Iteration Ranking Rules

Updated October 1999, based upon the BAOC Rankings done at that time.

Since people have asked, and it has evolved slightly over the last few years, and because I haven't explained it in a while, I thought I'd re-explain the rules of the iteration rankings method.

It is similar to USOF's method, with a few exceptions generally noted within the text below.

• 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 their 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 they took 2 hours = 120 minutes, they 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 their score.
  • It is possible to end up ranked lower than someone who 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 apparantly 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 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 (#7 is not used by USOF) 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. (USOF rules use the 40th percentile, which often leads to an unstable loop, at which point USOF reverts to my rule #7. Even when it does not result in an unstable loop, the USOF loop is "drifting" so that loosely-coupled groups of people are more likely to end up with somewhat skewed rankings with respect to each other.)
• 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 such as OT, DNF, MSP, etc. are scored at 2/3 the points of the slowest valid finisher on the course.
• 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.
• 11) The number of races you throw out can be fractional. If you run, 5 races, you get to throw out (5-4)/2 = 1/2 a race. This means that your lowest score is weighted at 1/2 the level of your top 4 races in determining your score.

  Illustration of Rule 11: Say you run 5 races, then half of your worst race gets thrown out. I.e. It's weighted 1/2 as much as the other races. E.g. If you score 100, 90, 80, 70 and 60, you're score will be: (100 + 90 + 80 + 70 + 1/2 * 60) / (4 + 1/2) = (370)/(4.5) = 82.2 which is 2.2 points more than the normal average.

  Note that rules 10 and 11 are provided as an incentive to attend many races, because the more you run, the closer you get to only your top 50% of scores counting toward your result. Rule 10 is used by USOF, rule 11 is not.

• 12) The scores are normalized (multiplied by a constant) so that the top three finishers average 100 points.
• 13) Also included next to the result is a "Time". This time is the based upon a course where a 100 point BAOC competitor would finish in the "ideal" time for the course. The "ideal" times were chosen at the lower end of the USOF goal time range: 45 minutes for Brown, 50 for Green, 60 for Red, and 75 for Blue.
  The 100 point USOF competitor is slightly different from this.

Questions and comments are welcome to WyattRiley@hotbot.com