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.