A randomized control group isolates a causal effect because regression to the mean affects both arms equally and cancels in the comparison

Without A/B testing, we wouldn’t be able to tell how much of the result can be attributed to the isolated change we’ve made, and how much to the noise in the data. Splitting the data into 2 random samples and only applying the change in one of them, allows us to estimate the impact of our change by comparing the outcomes of the two groups. Given the test satisfies ceteris paribus principal, we now have 2 samples with equivalent size and noise-to-signal ratio, therefore any drift can be attributed to the change that we’ve made.