Here's another idea to consider. Rather than (or in addition to) awarding points based on finish order, how about awarding points based on time instead? [Edit: I see Birgit was thinking about this, too.]
Note that I mean relative time, not absolute time. Let me explain:
Every individual race would be "calibrated" by establishing the winner's time as the point of reference. The winner would be awarded a certain predetermined number of points, and all other finishers would then be awarded points based on how their time compares to that of the winner. This would be based on the difference between any one skater's time and the winner's time, taken as a fraction or percentage of the winner's time.
(If there are different categories or divisions of skaters competing within their group but not across groups — examples of such groups including Pro Elite Men, non-Pro women age 30–39, non-Pro men age 50–59, etc. — then the benchmark time for each group could be different, most likely being set by the fastest finisher of that group, if this is deemed to be the best policy. For instance, non-Pro women would not be benchmarked against Pro Men, but only against themselves.)
For example, suppose there's a marathon race in which the winner finishes in exactly 80 minutes (1:20:00). A skater who finishes in 80.8 minutes (1:20:48), or 48 seconds back, would be at +1% off the winning time; a skater who finishes 4 minutes back (1:24:00) would be at +5%; 20 minutes back (1:40:00) would be +25%; and so forth.
You would just have to choose a mathematical function to convert the diff percentages to number of points awarded. I've been experimenting with several candidates, and the best choice seems to be exponential functions of the form...
P = Pwin * exp(–a(tdiff/twin)^b)
...where Pwin is the number of points awarded to the winner; twin is the winning time; tdiff is the difference between the winning time and the time of the racer for whom we're computing points; and a and b are scaling factors that determine how steeply the number of points awarded drops off after the winner's time, and how quickly that initial drop levels out.
An interesting feature of a time-based points system is that it makes no difference how many competitors are in a given race. All that would matter is how much slower each racer was than the winner. This also means racers would be rewarded appropriately for finishing well ahead of their competitors (consider the solo-flyer Pro finishes at St. Paul and NorthShore this year, for example). It would also provide an incentive for racers who are "off the back" to keep working hard anyway so as to minimize their time difference, even if it doesn't affect their finish order.
Continuing with my example of a marathon won with a time of 1:20, and supposing we award the winner 100 points, ask yourself this... what finish time should be worth 90 points? 50 points? 10 points? etc.
Or, to put it another way, how many points should be awarded to a skater who finishes 5 seconds (0.1%) back? How about 48 seconds (1%)? Four minutes (5%)? Twenty minutes (25%)?
Cheers,
~ Justin
