Higher frame-rates are essential in achieving more realistic representations. Since increasing the frame-rate increases the total amount of information, efficient coding methods are required. However, the statistical properties of such data, needed for designing sufficiently powerful encoders, have not been clarified. Conventional studies on encoding high frame-rate sequences do not consider the effect on the encoding bit-rate of the motion blur generated by the shutter being open. When the open interval of the shutter in the image pickup apparatus increases, motion blur occurs, which is known as the integral phenomenon. The integral phenomenon changes the statistical properties of the video signal. This paper derives, for high frame-rate video, a mathematical model that quantifies the relationship between frame-rate and bit-rate; it incorporates the effect of the low-pass filtering induced by the open shutter. A coding experiment confirms the validity of the mathematical model.