Dear Golden Oldie:
To find the percentage of the hoop that is filled by the basketball (at the widest point), I used the area of the hoop and the area of the basketball at the widest point. Calculations are given below.
All official basketball hoops are 18" in diameter.
Official Hoop: Area = 254.47 in2
Men's Basketball: Area = 69.25 in2
69.25 / 254.47 = 0.272
Men's Basketball fills 27.2% of an official hoop.
Women's Basketball: Area = 64.61 in2
64.61 / 254.47 = 0.254
Women's Basketball fills 25.4% of an official hoop.
Just for a visual, here's a picture I think shows the numbers to be pretty accurate:
Now, as far as county fair hoops go... there's not a great way to get the numbers. Why? Because each hoop is altered in a different way. The hoops of county fair basketball shoot games are often pounded subtly into ovals, and the balls are over-inflated so they bounce more. So the hoops are misshapen and the balls are slightly larger, though never in a measurable or consistent way. An oval hoop and a slightly bigger and bouncier ball probably make it (I'd guess) about a 10% or less chance of successfully making a basket on the fair hoops. Regardless of what percent of the oval hoop is taken up by the balls, the widest point of the oval is what would determine the likelihood of a solid shot.