... is interesting, but let me try a simpler approach. Let's assume
that Dean Smith's way of measuring rebound performance, the
difference in total possessions, is an appropriate measure, although
certainly not the only statistic that could be used. (See page 4 of
Smith's 1981 book.)
With this assumption, we could then determine whether the difference
in offensive rebounds correlates more strongly with the difference in
total possessions than does the difference in defensive rebounds.
Without having done any such calculations, the answer is
obviously "yes" because there are many possible sequences that will
affect the difference in defensive rebounds but will not affect the
difference in possessions.
For example, assume that total possessions are the same at some point
in the game, with a possession recorded when a team attempts a field
goal, goes to the field throw line or has a turnover. Team A has the
ball, which is stolen in backcourt by Team B, which promptly misses a
shot and Team A gets the rebound, then Team B again steals the ball,
misses a shot and Team A gets the rebound.
Now, let's analyze what has happened. Team A has a rebounding
adavantage of +2 for this sequence. There has been no change in total
possessions, however, and with Team A holding the ball in the
backcourt, they are back to the same position, with the score
unchanged, that they were in before they started losing the ball.
Now, if we measure rebounding performance by the difference in total
possessions, as Dean Smith did, then the two defensive rebounds that
Team A garnered "don't count". That would undoubtedly seem illogical
to most people, but it makes perfect sense to me. After all, when
Team B missed the shot, Team A SHOULD have gotten the rebound because
these were defensive rebounds.
On the other hand, now let Team A successfully bring the ball across
midcourt, miss a shot and get the rebound, then do the same then
again and then make a shot. Their total possessions have just
increased by 3 (i.e., 3 FG attempts), so if total possessions were
even when Team A was crossing midcourt, Team A is now +3 in total
All of this makes perfect sense to me but I suspect that I may be in
the minority. :-)