Adding more variables to a linear model can increase the variance of coefficients, but using a technique called ANCOVA can help control this. The variance inflation factor (VIF) measures this increase in variance. By adjusting for additional covariates in a randomized experiment, we can reduce variance when averaging over treatment indicators, but this may come with a trade-off of increased bias when conditioning on treatment indicators. So, while it may seem paradoxical, there are ways to balance variance and bias in statistical analysis.