# Z-Score

Source: https://www.yieldcurve.pro/learn/z-score

A **z-score** measures how many standard deviations a current observation is from its historical mean. It provides a standardized way to assess whether a yield, spread, or auction metric is at an extreme relative to history.

*Z-score = (Current value - Mean) / Standard deviation*

Interpretation:

- **z = 0**: the value equals its historical average
- **z = +2**: the value is 2 standard deviations above average (approximately the 97.5th percentile in a normal distribution)
- **z = -2**: the value is 2 standard deviations below average

On this site, z-scores appear in several contexts:

- **Morning Dashboard**: each tenor's yield is shown with its z-score relative to its full history, identifying which maturities are at extremes
- **Auction grading**: the [auctions tool](https://www.yieldcurve.pro/auctions) converts raw auction metrics (bid-to-cover, tail, bidder shares) into z-scores using an expanding historical window, then maps z-scores to letter grades from D- to A
- **ChatYCP**: the AI assistant uses z-scores and percentile ranks when answering questions about where current data stands relative to history

Z-scores assume roughly normal distributions. For metrics with fat tails (common in financial data), extreme z-scores may be more frequent than a normal distribution implies. The expanding-window approach used in the auction grading system (documented in "Grading US Treasury Auctions") mitigates this by using all available history rather than a fixed window.