USOF Iteration Ranking Rules

Adapted for USOF from Wyatt Riley's BAOC ranking rules, 1999.

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
    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 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 such as OT, DNF, MSP, etc. are scored at the course time limit plus 20 minutes.
    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 scores are normalized (multiplied by a constant) so that the top three finishers
    average 100 points.
    12) Also included next to the result is a "Time". This time is the 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 USOF goal time range: 45 minutes for Brown, 50
    for Green, 60 for Red, and 75 for Blue.
 
 
 
 

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