The use of time-tagging single-photon lidar for high-resolution ranging and backscattered count rate measurements requires special attention to mitigate biases and distortions typically not seen in full-waveform lidar sensors. Specifically, sub-pulse sampling and the presence of non-zero receiver dead-time generates an effect named first photon bias (FPB). FPB manifests itself as an intensity-induced ranging offset, previously documented, and a nonlinear count rate with integrated distribution distortions. These combined effects require special attention when integrating lidar point clouds to accurately estimate the backscattered signal strength and true range. This Letter indicates that correcting solely for the introduced range bias does not address the nonlinear shape distortions in the accumulated photon distribution. Analyses of distribution widths and estimated signal strengths must consider both effects. We present an analysis that demonstrates the cause and effect of the FPB on photon time-tagging integrated photon distributions using the Monte Carlo method, relates the modeled results to previously published data and statistics, and provides a framework for interpreting range and backscattered signal strength measurements from these sensors.