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It is common knowledge that the better shape a person is in - the lower their heart rate is at rest, and, I think, the lower their heart rate is for a given speed when running.

I would like to know:

  1. Is there a standard indicator to express the relation between one's heart rate and their running speed? (e.g. BPM/mph).
  2. If so, are there standard tables or graphs that provide the normal/desired values per age group / gender?
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If the heart rates from the smart watches can be trusted, then a short analysis of Strava Leaderboards would suggest a clear no. For the segments I've got a high position, I've seen people above me having higher HR, as well as people below me with much higher HR. The segment leaders have normally high HR, but there's no direct relation between the HR of the participant and their speed.

With the training, your heart can pump blood better, but also your muscles can absorb oxygen better, and they can use the oxygen better. That 3 factors depend on the training and the physiological predispositions, because they are very individual, building the tables would not be viable, unless we tabelarise those factors first.

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    This. A lot of things for running speed, swimming speed, depend very much on efficiency. N=1, I ran x-country and swam for many years. My pace at a given heart rate will generally be much faster as someone that doesn't have that same training, regardless of fitness. Plus, there are many variables (rest, hydration, caffeine intake, etc) that can affect heart rate without affecting pace.
    – JohnP
    Jun 14 at 15:00

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