The reasoning is simple and it boils down to Points Per Shot. You make shots inside the lane at approximately a 60% rate. You take .6 x 2 and you get 1.2 points per shot. You take a mid range shot and it's about 38% x 2 points or .76 points per shot. When you take a three pointer players make that about 33% of the time on average and it's 3 points for roughly 1.0 points per shot. So as you can see, the best bet is in the layups and three pointers.
What's the worst shot in the game? Well this Tweet by Coach Karius pretty much sums it up...
The pull up jumper is the shot that we DON'T want players taking. It's just not that efficient, especially at the high school level. Many coaches will point to people like LeBron James and other good NBA players who shoot pull ups. My response is twofold: First, look at the stat above for NBA players, imagine the poor shooting at the high school level. Second, if you've got LeBron on your high school team by all means let em fly! Otherwise, stop letting your players settle for mid-range pull up jumpers.
Why not adopt a three or key mentality? I really do think it helps your players to understand shot selection better. It also makes more sense statistically. What do you have to lose?