Right, exactly like that. And HD does not have historical shooting rates to determine the chance a shot is for player A or Player B, etc. That is where distribution comes in. So, if you have 5 guys in the game, with distro settings of 4, 1, 1, 1, 1.. Then the guy with 4 has a 4/8 chance of being the shooter, each other player has a 1/8 chance in being the shooter. In HD, the distro rating can be modified by double teaming. (making the Double teamed guy shoot less by lowering his distro).
Once they pick the shooter, the game proceeds event by event.. The outcome for the game is not predetermined, things like guys picking up fouls and sitting (so your leave in longer or take out quicker) have an impact, etc.
Each play happens individually, in series, totally independent of any other play. If a game is played 100 times, there will be 100 completely different outcomes.