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This is a postion I teach to many of my players. It allows for more offensive freedom once the ball is caught, but the disadvantage is you lose 1-2 feet of post position. IMO it is well worth this couple feet of floor space with the freedom it allows the post player. First I will breakdown the normal post position and compare it the inverted post position.
Normal Post Position From the Right Side of Rim: Normal post position would call for the post player to have his left foot back, a wide base, right hand would be the passer's target. As the pass reaches him, he would meet the ball by extending his right foot, keeping his left foot planted, to "save" his place on the court. As he catches the post entry pass, his left foot would now be his pivot foot as he goes to work on the block. Sounds great, but the problem is, half the court is now shut off to the post player. He can't spin baseline without first dribbling or traveling. Both of which usually lead to turnovers.
Inverted Post Position From the Right Side of Rim: Starts off exactly the same as before. Left foot back, wide base, right hand is passer's target. As you go recieve the ball, this is where the change in foot position occurs. Instead of extending with your right foot, keeping the left planted, you instead lead with the left, keeping your right foot planted. Once the ball is recieved, your right foot is now your pivot. Again, you lose a shoulder's length of position, but the entire baseline is now open for business. You can use a baseline spin move without a set-up dribble. It's a beautiful thing.
How would this be any better than recieving the ball with a short low/wide jump stop. Then, you can decide which foot you want as your pivot depending on defenders position.
Good question. For one, it's not always possible to catch a low post pass with a jump stop, where both feet are potential pivot feet. It's quite difficult actually. And two, and most importantly in my opinion, the inverted post position allows for proper "explosion" balance. When both feet are spread out, there is no room for exploding in either direction. For the baseline spin, which Pau Gasol, uses quite frequently, the inverted post position allows you to fake inside, then explode around your pivot to the baseline. When mastered, it really is quite unstoppable.