It's not "unpossible". Protons (like most things at the sub-atomic scale) are not like the physical objects you're accustomed to, with seemingly concrete boundaries. It's not like a very small kind of baseball.
Protons are more like the broadcast range of a wifi hotspot (assuming, like any good physicist, that the hotspot signal is exactly spherical, to make the math easier). You might look at signal-to-noise ratio, which will produce one definition of "size", or you might look at wattage, which produces a different measurement of "size", or you might look at some other factor entirely, producing yet another definition of "size". These will not give you the game size, but are all "correct" within their contexts.
And, of course, since protons are actually composed of 2 up quarks and 1 down quark, that complicates the question of "size" further, since you could define proton size based on measurements and modeling of the quarks, which would be analogous to considering the shape and location of the antennae in the aforementioned wifi hotspot.