Barbara McCrary wrote:
*There are too many champions, too many weight divisions, and many
*of us don't remember who was the champion of what 5 minutes after we
*walk out of the awards program. This was all brought up when one
*rider, riding slowly but covering huge numbers of miles in one year,
*was proclaimed the National Champion. A lot of us didn't like that
*We thought the NC should have at least ridden a little faster. But
*I have come to regret our decision to change the format.
*
While perusing the PNER point standings last fall I noticed a large
disparity in the numbers of miles required to collect a given number
of points. Clearly some people were riding lots of slow miles while
others were doing fewer faster miles and placing significantly higher.
For the heck of it I decided to compare the results after making a few
mathematical corrections.
Hypothetical data:
Points Miles Miles
Place Points Complete Attempted
1 Horse 1 2040 1350 1575
2 Horse 2 1895 755 755
3 Horse 3 1605 650 850
4 Horse 4 1550 550 700
5 Horse 5 1549 550 600
6 Horse 6 1520 375 525
First I created a ratio of points per mile ridden to grade the quality
of ride.
Quality Ratio = points / completed miles
Quality Ratio
Horse 1 = 1.51
Horse 2 = 2.51
Horse 3 = 2.47
Horse 4 = 2.82
Horse 5 = 2.82
Horse 6 = 4.05
This seemed to be too large of a correction to use so I compressed them
by using the log function:
Modified Quality Ratio = Log(Quality Ratio) + 1
So the new Modified Quality Ratios (MQR) would be:
MQR
Horse 1 = 1.18
Horse 2 = 1.40
Horse 3 = 1.39
Horse 4 = 1.45
Horse 5 = 1.45
Horse 6 = 1.61
Then I took the standard points and multiplied them by the MQR to yield
these new point standings:
Place
1 Horse 2 1895 * 1.40 = 2653
2 Horse 6 1520 * 1.61 = 2447
3 Horse 1 2040 * 1.18 = 2407
4 Horse 4 1550 * 1.45 = 2247
5 Horse 5 1549 * 1.45 = 2246
6 Horse 3 1605 * 1.39 = 2231
End of Part 1
