In this paper a full analytic model for pause intensity (PI), a no-reference metric for video quality assessment, is presented. The model is built upon the video play out buffer behavior at the client side and also encompasses the characteristics of a TCP network. Video streaming via TCP produces impairments in play continuity, which are not typically reflected in current objective metrics such as PSNR and SSIM. Recently the buffer under run frequency/probability has been used to characterize the buffer behavior and as a measurement for performance optimization. But we show, using subjective testing, that under run frequency cannot reflect the viewers' quality of experience for TCP based streaming. We also demonstrate that PI is a comprehensive metric made up of a combination of phenomena observed in the play out buffer. The analytical model in this work is verified with simulations carried out on ns-2, showing that the two results are closely matched. The effectiveness of the PI metric has also been proved by subjective testing on a range of video clips, where PI values exhibit a good correlation with the viewers' opinion scores.