Given how frequently people can tell when someone is looking at them from behind or at a distance, the book on attention as a material force is anything but closed.
> One of the most common extramission beliefs is that people can “feel” someone else’s gaze as a pressure or heat on the skin. In the late nineteenth and early twentieth century, Titchener (14) and Coover (15) showed that, although people may believe in eye beams, no such beams exist; people cannot actually detect the gaze of another in the absence of specific sensory information.
> 14 Titchener EB (1898) The feeling of being stared at. Science 8:895–897.
> 15 Coover JE (1913) The feeling of being stared at. Am J Psychol 24:570–575.
Have you come across later studies that suggest it does have a statistically verifiable reality?
Edit: debate about this topic further down in this thread https://news.ycombinator.com/item?id=18852698
I'm going to say "exactly the same as random chance".