CUPED (controlled-experiment using pre-experiment data)

CUPED adjusts each user's outcome metric during an experiment by subtracting a portion of that same metric's value from before the experiment started, using the correlation between pre-period and in-experiment behavior to strip out variance that has nothing to do with the treatment. A high-spending user who was already a high spender before the test contributes less noise to the treatment-effect estimate once that pre-existing tendency is accounted for.

Mechanically, the adjusted metric is Y_cuped = Y - θ(X - X̄), where Y is the observed outcome, X is the user's pre-experiment value of the same or a correlated metric, X̄ is its average, and θ is chosen to minimize the resulting variance. The adjustment does not change the expected average treatment effect; it only reduces the spread around it.

Because it lowers variance without changing the true effect, CUPED effectively shrinks the minimum detectable effect achievable at a given sample size, or lets the same effect be detected with less traffic and a shorter run time. It works best for metrics with strong pre-period to in-period correlation, such as spend or usage frequency for existing users, and offers little benefit for new users with no pre-experiment history.