John Beilein likes to say that the best defensive rebound is one by his point guard. Why? That's the best way to get out in transition. I decided to investigate Beilein's claim—at least as it applies to Michigan—by going through this season's play-by-plays and charting each defensive rebound.

In the (chart?) chart below, I've tracked each defensive rebound as well as any resulting fast break field goal attempts or drawn shooting fouls—a fast break, in this case, being defined as any shot coming within 10 seconds of the defensive rebound, so long as the ball remained in play the whole time. Also in the chart is how often each player gets a fast break assist or made basket off their own defensive rebound. "% Opp" is the percentage of individual defensive rebounds that result in fast break field goal attempts or drawn shooting fouls, and "% Conv" is the percentage of made fast break FGA and shooting fouls drawn.

SPOILER ALERT: Beilein's theory is correct.

PLAYER	Def. Reb.	FB FGA	FB FGM	Assist	Self Make	FT	% Opp	% Conv
Hardaway	76	33	16	7	7	3	47.4	25.0
Morgan	56	20	14	0	2	1	37.5	26.8
Robinson	56	18	12	3	0	0	32.1	21.4
McGary	54	25	14	3	0	1	48.1	27.8
Stauskas	49	25	16	1	1	1	53.1	34.7
Burke	42	23	11	3	7	2	59.5	28.6
Vogrich	13	5	5	0	1	0	46.2	46.2
Horford	13	2	1	0	0	0	15.4	7.7
Bielfeldt	12	6	2	0	0	0	50.0	16.7
Albrecht	10	3	0	0	0	0	30.0	0
LeVert	7	3	0	0	0	0	42.9	0
Akunne	6	2	1	1	0	0	33.3	16.7
McLimans	5	1	0	0	0	0	20.0	0
Person	1	0	0	0	0	0	0	0
TOTAL	400	166	92	18	18	8	43.5	25.0

Some takeaways:

GOOD PLAYERS ARE GOOD

Trey Burke is far and away the best on the team at turning defensive rebounds into transition opportunties, and the reasons are two-fold. For one, it's Trey Burke—you know, the guy you want running the fast break. Second, as you can see in the video at the top of the post, as a diminutive point guard many of Burke's rebounds come on shots that carom far away from the basket, providing a better chance to turn and run than a rebound in the charge circle.

Burke is also the best at converting his own rebound at the other end, with—surprise!—Tim Hardaway Jr. second in that regard; both have seven made baskets off their own rebounds while Hardaway has one more free throw opportunity... off 34 more defensive boards. Though Burke converts at a higher rate, Hardaway has the highest defensive rebound rate on the team by a non-center, and you can see just how valuable his newfound dedication to that area is to the team.

MCGARY'S OUTLET PASSING

Jordan Morgan (and, in small sample size territory, Jon Horford) has a rate well below the team average when it comes to turning defensive rebounds into transition opportunities, which is understandable: as a center, he's not turning and leading the break, and most of his boards come from right under the basket, where it's hardest to spark a transition opportunity.

That makes McGary's ability to turn 48.1% of his defensive rebounds into fast break chances—a better rate than Hardaway—all the more impressive. The difference, as far as I can tell, is in McGary's outlet passing; he's got surprisingly good court vision, which allows him to turn quickly off a rebound and find his point guard. This is one area where McGary has a decided edge on Morgan, especially since his defensive rebound rate is also higher.

GAP BETWEEN FRESHMEN: NOT THE ONE YOU'D EXPECT

What surprised me most when putting this together was the gap between Nik Stauskas (53.1% Opp) and Glenn Robinson III (32.1%). While Robinson matches up against bigger players, ending up closer to the hoop for rebound opportunities, he's also the more athletic of the two. It's Stauskas, however, who's the only player besides Burke to crack 50% in major minutes—this despite rarely being involved in the play at the other end of the floor.

Perhaps there's a lot of noise in these numbers given the sample size (I'd say yes—I'm mostly ignoring the "% Conv" figure because of this) but that doesn't entirely explain that large a gap. Like with the big men, I believe this has to do with the difference in court vision and passing ability; so far this season, Stauskas has proven himself the more adept passer. Meanwhile, Robinson still seems to be adjusting to the college game; in a year, I'd bet his transition rate will be better than Jordan Morgan's.

[Hit THE JUMP for an update on the Kobe Assist and Adjusted Points Per Shot numbers from last month.]

Revisiting Kobe Assists/Adj. PPS

Last month, I took a look at the concept of "Kobe Assists"—a missed shot that immediately results in a converted offensive rebound—and used that to come up with a stat called "adjusted points per shot". For further background, check out last month's post. I wanted to update the numbers now that conference play in under way. First, the shot chart (KA=Kobe Assist):

Player	2PA	2PM	OReb	KA	3PA	3PM	OReb	KA
Trey Burke	153	87	25	11	85	34	17	2
Tim Hardaway	114	63	17	4	84	33	20	3
Nik Stauskas	49	24	10	6	95	47	13	3
Glenn Robinson III	106	68	8	0	36	14	6	1
Jordan Morgan	85	54	11	4	0	0	0	0
Mitch McGary	74	45	12	0	0	0	0	0
Spike Albrecht	9	4	3	2	16	6	4	0
Jon Horford	15	7	6	1	0	0	0	0
Caris LeVert	18	6	4	1	21	9	4	1
TEAM	623	358	96	29	337	143	64	10

Standing out here, as usual, is Trey Burke; not only is Burke lethal inside the arc (56.9 2P%), but Michigan rebounds 37.9% of his two-point misses. In other words, on 73.2% of Burke's two-pointers, he either scores or the Wolverines retain possession. That figure is 60.0% for his three-pointers. Again, Trey Burke is good. You know this.

In fact, let's calculate those make/retain rates for Michigan's main rotation (players with >50 FGA): 

Player	2P Make/Retain %	3P Make/Retain %
Trey Burke	73.2	60.0
Tim Hardaway	70.1	63.1
Nik Stauskas	69.4	63.2
Glenn Robinson III	71.7	55.6
Jordan Morgan	76.5	--
Mitch McGary	77.0	--

Again, sample size caveats apply, but it's interesting that Burke and Hardaway nearly make up the gap with Stauskas from beyond the arc despite both shooting around 10% worse from three. That doesn't mean a Burke/Hardaway three is as good as one from Stauskas—offensive rebounds are usually converted into twos, not threes—but it suggests that there's something different about the nature of Stauskas's threes. It's not that he's the one rebounding Burke/Hardaway misses—Stauskas has a lower OR% than Burke, in fact.

A potential explanation is how they get their threes. Burke, especially, and Hardaway get a lot of their three-point attempts off the pick-and-roll, which means a big man is rolling to the basket—and prime rebounding territory—as they shoot. Stauskas, meanwhile, is more of a spot-up shooter; the defense isn't scrambling as much when he's lining up his shot and there isn't a big man rolling towards the basket (EDIT: holy timing, UMHoops). That may help explain the disparity, though sample size is also an issue.

Before the adjusted points per shot chart, here's the explanation of the statistic from the original post:

The formula: (2*2FG + 3*3FG + 2*KobeAssists + [team's points per possession][KobePasses - Kobe Assists]) / FGA.

In layman's terms, add a player's points to the points scored directly off his misses and the (admittedly approximate) expected points scored when the team gets a rebound off his miss and doesn't immediately put a shot back up, all divided by his field goal attempts. This gives the expected number of points a team will score on a possession in which a certain player takes a shot.

Changes since December 11th are noted in parentheses:

Player	Adj. PPS (2P)	Adj. PPS (3P)	Adj. PPS (Total)
Trey Burke	1.40 (+0.02)	1.47 (+0.05)	1.42 (+0.03)
Tim Hardaway	1.32 (+0.08)	1.50 (+0.13)	1.40 (+0.11)
Nik Stauskas	1.33 (+0.09)	1.68 (-0.34)	1.56 (-0.12)
Glenn Robinson III	1.38 (+0.08)	1.40 (-0.01)	1.38 (+0.05)
Jordan Morgan	1.47 (--)	-	1.47 (--)
Mitch McGary	1.42 (-0.02)	-	1.42 (-0.02)
Spike Albrecht	1.47 (+0.16)	1.44 (+0.02)	1.45 (+0.08)
Jon Horford	1.48 (+0.09)	-	1.48 (+0.09)
Caris LeVert*	0.99 (--)	1.56 (--)	1.30 (--)

*Caris LeVert wasn't included in last month's chart.

Notably, Stauskas has come back to earth with his three-point shooting; despite the drop, a three-point attempt by him is still easily the best shot this team can create, while his efficiency inside the arc has improved. Hardaway has rounded into form in recent weeks, while Burke has maintained an impressive pace. Caris LeVert, whom I didn't even bother charting the last time around, has great potential from outside, but needs to work on his shot selection from two-point range.