Dividing strength by bodyweight rewards the wrong kind of change

Relative strength can improve without a single extra newton of force, simply because the denominator got smaller.

Newtons per kilogram is the standard way to report strength, and it has a property that is rarely said out loud: the number goes up when an athlete gets weaker, provided he gets lighter faster.

A player loses three kilos over a hard month, largely because he was ill for a week and did not eat properly. His absolute force falls slightly. His relative score rises. On the report he has improved, and if the report is what feeds the return-to-play criterion or the selection conversation, then the illness has been recorded as progress. Nothing in the ratio can distinguish that from genuine gain, because a ratio only knows the quotient.

This is not a rare edge case in sports where weight is watched. Any environment where athletes are encouraged to lean out will generate a steady upward drift in relative strength scores across a preseason, and much of it is the denominator moving. The staff who introduced the metric to control for size have accidentally built a measure that pays a bonus for losing mass regardless of what the mass was doing.

There is a second issue in the exponent, and it is more technical but it changes rankings. Force does not scale with body mass in a straight line. Bigger athletes produce more total force and less force per kilo, roughly for geometric reasons, so dividing by mass overcorrects and systematically favours the smallest athletes in the squad. A featherweight and a heavyweight compared on newtons per kilogram are not being compared fairly in either direction, and the ranking that comes out is partly a ranking of body size.

So report both. Absolute force, and the ratio, side by side, along with the weight on the day. Three columns, and the disagreements between them are informative rather than annoying. When absolute is flat and relative is climbing, you know immediately what has happened and you can go and ask about it.

For rehabilitation the absolute number is usually the one that matters anyway, because a knee has to absorb the forces of a body at the weight that body actually is.

A player who has lost mass has not made his landing easier in proportion to his loss, and the ratio will tell him he has.