What I suspect in cases that the self defense wasn't lethal or didn't cause any serious bodily injury, a good deal of them go unreported. Back in my younger years that was the case many times. Someone gets the better of the assailant and all parties go home. I'm sure many times a bad guy had a gun to his face and changed his mind and the victim didn't report it.
Different country, but all the cases which I personally know of (meaning, I know the people involved) in my country were not reported unless someone was shot.
Eg. an example - someone whom I know had a burglar on the balcony trying to find their way in. Homeowner brought out the gun from the safe and displayed it casually, burglar saw it and decided he had urgent business elsewhere, fast.
Naurally the incident wasn't reported. Since there was no justification to shoot yet, a display of a firearm could be consituted as an illegal threat (not necessarily - a casually displayed gun in the home could be lawyered away without too much trouble, but why take the trouble), and it was an illegal gun (here, a misdemeanor punishable by a 2000$ fine and confiscation). So the homeowner didn't have an interest in reporting it. The burglar was of course caught doing something illegal and had no interest in reporting it either. Everyone walks and lives to see another day, pretty much the ideal outcome, but such a thing never shows up in statistics.
I know of a number of similar situations which were all not reported. The police are there to keep the peace, you don't want to disturb their peace Of course, in more 'civilized' parts of the world things might be different.