# What probability distribution best describes the place of a dart?

I've been asked to provide a distribution that best describes the place a dart might hit on the dart board. At first glance I though it would be uniform, but that would be true if we were talking about someone throwing it with a blindfold on, then I thought a bivariate normal distribution might do a better job, but I cannot seem to give a reasonable explanation for it.

• I would say: radius is one-sided normal centered at $0$. Angle is uniform on $[0,2\pi]$. Or, equivalently, let the radius be normal centered at $0$ and angle uniform on $[0,\pi]$.
– lulu
Jun 20 at 17:20
• Your reason would be that they are trying to hit the center and don’t suck. Jun 20 at 17:25

It depends on factors such as precision and accuracy. If the dart is precise but not accurate, you’ll get a bivariate normal but not at the center. If it is precise and accurate, you’ll get a bivariate normal at the center. If it’s accurate but not precise, you could get a bivariate normal with large variance, or a uniform if you wish. The same is with not accurate and not precise—the hits are centered outside the target but have large spread, so could be modeled using a bivariate normal or a uniform.

• Spell checker is your enemy. Jun 20 at 17:45
• Drats, I wanted to talk about bicarbonate ions. Jun 20 at 18:25