Here is a mathematical diagram. (Click for full size) It is showing the diffuse reflectance of an idealized surface. A real surface is a little more complicated, but for something like smooth clay or dull plastic, this is actually quite correct information.

I have annotated the graph heavily, but let me summarize.

The dashed lines show how much light is reflected from a single 100% infinite light, or spotlight, or pointlight, based on the angle of incidence. Angle of incidence is the angle formed between the vector pointing at the light, and the vector pointing straight out from the surface, i.e. the surface normal.

When the angle is 0, maximum reflection occurs. Here in this diagram, the value 1.0 in the Y axis indicates the amount of diffuse reflection, as a proportion of the maximum possible. Of course this curve moves up or down depending on the intensity of the light and the color of the surface.

When the angle is 90 degrees, no reflection occurs.

The solid lines show the same reflectance but assuming a 60% white IBL and a 40% infinite light.

The blue lines are the actual correct calculated linear value. The red lines are how bright those values appear on a computer monitor which has been properly calibrated to the sRGB color space. sRGB is the standard for all (S)creens. S.

The black lines show the difference between the correct value and the perceived value. The little dots highlight all these corresponding values for a single angle of incidence.

Notice that the solid black line (actual illumination difference with extra lighting, such as IBL) is lower than the dash black line (actual illumination difference with just a single directional light) for most angles. The dashed line peaks around 60 degrees, while the solid line keeps going up all the way to 90 degrees. What this means is that when you add more light, you make the brightest parts look less wrong. But you also make the darkest parts look MORE wrong.

If you look at the blue and red dots, you'll see that at 25 degrees, the directional lighting is wrong by 11%, while the IBL lighting is only wrong by 4.5%. That is cutting the perceived error in half, and that's why you like to add more light. It makes most of a human face, which is within 25 degrees of your main light, look closer to normal or real. A perceived error of 4.5% is certainly tolerable, and if you light up your figure with lots of lights at all different angles around it, then it will look pretty good! But what if you're trying to use more realistic and directional lighting?

Things get ugly at other angles.

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Renderosity forum reply notifications are wonky. If I read a follow-up in a thread, but I don't myself reply, then notifications no longer happen AT ALL on that thread. So if I seem to be ignoring a question, that's why. (Updated September 23, 2019)