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Tendon stiffness is a ratio, and ratios amplify error

Two imprecise measurements divided by one another produce a third number less trustworthy than either parent.

Tendon stiffness is a ratio, and ratios amplify error

Stiffness is force divided by displacement. Neither quantity is measured cleanly on a human being, and dividing one by the other does not average out the trouble. It stacks it.

Start with displacement. You are tracking how far a tendon lengthens under load, typically a few millimetres, through skin and fascia, with a probe held by a person. Move the probe two millimetres and you have introduced an error the same size as the effect. Force behaves better but is not clean either, because the moment arm depends on joint angle and the joint angle depends on how firmly the ankle was strapped that morning.

Now divide. If the numerator carries five per cent error and the denominator carries ten, the ratio carries something like the two combined, which lands you near fifteen per cent on a measure where the seasonal change people care about might be eight. The noise is bigger than the signal. Repeat the measurement in the afternoon and you can produce a change that looks like a training adaptation and is entirely the probe.

What follows is unpopular but simple. Anything less than a large shift in a tendon stiffness figure should be treated as no information at all. Not weak information. None. And the threshold for large should be set from the same operator repeating the same athlete on the same day, which is a boring afternoon of work that almost nobody schedules and that instantly tells you how much of your data is real.

The reliability figures that do get published are mostly generated by researchers in a laboratory who do this all week, on a still and cooperative subject, with the limb clamped. A practitioner squeezing eight athletes into forty minutes before a session is not working under those conditions and cannot claim those error bars.

There is also a mismatch of ambition. Stiffness is being asked to predict injury risk, which requires sensitivity to individual change over weeks. It was validated for describing differences between groups, a far easier job.

A measure can be perfectly good at telling sprinters from swimmers and useless at telling one sprinter in March from the same sprinter in May. Most of the monitoring built on it wants the second thing and cites evidence for the first.