Have Solution for % Change, Unsure of Steps to Solve (a running coach)

CoachDean

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Aug 24, 2018
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Hello!

My apologies if this is in the wrong forum topic.

Short background:
I was reading an article by a running coach. He mentions that ideally, for the average person, there's a 20-21% decrease in speed for every doubling of a distance (i.e. from 400 meters to 800 meters, from 800 meters to 1600 meters, etc.).
He then gives an example of a client he worked with who had a 400-meter time of 1 minute, and a 1600-meter time of 6 minutes. The coach mentions that this is roughly a 28.5% decrease in speed, meaning the goal is to get this client's 1600-meter time down to 5:25 (which he says brings the client to the ideal 20-21% speed decrement).


I've spent an embarrassingly large amount of time trying to figure this out to no avail. I can't figure out how the coach is calculating ~28.5% decrement in speed from a 1 minute 400 meter, vs a 6 minute 1600 meter. And I don't understand how a 1600-meter time of 5:25 is around a 20% reduction in speed from the given 60 second 400-meter.

This is what I keep thinking WOULD have been the right way to do it, but clearly not:
If we're given a 400-meter time of 60 seconds...
Then an ideal 800-meter time (based off the idea that every doubling of distance decreases speed by 20%) would be 2 minutes 24 seconds. (20% of 1 minute = 12 seconds -> 1 minute 12 seconds * 2 = 2 minutes 24 seconds).
Then the ideal 1600 meter time would be 5 minutes 45 seconds. (20% of 2 minutes 24 seconds = 28.5 seconds -> 2 minutes 52 seconds * 2 = 5 minutes 45 seconds).



All help is very greatly appreciated!
Please let me know if any clarification is needed.

Thank you very much for your time.
 
Hello!

My apologies if this is in the wrong forum topic.

Short background:
I was reading an article by a running coach. He mentions that ideally, for the average person, there's a 20-21% decrease in speed for every doubling of a distance (i.e. from 400 meters to 800 meters, from 800 meters to 1600 meters, etc.).
He then gives an example of a client he worked with who had a 400-meter time of 1 minute, and a 1600-meter time of 6 minutes. The coach mentions that this is roughly a 28.5% decrease in speed, meaning the goal is to get this client's 1600-meter time down to 5:25 (which he says brings the client to the ideal 20-21% speed decrement).


I've spent an embarrassingly large amount of time trying to figure this out to no avail. I can't figure out how the coach is calculating ~28.5% decrement in speed from a 1 minute 400 meter, vs a 6 minute 1600 meter. And I don't understand how a 1600-meter time of 5:25 is around a 20% reduction in speed from the given 60 second 400-meter.

This is what I keep thinking WOULD have been the right way to do it, but clearly not:
If we're given a 400-meter time of 60 seconds...
Then an ideal 800-meter time (based off the idea that every doubling of distance decreases speed by 20%) would be 2 minutes 24 seconds. (20% of 1 minute = 12 seconds -> 1 minute 12 seconds * 2 = 2 minutes 24 seconds).
Then the ideal 1600 meter time would be 5 minutes 45 seconds. (20% of 2 minutes 24 seconds = 28.5 seconds -> 2 minutes 52 seconds * 2 = 5 minutes 45 seconds).



All help is very greatly appreciated!
Please let me know if any clarification is needed.

Thank you very much for your time.

Speed
1 minute 400 meter ==> 400 m / min
6 minute 1600 meter. ==>
267 m / min

% Decrease
(400-267)/400 = 33% -- Doesn't look like a 28.5% decrease to me.
 
Speed
1 minute 400 meter ==> 400 m / min
6 minute 1600 meter. ==>
267 m / min

% Decrease
(400-267)/400 = 33% -- Doesn't look like a 28.5% decrease to me.

Right, it's been frustrating. Wasn't sure if the articles are getting it wrong (i.e. typo) or I had been doing something wrong.

However, after a bit more in-depth research, I did find a way of getting the ideal mile time based on an input of a starting distance.

Example:
The formula is the following: t2 = t1 * (d2 / d1)^1.21 (where ".21" represents the percentage of slowing for every doubling of distance, and for "average" people that's around 20-21%... side note: elite runners are around 6%)
t1 => initial time
d1 => initial distance
d2 => new distance being calculated for
t2 => predicted time for new distance

If we're given an individual's 400-meter time of 60 seconds...
And we're trying to calculate the "ideal" 1600-meter time...

60 * (1600 / 400)^1.21 = 5 minutes 21 seconds

This formula published by a coach named Pete Riegel in 1977 in an issue of Runner's World.

If anyone is interested in why this matters (OFF TOPIC):
Using the above example, say you run a 400-meter in 60 seconds, the ideal 1600-meter time would be roughly 5:21.

If you test your 1600-meter time and it's HIGHER than 5:21, you'd do the best working on more endurance work to get that time down.
If you test your 1600-meter time and it's LOWER than 5:21, you'd do the best working on more speed work to achieve the proper ratio.
Even if you're not an athlete (which is what this formula is based around) this is the best way to decide where to spend your time training to get a well-balanced body.
 
It is important to note that the original article was written by a coach. We can't expect him/her to be able to do arithmetic!
 
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