Here's a clarification on how to read that figure:
h = probability that someone illegally obtains a firearm when it is not allowed (e.g. felon with a gun, ranges from 0 to 1, 1 being felons always have guns)
c = fraction of people who take up their legal right of gun ownership and have the firearm in possession when attacked (ranges from 0 to 1, with 1 meaning the person always has a gun when attacked)
g = gun control policy, 0 being no one is allowed to legally have a gun, 1 is everyone is able to possess.
Beta 1 = probability for an unarmed person to die in an attack
Beta 2 = probability for an armed person to die in an attack
Beta 2 / Beta 1 = 1 means that the armed person always dies in an attack (e.g. having a gun makes no difference)
Beta 2 / beta 1 = 0 means that the unarmed person always dies in an attack (e.g. having a gun offers the greatest protection)