I don't understand how you could think Player 18 is better than player 15.
Player 15 has prevented 28 points and allowed none.
Player 18 has prevented 32 points and allowed 2 points.
Surely player 15 is better.
From an individual performance perspective, they're both really good stat lines. Nothing wrong with either.
At the end of the game it doesn't matter how many times your opponent missed, it only matters how many times your opponent scored. And scoring is what you want to minimize.
Making your opponents miss most shots is great, but not as great as making your opponent miss EVERY shot.
Scoring is what you want to minimise, correct. You do this by playing defense. Player 18 defended FAR better than player 8. You can't deny him a great performance cause he allowed 1 basket. He was under more pressure cause the player(s) he was defending took far more shots, so his defensive work load was far higher, and to allow only 1 basket from 17 attempts is amazing. 0-8 is great too, but it says that the defender had less work to do, although he did his work brilliantly as well.
What do you mean by possessions in a game are limited? Do you mean simply because there is a time limit?
Yes, there are only a limited number of possession in a game, 48 minutes worth to be exact. Around 80-90 possessions per team in the game, so yes, there's limited possessions. By jacking up more shots that don't hit, you're effectively reducing the number of scoring possessions your team has.
Let me try and explain this differently, if every player on team A kept the opponent to 0-8, and every player on Team B kept the opponent to 1-17, then which team is going to win? Obviously Team A is going to win because the other team didn't score any points, but Team B will let 2 points * the number of players on the team.
We're talking about individual match ups here.
A player that shoots defends someone who shoots 1-25 will have defended better than someone who defended a guy who went 0-12.
Double the number of shots taken, meaning more empty trips, less points for the other team. Yes, they did score two, but they missed out on a potential 48 points that could have been scored by another player taking (and making) the shot.