CUPED (controlled-experiment using pre-experiment data) exploits the fact that a user’s past behaviour strongly predicts their in-experiment behaviour, and that this predictable spread is pure noise for the purpose of comparing arms. Adjusting the metric by θ times the centred covariate, with θ the regression slope of metric on covariate, leaves the treatment effect unbiased and multiplies the variance by one minus the squared correlation.
With the metric’s own one-to-four-week pre-period as the covariate, correlations around 0.7 are routine, halving the variance and therefore the required sample size or duration. The original Microsoft paper reported roughly 50% reductions in production, and the technique is now a default in commercial experimentation platforms. The legality condition: the covariate must be measured before assignment, or the adjustment reintroduces the bias randomization removed.