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In 1-pass ABR, the goal is to hit an average bitrate for the whole video, without any constraints. The encoder does not know the length of the video, so the "buffer size" for this decision increases as it gets more and more frames. Ideally (as in 2-pass), the "buffer" would be the entire video.
As far as I can tell though, the sqrt is of the duration of the video so far, not the fps.
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