Z-Score Normalization
A statistical transformation that converts raw metrics to a comparable scale by measuring distance from the average in standard deviations.
Definition
A z-score is the number of standard deviations a value sits above or below the mean of a reference distribution. A z-score of zero is exactly average; +1 is one standard deviation above average; -2 is two standard deviations below.
Z-scoring is essential when combining metrics with different units. You cannot meaningfully average a P/E ratio (typically 5–40) with a year-over-year revenue growth percentage (typically -20% to +60%) — the units are incompatible. Z-scoring puts both onto the same dimensionless scale before any combination happens.
The transformation is also robust to outliers when paired with winsorization (capping extreme values at, say, the 5th and 95th percentile before computing the mean and standard deviation). Without that, a single distressed company with a P/E of 500 can pull the reference mean enough to distort scores for everyone else.
Formula
z = (x − μ) / σx is the raw value, μ is the mean of the reference distribution, σ is the standard deviation.
How QScoring uses it
Every metric in the QScore is z-scored against the distribution of that same metric across the stock's sector. The z-score is then mapped linearly to a 0–100 score (z=0 → 50, z=±3 → 100/0). Reference statistics are winsorized at the 5th and 95th percentile so a single outlier can't skew the distribution. For metrics where lower is better (P/E, volatility), the sign is inverted before mapping. See the combining section for the full pipeline.