```For complete understanding of this rating system see please check out
previous difficulty rating systems.

This is a 3rd proposal ( in 2 years) for rating X-country courses.

VIRTUAL METERS ADDED TO X-COUNTRY COURSES FOR DIFFICULTY RATINGS.

Using Purdy Points for Rating X-country running courses.

Purdy points seemed like a nice idea for rating X-country courses,
hence the previous rating system on my web page. I've actually
modified the program and calculated about 50 courses using Purdy points.
Here are the 5 courses involved in the Footlocker finals and
times to compare with Balboa Park. ( from years 92,93,94, and 95)

ABSOLUTE COURSE RATINGS IN PURDY POINTS.
"KENOSHA1",   23.886,55
" VANCORT",   32.670,55
"MacAlpine", -16.190,54
"Woodw-pk",  -11.648,53
"BALBOA-P",   17.000,217

As seen above Van Cortland is the toughest (32.7 Purdy pts.)
and MacAlpine is the easiest (-16.2 pp).  Now Balboa Park was arbitrarily
chosen to have a rating of 17, and the rest of the courses are calculated
relative to Balboa. This is probably incorrect since a rating of 0 would
be the same as a 5k track. Question: is running a 5k course at MacAlpine
Greenary easier than running on a 5k track ? Probably not. If we set
MacAlpine to a 5 than we get:

"KENOSHA1",   44
" VANCORT",   53
"MacAlpine",   5
"Woodw-pk",   10
"BALBOA-P",   38

Well, this rating system seems straight forward enough:
Calculate the average Purdy point performances for two courses
and the average difference is the Relative Purdy point value for
the course.
This is the output of a program that does that...
For all courses compared with Balboa Park
PP rel   # of runners
team    days between races
KENOSHA1   42.551  14 MWest92 14  ** Year of Heavy rains & Mud at Wisconsin
KENOSHA1   -4.810  13 MWest93 14        (makes it look a lot tougher)
KENOSHA1   -6.566  14 MWest94 14
KENOSHA1   -4.467  14 MWest95 14
VANCORT   14.772  14 NEast92 14
VANCORT   21.089  14 NEast93 14
VANCORT   24.416  14 NEast94 14
VANCORT    1.383  13 NEast95 14  ?? very cold... heat at Balboa
MaAlpine  -51.159  13 South92 14
MaAlpine  -10.499  13 South93 14
MaAlpine  -40.821  14 South94 14
MaAlpine  -29.944  14 South95 14
Woodw-pk  -53.101  13 West92   7
Woodw-pk  -18.842  14 West93   7
Woodw-pk  -12.862  14 West94   7
Woodw-pk  -32.015  12 West95   7

The data seems pretty consistent, except for a couple of oddball
exceptions (rain * heat ?).  Averaging in all the relative course difficulties
gives the above absolute ratings.

So far so good right? .........nope or NOT !!!!

When checking this system against courses of unknown distances I discovered
a flaw in this wonderful system.

Example....  same runner on 3 courses... same performance level
Assume this "virtual" runner always can do a 612 Purdy performance.
1.        2.5 mile course   15:00 time     612 Purdy point
2.        3.1 mile course   18:55 time     612 Purdy point
3.        2.5   "           18:55 time     485 Purdy pints

course 3.   is 127 ppts (612-485) more difficult than course 1.
ok...  now a faster runner. (always does a 706)
1.          2.5 mile course   13:00        706 Purdy point
2.          3.1 mile course   16:24        706 Purdy point
3.          2.5 mile course   16:24        560 Purdy point
in this case
course 3. is now 146 ppts (706 - 560) more difficult than course 1.

The system fails..... A course that is .6 of a mile longer than
another course should produce the same difficulty rating for
faster or slower runners.

So (: (:  I went back to the drawing board...

VIRTUAL METERS  as a difficulty rating.

My latest system now uses "Virtual Meters" as a difficulty rating.

That is two courses are compared, and if performances are slower on the
2nd course then the 2nd course is "virtually" longer by so many meters.
If performances are faster the 2nd course is "virtually" shorter by so
many meters.  The concept is that difficulty of a course is entirely equivalent
to increasing or decreasing the length of a course.
In the above example the relative difficulty of course 1 and 3
would be 965 meters ( .6 miles).  All runners should generate the
same difficulty rating on the 2 courses.

Using the old (Harrier ratings) course A thru G rating system as an example
(same runners on easy A course and a very difficult G course)
a 5k track 849 Purdy pt. performance =  14:50.58 secs

time    Purdy      Old rating    Dist rating  pace(meters/sec)
(V. meters)          rough V. meters
A   15:00  832  (849/832)   17      48.2      5.6101    *10sec = 56
B   15:15  806  (849/806)   43     126.3      5.6035    *25sec = 140
C   15:30  781  (849/781)   68     204.8      5.5976    *40sec = 223
D   15:45  757  (849/757)   92     283.2      5.5917    *55sec = 307
E   16:00  733  (849/733)  116     361.4      5.5858    *70sec = 391
F   16:15  711  (849/711)  138     440.1      5.5807    *85sec = 474
G   16:30  688  (849/688)  161     518.7      5.5755    *100sec= 557

Multiplying the pace in meters/sec (times) the amount of time slowed,
gives a rough approximation to the Virtual Meter difficulty factor.
(not exactly since you still need to model the way a runner slows down
with increased distance - Purdy points does this)
This also works if a course is easier than another course.
So theoretically you can make a rough estimate of the V-meter difficulty
factor of a course without using Purdy points at all.

The method used in my modified program uses Purdy point calculation
to predict a distance for a given Purdy point performance and time.
Each runner's two performances compared on two different courses are used
to calculate the Virtual Meters difference between the two coarses.
Once the relative V-meter for each course is calculated an absolute v-meter
difficulty rating can be established by having a fixed course like
Balboa Park with a given v-meter rating.  All absolute course ratings
can then be computed via Chains of comparisons back from Balboa.

USING THE SYSTEM

A runner with a time on a given rated course can find out their "true"
performance by using the same time and "adding in" the V-meter rating for
a course to the actual course distance.  For most X-country courses this
will be a positive value, hence the runners performance or Purdy point
value will increase.  Typical courses will add 50 to 600 v-meters to
a courses actual distance.

Here are a few courses with Absolute Virtual Meter ratings

This was done with arbitrarily setting Balboa to be 150 v-meters.
That is equivalent to a 5k track + 150 meters.

"KENOSHA1", 173.099,55
" VANCORT", 201.766,55
"MaAlpine",  34.484,54
"Woodw-pk",  55.929,53
"BALBOA-P", 150.000,217

Question:  Is MacAlpine Greenary equivalent to a 5k track
+ 35 meters ?  or should we add in more meters ?
(which effectively will raise all the other ratings)

This may not be the ideal rating system but in thinking about a system
it would seem that :

A X-COUNTRY RATING SYTEM SHOULD DO THE FOLLOWING...

1. A Rating system should be independent of actual course length.
That is the exact course length need not be known but
ratings can be assigned using an "assumed" distance.

2. A Rating system should be consistent using slower or faster runners.
3. A Rating system should allow relative course difficulties
and absolute course difficulty ratings.
4. Increased difficulty should be equivalent in some way to
increased distance ( and vice a versa).

Here are the Balboa Pk relative V-meter comparisons with the
Footlocker regional courses. The 4 year results average to
get the current ratings.

KENOSHA1  144.437  14 MWest92 14   * heavy rains & mud @ Kenosha
KENOSHA1  -15.964  13 MWest93 14
KENOSHA1  -23.040  14 MWest94 14
KENOSHA1  -15.828  14 MWest95 14
VANCORT   49.706  14 NEast92 14
VANCORT   69.917  14 NEast93 14
VANCORT   78.759  14 NEast94 14
VANCORT    5.368  13 NEast95 14   very cold - Balboa hot !!!????
MaAlpine -176.689  13 South92 14
MaAlpine  -36.533  13 South93 14
MaAlpine -139.154  14 South94 14
MaAlpine -108.415  14 South95 14
Woodw-pk -177.795  13 West92 7
Woodw-pk  -61.064  14 West93 7
Woodw-pk  -40.643  14 West94 7
Woodw-pk -104.213  12 West95 7
```