JohnS wrote:nolevault wrote:As a mathematician, by trade, i'm a little bamboozled about the way that the IAAF, NCAA, USATF, or whoever is converting from metric to english. I've looked at all the numbers to figure out a reason for the conversion, but nothing seems to work for every conversion. I realize what the correct numbers are based on posts, etc., but I am frustrated that I can't calculate them mathematically. If anyone knows why the conversions are the way they are, PLEASE fill me in on it.
Obviously, this response is years too late. However, the rounding algorithm is pretty simple. The converted mark is either that obtained by truncation or the next mark higher. Whether it truncates or rounds up is controlled by a rounding offset (which depends on the event) and is roughly explained in the introduction to the Big Gold Book (BGB). Except for the offset, they use exact conversions, 1" = 2.54 cm.
For pole vault (and high jump), BGB asserts the rounding offset is 0.2 cm. What they don't explain is that because the both metric and english marks are quantized, a small range of offsets performs exactly the same. Any value such that 0.200 cm =< offset < 0.205 cm. I like to use 0.202 cm (0.00202 m).
Example:
4.90 m
Add offset, 4.90202 m
Convert 16' 0.9929"
Truncate to lesser 1/4 in, 16-00.75
2.00 m, add offset, 2.00202 m
Convert 6-06.8197
Truncate to lesser 1/4 in, 6-06.75
Long jump, triple jump, and shotput are similar but use a different factor, such that
0.495 cm =< offset < 0.5 cm (BGB states they use 0.4999 cm, I suggest 0.497 cm)
In floating point, it is best to avoid the lower equality, tiny floating point errors may cause rounding problems. It is not necessary to use the exact center value, but use a value away from both ends. The upper inequality must be avoided.
JohnS wins a gold star for most informative first post ever!
