drawn in orange, the 15% curve in red, and the 20% curve in green. In addition, each curve has a straight dashed blue line intersecting it at the half-points threshold, that shows what would happen if points were deducted at a uniform linear rate instead of on an exponential curve.
Please study the table and chart for a bit, try to get a feel for how the calculations work, and see if you can judge which choice of half-points threshold (10%, 15%, 20%) you think would be the most appropriate.
(And yes, you can now tell me to turn off the dang computer for a while and go skate!)
