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I think it has to do with atmospheric diffusion of the sunlight. Even if the photons coming straight down at you are blocked by the moon, a lot of them bounce around in the atmosphere and end up reaching your eyes. Kinda like when it's not complete darkness at sunset even after the sun has gone over the horizon. Also explains why the sky is blue, since "blue photons" are better at bouncing around on the atmosphere molecules. See : diffuse sky radiation
Quoting form the Wikipedia article: Approximately 23% of direct incident radiation of total sunlight is removed from the direct solar beam by scattering into the atmosphere; of this amount (of incident radiation) about two-thirds ultimately reaches the earth as photon diffused skylight radiation.
Edit : probably mostly has to do with your eyes adapting to the luminosity and non linearity of light intensity perception by our eyes. See posts below about Weber-Fechner law of perception.
Edit Edit : This is an intersting read. The TLDR is it mostly has to do with our eyes slowly adapting to the amount of light they receive, and during totality, light bouncing from beyond the umbra comes into play.
This is not it (edit: "this" referring to atmospheric scattering), because if you look at the range of what is in shadow, it is significantly larger than the portion of the sky that you can see. If you could see that far, people in more of a 50% zone would be able to see the sky darken significantly in one direction and be bright in another. What we saw instead was the entire sky darkening evenly.
The real answer lies mostly in our nonlonear perception of light, meaning that we're much more sensitive to the absolute change in amount of light when there's less light than when there's a lot. So the difference between 100% bright and 50% bright is a lot smaller to us than 50% bright and 0% bright.
try turning on a flashlight during the day and during the night and you can see the difference the same absolute change in brightness makes in different lighting scenarios. Let's say that some flashlight is 5% the brightness of the sun. Going from 100% to 105% feels like nothing, but going from 0% to 5% is massive.
In fact you can model this difference using existing perceptually accurate color spaces. Let's take the CIE L*a*b* color space. To find the perceived brightness (L*) you take Y, which is the absolute brightness in the CIE XYZ color space and run it through the following function: 116 f(Y/Yn) - 16 where Yn is the brightness of some predefined white point, and f is effectively the cube root (though it's linear when lower than (6/29)^3 (less than 1%)).
If you look at the perceived brightness at 20% absolute brightness, you see that it's not too far from the 75% brightness OP was describing.
I imagine there are other factors at play, but this is probably the biggest one.
You're probably right, I have edited my comment to reflect this.
source
This article actually talks about how your eyes adjust during an eclipse, which is a bit different from what i was talking about, but also likely just as important.