How it works

A score is a rank, not a quantity

Most rating scales are ordinal, and treating the gap between two scores as a measured amount is where interpretation goes wrong.

4 min readHow it works

A score of 8 is higher than a score of 6, and that is almost the entire claim a typical rating scale is actually entitled to make. Whether the distance between them is the same distance as between a 4 and a 2 is a separate question, and for most scoring systems the honest answer is that nobody knows, because nothing about how the scale was built established it.

Two kinds of scale

An interval scale has equal, meaningful gaps between its points - a temperature in Celsius is one, because the distance between 10 and 20 degrees represents the same physical change as the distance between 30 and 40. An ordinal scale only guarantees order - each point is higher or lower than its neighbours, but the size of the gap between any two points is not defined to mean anything in particular. Most rating scales, including the ones underlying AI scoring tools, are ordinal by construction: they were built by asking people to compare or rank examples, not to measure a quantity on a fixed unit.

Where the labels come from

A model learns its scale from labels, and those labels were usually produced by people choosing a number, or a bucket, or a comparison, for a given photo. When a labeller picks "7" over "6," they are expressing that one example seemed a bit better than the other - not that the difference is precisely one unit of some underlying quantity, and not that it is the same size of difference as between any other adjacent pair. A model trained on those labels learns to reproduce the ranking behaviour, because that is what the training signal actually contains; it has no separate channel telling it that gaps should be uniform, and no reason to have learned that they are. Where those labels came from in the first place, and what that origin does or does not guarantee, is covered more fully in where the labels come from.

Why averaging is dubious on an ordinal scale

This matters directly for anything that averages scores together - across axes, across repeats, or across people. Averaging assumes the numbers behave like an interval scale, where adding and dividing produces a meaningful result. On a genuinely ordinal scale, the mean of a 4 and an 8 is arithmetically a 6, but there is no guarantee that a 6 given directly, on its own terms, represents the same thing as that averaged 6 - the averaging has invented a precision the scale was never built to support.

This is a real caveat and also a common one across almost all rating systems, including ordinary star ratings and review scores well outside this domain, so it is not a flaw unique to AI scoring - it is a property of ordinal data generally, and most systems that average ordinal scores do so anyway because the alternative is more cumbersome, not because the averaging is justified. Multi-axis systems that keep several ordinal scores separate rather than collapsing them into one average sidestep part of this problem, which is one more reason a breakdown is more honest than a single aggregate figure - covered at length in why a rubric beats a single score - though even a single axis reported alone still carries the ordinal caveat on its own.

What a model actually learned

None of this means the model's ranking is arbitrary. Ordinal training data still teaches real, useful structure: which images tend to be judged better than which others. What it does not teach, and cannot teach from ordinal labels alone, is a consistent notion of how much better - that is a claim about magnitude, and the labels never carried magnitude information for the model to learn from in the first place. This is also distinct from the question of where a raw model output gets mapped onto the 1-10 scale you actually see, which is its own separate step, covered in from logit to a score out of ten.

Reading a score with this in mind

The practical upshot is modest but worth keeping in mind: treat a gap between two scores as "somewhat more" or "somewhat less," not as a precise quantity you can do further arithmetic on with confidence. This is a scale design question, not a guide to interpreting your own result, which Penis Rater covers from the user's side in more practical terms than fits here. It is also worth noting that a human reviewer's comparative judgements have the same ordinal character, if not more so - a person saying "this is better" is making exactly the same kind of ranking claim a model's training label makes, a similarity Rate Penis's judging notes touch on from the human side. Rate Cock reports each of its six axes as its own figure rather than folding everything into one blended average, which keeps the ordinal caveat contained to each axis individually rather than compounding it across an average of averages. For a genuinely interval quantity - one where a gap of two centimetres really is twice a gap of one - Measure My Cock's method is the place that starts from a ruler rather than a rank.

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