```Question on X-country course ratings:
Why not just take times or average times and use the percentage
difference to produce course difficulty ratings ?

This is actually a lot simpler than calculating Purdy points
(especially since calculating purdy points is not trivial)
and using that percent difference to rate different courses.
Every coach could do this easily.

One reason  is that Purdy points measures somewhat the
"level of performance".

When improving 20 seconds from 16:00 minutes in a 5k race to get
to 15:40 requires a lot more effort (training etc.) than improving
24 seconds from 20:00 minutes in a 5k race to get to 19:26.
Even though the percent improvement in time is the same
(.020)

Originally, I figured that just taking the percent difference
in average purdy points for two different courses would do the trick.
But when I tried to prove why this method was better by printing
out percent differences (see table below) I found a problem.
At high purdy values the percent differences go down (as they should)
for awhile. Percent differences based just on times (15 second incr.)
go down much more rapidly, but Purdy percent differences start to go
up (right when you get to top female performances)
Absolute Purdy differences also go down.(see table)

What's really happening is that for every 15 seconds slower
the difference in performance is less and less.

Using Absolute purdy difference we can see that around
15:00, 15 seconds means a change in "level of performance
of 27 purdy points, but at around a time of 21:00
27 purdy points corresponds to about 30 seconds difference.

If 15:00 5k runner drops to a 15:15 on a "more difficult" course
a 21:00 runner should drop about 30 seconds.
Both correspond to 27 purdy points.... therefore
the second course is 27 pp more difficult than the first.

My old method would not work, and neither would using
percent times differences.

New system proposed:  *********************
Use average purdy point difference of runners in two races.
Difficulty (pp)
A course as easy as a 5k track       0
Balboa pk                           17   (add 17 purdy points to get
true performance)
Van Cortland pk                     49

Using the old course A thru G

time   Purdy     old dif. factor   New rating
A       15:00  832    1.020  (849/832)   17
B       15:15  806    1.053  (849/806)   43
C       15:30  781    1.087  (849/781)   68
D       15:45  757    1.122  (849/757)   92
E       16:00  733    1.158  (849/733)  116
F       16:15  711    1.194  (849/711)  138
G       16:30  688    1.234  (849/688)  161

True dif.  old rating
Kenosha Wi.                           9     1.011
Van Cortland Park, NY                49     1.058
MaAlpine Greenway, Charlotte, NC    -17      .959
Woodward Park, Fresno, Cal.           2     1.002

So to find a runners true performance on a course simply add
in the course difficulty factor (purdy points) to his calculated
purdy points (from his time and distance) which will give his true
performance.

Someday I may recalculate the old courses......
phoffman@cs.uml.edu

TABLE OF 5K TIMES - WITH PERCENT DIFF, AND PURDY POINTS
5k times, 15 seconds apart, % diff, purdy points,%dif, Absol. diff
00:13:00 1.961 1075.81  -------------
00:13:15 1.923 1041.35  3.203  34.458
00:13:30 1.887 1008.17  3.186  33.182
00:13:45 1.852  976.20  3.172  31.975
00:14:00 1.818  945.36  3.159  30.833
00:14:15 1.786  915.61  3.147  29.751
00:14:30 1.754  886.89  3.137  28.726
00:14:45 1.724  859.13  3.129  27.752
00:15:00 1.695  832.31  3.123  26.827
00:15:15 1.667  806.36  3.117  25.947
00:15:30 1.639  781.25  3.114  25.110
00:15:45 1.613  756.94  3.112  24.313
00:16:00 1.587  733.38  3.112  23.553
00:16:15 1.562  710.56  3.113  22.828
00:16:30 1.538  688.42  3.115  22.137
00:16:45 1.515  666.94  3.120  21.476
00:17:00 1.493  646.10  3.125  20.844
00:17:15 1.471  625.86  3.133  20.240
00:17:30 1.449  606.20  3.142  19.662
00:17:45 1.429  587.09  3.152  19.108
00:18:00 1.408  568.51  3.164  18.577
00:18:15 1.389  550.44  3.178  18.068
00:18:30 1.370  532.86  3.194  17.580
00:18:45 1.351  515.75  3.211  17.111
00:19:00 1.333  499.09  3.230  16.661
00:19:15 1.316  482.86  3.252  16.228
00:19:30 1.299  467.05  3.275  15.812
00:19:45 1.282  451.64  3.300  15.412
00:20:00 1.266  436.61  3.327  15.026
00:20:15 1.250  421.96  3.357  14.655
00:20:30 1.235  407.66  3.388  14.298
00:20:45 1.220  393.71  3.423  13.953
00:21:00 1.205  380.09  3.460  13.621
00:21:15 1.190  366.79  3.499  13.301
00:21:30 1.176  353.79  3.542  12.991
00:21:45 1.163  341.10  3.588  12.693
00:22:00 1.149  328.70  3.637  12.404
00:22:15 1.136  316.57  3.689  12.125

```