You don't VARY your head height in the GD stance...
However, your head height is significantly higher in the GD stance than it is in the heel-toe, hide behind the catcher stance.
And physics is the wrong term... geometry would be more correct.
Imagine, if you will, heel-toe stance, close to the catcher, nose on the inside edge (unless the catcher wants to be there), eyes at the top of the individual batter's zone (again, unless the catcher wants to be there or hold his glove there). Now think of the angles...
High inside pitch in the zone: there is no angle the pitch is coming straight for your eyes. If you can not flinch, this pitch is easy to judge - up/down, in/out. It is either above or below your eye and left or right of your nose. Simple.
Low inside pitch in the zone: It is still inline with your nose and the edge of the plate. But, now there is a significant "down" angle from horizontal view at your eyes to the ball as it crosses the plate (30-45 degrees?) because you are close to the plate. As an umpire you must now judge the distance from your eyes to that ball. Does that distance place the ball below the zone or still in it? The catcher's method can add clues to assist in your judgement. Additionally, distance judgement requires the use of both eyes - you can't accurately judge distance with one eye. So were both eyes on the ball? Did a bar from your mask partially block your vision? Did the catcher move in front of one of your eyes? Yes, because you are closer to the catcher you are more occluded and protected from the incoming pitch but you are also more likely to have your vision occluded and not be able to see the full flight of the ball. Hence it is more plausible to make incorrect judgements because you got blocked out and did receive the full set of information.
High outside pitch in the zone: pitch is still level with your eyes at the top of the zone. But the decision of in and out of the zone (over the plate or not) requires the same visual acuity as for the down-and-in pitch (20 degree angle?). Both eyes on the ball is still required, perhaps a slightly less significant angle, and the actions of the catcher are often less patent for an outside pitch (mitt swipes across the zone and swings beyond the zone). For the umpire it is just as difficult to judge and perhaps more difficult to sell because the catchers actions don't allow a solid "frame."
Low outside pitch in the zone: double the angles (20 degrees out and 30 degrees down) and the location of the catch is nearly always through or behind the catcher from your visual vantage point - the ball goes out of sight! Way difficult to do a good job here. Dare I say guess? As umpires we can act all kinds of confident and be assured the we are doing the best we can for judging that pitch. But I'm betting that for many of them you feel the decision was an educated guess. And that you may justify your call based upon the catcher's actions rather than the ball's location, which you couldn't discern.
My understanding of the GD Stance is that you are significantly farther back from the plate and you place your head above the zone. Head placement is in the same place every time, looking down into zone and independent of the batter's height. This is how I do it. I feel it offers consistency.
This distance away from the plate changes several things:
The angles for judging distance and ball location are less significant - you are more in-line with the flight of the ball. It is easier to judge location when you are closer to in-line with the flight of the ball - just like the high inside pitch.
The distance also gets you farther away from the catcher. Yes, the catcher doesn't block as much of the area in front of you. Perhaps you will get hit by more wild pitches or foul balls - perhaps fewer, as Tim pointed out, because the ball has more time to expand away from you. Who knows? I was working the GD Stance and took two nasty shots last week - thigh/groin area and left bicepts; both glanced off of the handle end of the bat.
But the catcher doesn't block as much visual area either. You now can see the batter and immediately see whether the ball nicked him or not. You can see his check swings without worrying about the catcher rising up in front your eyes or putting his mitt in your face.
All in all, for me, the stance is far superior. It offers a more consistent view of the pitch and therefore more consistent strike/ball judgements. It also offers a vastly improved view of the other elements of the game. It is the quickest and most significant improvement I have made in my umpiring since I began... in 1980.
