Is there a way to get the bitrate of a specific region of a video? I have some videos I recorded with my cell phone that I want to crop using Avisynth's crop().  I am using x264vfw with VirtualDub which asks for a target bitrate.  I usually just get the bitrate from the vid's properties in Windows Explorer and plug that value in for the target bitrate for the new encoded video, but, since I am cropping it, I don't want to use the full bitrate.  Ideally, I would be able to find out the bitrate of only the region I am wishing to crop.  After all, if the original video is 1920x1080 with a total bitrate of 30 mbps (30,000 kbps) and I want to crop it down to a 1080x1080 region, I don't want to use the bitrate of the full, uncropped video.
You can only estimate the bitrate as proportion of your crop. If you have 30,000 Kbps for 1920*1080 pixel, then for 1080*1080 pixel this would mean 16,875 Kbps. If there is more complexity inside the crop region than outside, I would even increase the target bitrate further.

However, if your videos are not that long and not intended for streaming I wouldn't invest too much thought into saving some disk space. The video quality will degrade anyway with the encoding process and a high bitrate will help you avoiding too much loss.