cases, this is the difference between left-going and right-going scans, however, for observations which used elevation scans, this is the difference between upward-going and downward going scans. The weight array is smoothed with a Gaussian kernel of width $\sigma_{\ell}=1000$ to reduce the scatter in the noise power, and is normalized such that $\sum_{\ell \in b}H_{\ell}=1$ for each bin $b$. A separate weight array is calculated for each observation field. Application of the weight array improves the signal-to-noise of the power spectrum by approximately 15%.

### Simulations {#sec:sims}

Noise-free simulations are used to estimate the sample variance and transfer function from map-making. For each field, we create 100 sky realizations that are smoothed by the appropriate beam for each frequency. We then simulate observations of these sky realizations by sampling each realization using the SPT pointing information. These simulated TOD are filtered and processed into maps identically to the real data.

Each simulated sky is the sum of Gaussian realizations of the best-fit lensed WMAP7+S13 $\Lambda$CDM primary CMB model, a tSZ model, a kSZ model, and point source contributions. The simulation inputs have been updated to be consistent with the R12 bandpowers, which have point sources masked at the same significance 