(On older laptops, watching a video in the background while you work would increase fan noise and shorten the already short battery life.)
First, it only negatively affects my work performance if I haven't seen the video before, it's interesting or riveting, and I really need to get work done now.
Second, I measured unrelated-video-watching during work as a very high personal motivating factor. Similar to listening to favorite music. So I immediately went to work on more of that:
1) I watch more new-to-me movies more often, so that I have a larger queue of stuff I've already watched & really like (see first point above). Since I've already seen it, it doesn't get in the way of me doing my work.
2) I wrote a script to specifically make a low-power-video shuffled playlist for me, in addition to my normal shuffled video playlist cron job. So the low-power version has lower-resolution videos that I can watch on an MSI Wind netbook with 2GB RAM and Q4OS while I'm doing some casual planning or journaling.
Maybe not what you wanted to hear but those have been my results.