Proofing a dog's obedience behavior through training under the 3 D's (distraction, duration, and distance) is an effective method to ensure that the dog can reliably follow commands even in challenging situations. Here's an explanation of why this approach works:

1. Distraction: Training a dog in the presence of distractions helps them learn to focus and respond to commands despite external stimuli. Dogs are naturally curious and easily distracted by their environment, so it's crucial to expose them to various distractions during training. By gradually increasing the level of distractions, such as other animals, noises, or people, the dog learns to stay attentive and obedient even in distracting situations.

2. Duration: Training for duration involves gradually increasing the length of time the dog must maintain a specific behavior or command. Initially, dogs may respond quickly to a command but struggle to sustain the behavior for an extended period. By gradually increasing the duration, the dog learns to remain focused and obedient for longer periods, reinforcing their understanding of the command and building their self-control.

3. Distance: Training for distance involves teaching a dog to respond to commands even when the handler is far away. This is particularly useful for commands like "stay" or "come" that require the dog to maintain their position or return to the handler from a distance. By gradually increasing the distance between the dog and the handler during training, the dog learns to respond reliably regardless of their proximity to the handler.