Over the past two decades, the surge in video streaming applications has been fueled by the increasing accessibility of the internet and the growing demand for network video. As users with varying internet speeds and devices seek high-quality video, transcoding becomes essential for service providers. In this paper, we introduce a parametric rate-distortion (R-D) transcoding model. Our model excels at predicting transcoding distortion at various rates without the need for encoding the video. This model serves as a versatile tool that can be used to achieve visual quality improvement (in terms of PSNR) via trans-sizing. Moreover, we use our model to identify visually lossless and near-zero-slope bitrate ranges for an ingest video. Having this information allows us to adjust the transcoding target bitrate while introducing visually negligible quality degradations. By utilizing our model in this manner, quality improvements up to 2 dB and bitrate savings of up to 46% of the original target bitrate are possible. Experimental results demonstrate the efficacy of our model in video transcoding rate distortion prediction.