In one sense, the way you describe it above is how it works. If all 5 starters have 20% distro, then there is a 1 in 5 chance that a play will be run for any of them. If the distro of the 5 starters is 20, 15, 10, 5, and 2 then the chances of having a play run for any of them is built on the ratio of those settings. However, there are several factors that play into what may happen on any given play.
First, the HD engine is set up such that each play is an individual event. Each trip up and down the court creates the opportunity for several different actions to occur. Some of these actions impact the distribution. For example, a play may be set up for player A but the ball is thrown out of bounds, the player may step out of bounds, there may be a foul called, there may be an injury that stops the clock, there could be a steal, or a blocked shot. Also, tip-ins do not count in distro. That is why you should never expect the distribution for a player to 100% match his shots taken. NOTE: Even a player with 0% distro may take a shot during the game depending on the situation.
The assigned distribution is not a target for the engine to meet. The stats at the end of the game will reflect a summation of the individual events that happen during the game. So, let's say player A with 25% distro makes 12 of his teams 30 1st half shot attempts. That does not limit him to only 3 of his teams next 30 attempts.
Your opponents defense, IQ, skills, double team, and +/- settings will affect distribution results. A player smothered by two A+ Man to Man opponents will likely not get off as many shots as he might against a weaker Zone for example. In the M2M situation, he will more likely be required to pass the ball or be forced to make a mistake.
Finally, fatigue and/or injuries may impact the success of a players distribution. Tired or seriously injured players do not play as well as rested healthy players. They will generate more turnovers and fouls and their shooting percentage will drop.
Probably the best things to do are to give your best shooters more opportunities and study your opponent and make your game planning the best you can based on that analysis. There is no substitute for experience. We've all had to go through the learning curve.
Good Luck and have fun.