That theoretical lead formula requires a stationary rifle, moving target and zero reaction time to work. That isn't quite the way it happens though.
Game is shot with a moving firearm which does a number of things. The swinging gun cancels the reaction time and introduces a vector into the equation. This horizontal component coresponds to the amount of distance the bullet moved in the plane of target movement while it was still in the barrel arc, and is heavily dependant on swing speed. That drift doesn't go away during bullet flight, and given that the distance to the target is significant it amounts to a lot of automatic lead. A fast swinger with a shotgun can kill a lot of birds without ever seeing any lead at all. I seldom lead more than the front edge of a moving animal with a rifle until the range gets out to 150 yards or so, or I'll shoot in front of everything. The calculated theoretical lead has to be there, but part of it comes from hidden sources. Actual lead comes pretty close to half of theoretical lead in practice.