The stance used by myself and many of the real-deal top instructors (Defoor, Lamb, MagPul Dynamics, etc.) nowadays is the “Modern Isosceles”. I also like to refer to it as a simple “Fighting Stance”. It is also used by most of the top competitive shooters as-well.
It is basically a boxing stance with a gun tossed into the mix. It can be used for all of the traditional weapon systems: Handgun, Carbine, Shotgun, and of-course Empty Hands.
It is NOT the same as the traditional “Isosceles” stance which has the shooters feet in-line, shoulder width apart, and squared up to the target/threat in a perfect triangle.
Instead, with the “Modern Isosceles” stance the shooters feet are again shoulder width apart, but the strong side or gun side foot is about a half or a full step back from the support side foot. Your upper torso is squared to the target/threat and your weight is slightly forward onto the balls of your feet with a slight forward lean in your back, and a slight bend in the knees.
The benefits of the Modern Isosceles stance over the Weaver and the traditional Isosceles are that it is first off a very natural stance, and it is what the human body typically does naturally in a fight. This is good!
Better all-around balance than either of the other two options.
The Modern Iso stance also gives the shooter a wider field of view & motion in-terms of addressing multiple threats without needing to take an additional step to address a threat that is not directly in-front of the shooter. With both the Weaver and the old school traditional Isosceles the shooter has a limited range that he can turn without needing to take a step to address a threat to either his gun or support side.
The “Modern Isosceles” stance is also more conducive to movement in all directions, off of the line of attack, to cover, etc.
It also gives shooters who wear body armor better ballistic protection from the front as the shooters upper torso is squared-up to a threat that they are addressing in-front of them.
I have not seen the compiled video evidence for myself, other than almost every O.I.S. dash-cam video I have seen for myself during my LE training, but there is supposedly a large federal agency that did a study showing that even Officers that were trained strictly in the Weaver stance revert to a squared-up “Fighting Stance” when attacked and fired upon by an assailant.
Kyle Defoor did an excellent demonstration of the “Modern Isosceles” during an episode of last seasons “Tactical Impact” TV series, when he and Larry Vickers were doing patrol tactics & scenarios from a patrol car. That particular episode was just re-runned last week.
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There is really nothing groundbreaking here, and there isn’t any absolutes for how you “must” do the “Modern Isosceles” stance. Basically what works for you, works for you…
Hope this info helps out the OP!