While most of us recognize the dog who has been pushed past a threshold and into reaction, it is harder to know exactly where the sweet spot is, the place where learning and thinking occur, where choices are possible, and where behavior changes (good ones!) can happen.
Understanding the Stimulus Gradient (SG) helps handlers recognize a threshold and make good decisions in any situation. Thoughtfully applied, the SG can make it much easier to keep a dog progressing without pushing him too hard (over-threshold), and help a handler understand what went wrong if a mistake occurs --- and thus know how to adjust for success. The SG can also help a handler avoid spinning their wheels by working under-threshold to such a degree no real learning occurs.
Whether over-stimulated or afraid or even seriously aggressive, the how of working with reactive dogs is based on appropriate use of the Stimulus Gradient.
There are 3 elements to the Stimulus Gradient (SG):
These 3 elements need to be juggled and adjusted with care & deliberate awareness of what effect any combination will have on the dog. When the balance is right, the dog can handle the situation without "losing it", can learn and improves (sometimes rapidly) in that setting. The dog "losing it" tells you that you've blown it and pushed the dog past his threshold.
What is an appropriate distance? Ideally, the dog is in the Think & Learn Zone meaning he can split his attention between the stimulus and on his handler. If the dog's attention is focused solely on the stimulus, no training can be accomplished, and you may trigger unwanted behavior or reactions. If the dog's attention isn't on the stimulus, no reaction occurs --- but neither does any learning about that stimulus. It's certainly sub-threshold, but it's also useless.
How long will you expose the dog to the stimulus? A good rule of thumb is not long! Many trainers work not only too close, but expect way too much in the way of duration. The ideal duration is one that leaves the dog just about as relaxed as he was prior to the presentation of the stimulus. Or looked at another way, ideal duration means that the dog is able to very quickly settle once the stimulus is removed.
Ideal duration depends heavily on distance and intensity. It might be only seconds. Again, seeing one cat sitting quietly 100' away would be something a dog would be able to handle for longer than seeing 24 cats tap dancing as a group 10' away. When in doubt, use brief duration exposures to the stimulus, and evaluate what the dog tells you. If the dog is slow to settle or completely loses his ability to be responsive to the handler, the duration (and/or intensity and/or distance) was too much.
Intensity is the easiest to vary, and by the same token, one that trainers often underestimate. Some hints when considering intensity:
DECREASE Duration & Intensity
Know what you're doing with all 3 elements of the Stimulus Gradient, and you can help reactive dogs learn new ways to think and respond.
"Understanding Thresholds: It's More than Under- or Over-" by Suzanne Clothier