Does adding metal plate/foil behind radiators increases their heat distribution?
Statistics? I'd argue this is a misuse of the word, unless you are asking what is the fraction of photons reflected by the reflective surface. Since that truly is a probabilistic question, we could indeed compute statistics on the distribution of such reflections.

Yes, this is not just a theory. Heat is transmitted in several ways. One such way is convection. So the radiator heats the air around it, which will rise, displaced by heavier cool air from the rest of the room. These convective air currents cause a transmission of heat from the radiator into the room.

A second way that heat is transmitted is by radiation. Infrared photons will carry off energy (heat) from the radiator. Some of these photons land on the wall behind the radiator. If the wall absorbs them, then it will get warmer. So the trick is to put a reflecting surface in the way. A SHINY metallic surface is such a solution, a heat mirror. Thus a shiny metal foil will suffice. Even a regular mirror, which is simply a piece of glass with a metallized reflective back surface that reflects light, will suffice.