Rankings Methodology

The basic rules are:

   1. Your Ranking "Result" is the average of your Scores for individual races.
   2. Your Score for an individual race is the Course Difficulty, divided by your time in minutes.

Example: The Course Difficulty is 5000, your time was 1:40:00 or 100 minutes. Your Score for that race is 5000/100 = 50.

If you want to know how well you did in each race, you can look up the Course Difficulty (usually reported with the rankings) and your finish time in minutes (converting the seconds to fractions of a minute) and divide the Course Difficulty by your finish time.

   3. The Course Difficulty is the average of the Personal Course Difficulty experienced by every finisher of the course.
   4. The Personal Course Difficulty for a finisher is the "Result" of that person, multiplied by his/her finish time in minutes.

Example: If your Result is 80 points, and your finish time on a course was 60 minutes, your Personal Course Difficulty would be 80*60=4800. Similarly, if your friend's Result is 40 points, and he/she took 2 hours = 120 minutes, he/she would have the same Personal Course Difficulty: 40*120 = 4800.

Some observations:

• If you are on average twice as fast as somebody, you should end up with about twice that score.
• It is possible to end up ranked lower than someone whom you beat every time you ran the same race. What? Why?

Say Charlie beats Albert by 1 minute in the only race they run directly against each other. Then, in a second race, Albert beats Bob by 10 minutes, and in a third race, Bob beats Charlie by 10 minutes. By implication from the second and third races, Albert is much faster than Bob who is much faster than Charlie, so Albert is much, much faster than Charlie.

The result of the first race suggests that Charlie is slightly faster than Albert. To reconcile the two apparently conflicting implications, the math averages things out, and between "Albert is much, much faster than Charlie," and "Charlie is slightly faster than Albert", lies the average "Albert is faster than Charlie". Therefore Albert would be ranked above Charlie, even though Charlie beat Albert the only time they ever raced head-to-head. The math in rules 1-4 above does all of this transparently.

The advanced rules

Don't read these unless you:

• already understand the above rules (1-4) and

• really want to know the nitty gritty details.

   5. Rules 1-4 are circular, i.e., in order to get the Results you need the Scores, for which you need the Course Difficulties, for which you need the Personal Course Difficulties, for which you need the Results. Where do you start? Everybody starts with 50 points for their result and then you loop through the rules again and again, hence the name iteration. Because of rules 6 and 7 the solution always converges, and is non-drifting. The iteration stops when the numbers converge (stop changing from one loop to the next).
   6. The "average" in rule #1 is a regular arithmetic mean.
   7. The "average" in rule #3 is a harmonic mean, which is the reciprocal of the arithmetic mean of the reciprocals.
   8. In order to do the final determination of Course Difficulties, all valid finishes are used, and all scores are averaged for the Result. Valid finishes are times (not OT, DNF, MSP, etc.).
   9. In order to do the final determination of Results, all results are used, except DNS. Results of OT, DNF and MSP are scored as 0.
  10. If you run 4 or fewer races, then all of your races are averaged together. If you run more than four races, you get to throw out one low score for every two additional races. For example, if you run 6 races, then you get to throw out (6-4)/2 = 1 score (your lowest) and the remaining (top 5) scores are averaged. If you run 7 races, then you get to throw out 1 1/2 scores. So your top 5 scores plus 1/2 times your 6th highest are added and then divided by 5.5.
  11. The Scores are normalized (multiplied by a constant) so that the top three finishers on each course average 100 points.
  12. Also included next to the result is a "Time". This time is based upon a course where a 100 point competitor would finish in the "ideal" time for the course. The "ideal" times were chosen at the lower end of the Orienteering USA goal time range: 45 minutes for Brown, 50 for Green, 60 for Red, and 75 for Blue.