What second chance points tell us about the relative importance of rebounds

Today Big Ten Wonk opined that defensive rebounds are more important to defense than offensive rebounds are to offense. As everything comes back to Points Per Possession (PPP), I wondered whether teams score more points after an offensive rebound than they do on an average possession. This is difficult to track down because "second chance points" don't always appear in the box score. Only eight of Illinois's box scores to date have included second chance points. The numbers below are PPP / PPrP (the latter being Points Per rebounded Possession, calculated as second chance points divided by offensive rebounds). The first set is Illinois's defense (the other team's PPP) and the second set is Illinois's offense.

11/19 Florida A&M 1.04 / 0.80
11/21 Savannah State 0.53 / 1.40
11/25 Bradley 1.03 / 1.08
11/28 Maryland 1.01 / 1.11
12/06 IUPUI 0.86 / 1.00
12/17 Belmont 0.70 / 0.80
12/19 Missouri 1.06 / 1.22
12/21 Idaho State 1.10 / 1.18

11/19 vs. Florida A&M 1.39 / 1.16
11/21 vs. Savannah State 1.26 / 0.77
11/25 vs. Bradley 1.08 / 1.20
11/28 vs. Maryland 0.92 / 0.95
12/06 vs. IUPUI 1.27 / 1.25
12/17 vs. Belmont 1.06 / 0.78
12/19 vs. Missouri 1.11 / 1.29
12/21 vs. Idaho State 1.30 / 1.62

The weighted averages on defense are 0.91 / 1.07 -- Illinois gives up 0.16 more points per possession on opponents' offensive-rebounded possessions than on opponents' possessions overall. The numbers for Illinois's offense are more difficult to grasp. I think the weighted averages of 1.16 / 1.10 are misleading, due to early-season rebound fests.

As Wonk often observes, offensive rebounding and defensive rebounding are different skills. Lumping the two together is like using assist-to-turnover ratio -- it provides some insight, but the two aren't that intimately linked. But my point is that if a team's (take a deep breath) offensive marginal points per rebounded possession exceeds its defensive marginal points per rebounded possession, then its offensive rebounds are more important to its offense than its defensive rebounds are to its defense. And if Off mPPrP < Def mPPrP, then its Drebs are more important to its defense than its Orebs are to its offense.

In Illinois's case, right now I'd say that defensive rebounds are more important to the team's defensive consistency than offensive rebounds are to the team's offensive consistency. [It's great to change the question while giving the answer.] We know what's going to happen from game to game when Illinois gives up a defensive rebound -- the other team gets a small boost on the continued possession. When Illinois gets an offensive rebound, though, we really have no idea what's going to happen from game to game.