peter, I agree the outcome is determined before it happens.... the question is does that really provide a demotivation to contest the ball? (BTW toss the coin and it potentially comes down 4 times in favour of one team and one in the favour of the other)
The argument of some is that the possession arrow removes incentive to fight for loose balls etc. (see anon above). Quite simply that is crap. Does a player, on seeing a loose ball, stop and think ... "possession arrow favours them" ... so I will not contest this? or does the player not contest the rebound because he/she is thinking "shit, better not try for this rebound cause the possession arrow favours them...."
What the arrow does is equally distribute possession after the contested ball. Its a much better situation than the lap of the gods that the jump ball presents.
So here is the situation. Tully Bevilaqua forces a contested posession against Margo Didek four times in succession- Didek wins four jump balls. Guess what - absolutely no return on effort for TB - versus the possession arrow which at least twice in that situation hands her team the ball.
Extreme example I know, but the jump ball NEVER guaranteed that you were rewarded for your hustle. The possession arrow guarantees u r rewarded 50% of the time. And, smart coaches prefer it because they can coach the situation - either having the ball or not having it. As opposed to the random outcome of a jump ball.