What is a z-score?

The definition

A z-score of 0 means the value is exactly average. A z-score of +1 means it is one standard deviation above. A z-score of −2 means two standard deviations below.

The subtraction removes the level; the division removes the units. What survives is a pure statement about unusualness — and because the units are gone, z-scores from completely different quantities can be added together.

Why it matters: units

Suppose you want one number combining sentiment and interactions. Sentiment runs 0–100. Interactions run into the millions. Adding them directly:

Weights do not fix this. A weight of 0.4 on a term that is a thousand times larger still leaves that term dominant. This is not hypothetical — it is exactly what happens in SMI, where interaction counts carry over 99 % of a composite whose stated weights suggest a three-way split.

Standardising first repairs it:

Reading the values

The right-hand column holds only if the data is normally distributed. Crypto data is not, which is the next section.

Where it breaks on crypto data

The z-score formula works on any data. The interpretation above assumes a bell curve, and quantities like interactions, turnover and social volume are heavy-tailed — a few assets sit enormously far from the rest.

Two consequences follow:

• Outliers inflate σ for everyone. One asset with a hundred times the median interactions raises the standard deviation of the whole set, which shrinks every other asset's z-score. Ordinary assets get pushed toward zero by the presence of one unusual one.
• The percentile equivalents are wrong. In a heavy-tailed distribution, far more than 15.9 % of assets can fall below z = −1, because the mean is dragged upward by the tail and most observations sit below it.

This is a real limitation of COR, stated on that page. It does not make the metric useless — the ordering is still meaningful — but z-scores computed on this data are not the tidy standard-normal quantities the textbook picture implies.

Z-score or percentile?

Neither dominates. Moonboard uses percentiles where robustness matters more and z-scores in COR, where the point is precisely to combine several metrics on equal footing. Comparing the two is instructive: when COR and OPS disagree about an asset, the disagreement is usually about magnitude versus rank.

The COR mapping

COR converts an averaged z-score to 0–100 with a fixed window:

Since z̄ is an average over five metrics, its spread is much narrower than a single z-score's, so real COR values cluster near 50 and the ends of the scale go unused. A COR of 65 is a strong result, not a middling one — the z-score calculator makes this visible.