Something to add.

I agree that during training you should use a quantifiable factor to determine when the dog will find something, so you can increase the time between finds and make a more productive dog, and increase drive at the same time, but in the field, you have to adjust to the circumstances.

During training you will begin to be able to read when your dog is getting bored. When you attempt to stretch out the "y" in this equation, keep an eye on the dog and make sure it is still searching properly. This will look different for different dogs, so you have to know your dog. You will learn to recognize this cue that your dog will soon need a drop aid. I try and stay away from hard fast numbers or times because outside stimulus and conditions have so much to do with how well a dog is working; such as temperature, distractions, feces and urine in the search area, air quality, energy level of the dog, and feral or domestic animals in the area. There are a lot of factors that go into drop aids, but you will learn to read your dog and understand when they are necessary. They can be used to put a dog back on task, to see if a dog is in fact searching or just going through the motions, or to see if they are crittering (looking for a place to scent mark).