This is just a mental masturbation.
Intuitively, one body weight pistol should provide about twice as much stress on that leg as one body weight squat would. So, for a 200 pound person, body weight squats should be about 100 pounds of stress on each leg, and pistols should be about 200 pounds on each leg. Holding a 100 pound weight, a two legged squat should be approximately 150 pounds per leg, and a pistol should be approximately 300 pounds per leg.
However, this is very rough, and does not take into account finer points such as what % of body weight is actually being squatted for either squats or pistols (the weight of your feet, your shins), leverages, and so on.
Can anyone propose a more precise formula for calculating “actual” squat weight for free squats and pistols?