Being a scientist by trade, this is incredibly interesting to me and I am also trying to provide the best diet I can, like many of you. We're so fortunate to have such knowledgeable people contributing to this thread and I have learned an incredible amount in the past few weeks. I've only had chickens for a litte over a year now and I notice my birds are much happier, their feathers are softer and glossier and they are more energetic and less irritable when they are foraging in addition to just dry or even fermented feed alone. Their condition definitely improved when I switched from dry to fermenting their feed on top of foraging, but the foraging adds that extra bloom to them that noticeably waned this past winter when they weren't foraging hardly at all with the snow.
I don't have enough birds to do it, but if one did, and had the room to separate them, and happened to be motivated enough to do a long term study, one could do a well controlled experiment to determine how much of different feeds the chickens ate and estimate based on that (you would have to have the offerings nutritionally profiled at some point) the relative amounts of various nutrients necessary for a chicken approved healthy diet. For example, 1 pen on dry feed ( layer and non-layer and another on non-layer + different calcium supplement options if you're REALLY motivated), 1 pen on those dry feed fermented, 1 on each of the afore + animal protein supplement, 1 pen offered free choice of multiple different feed sources separated, ex field peas in 1 bowl, oats in another, various types of animal sourced proteins in others, etc and come up with a list of measurable variables to test each pen against each other. You would learn which method produces the healthiest birds based on the variables you chose to measure in addition to (from the separate bowl/ingredient pen) approximately how much of each ingredient offered should be included in a mixed ration. However, its much more difficult to do an experiment to determine min and max nutrient levels because of how some nutrients require others for uptake/absorption or proper functioning. Each nutrient would be a pretty big experiment all on its own. This, of course, would depend on if the chickens ate to satisfy nutritional needs or tastes. The offering separate bowls for each ingredient wouldn't work if they ate purely for taste preferences. I would love to do this.