Thursday, March 29, 2007

Hopping Along

Wolfpack offense, last four seasons (full season numbers; nat'l rank in parenthesis):
        AdjOE (Rk)     eFG% (Rk)      TO% (Rk)       OR% (Rk)       FTR (Rk)
2004 121.7 (3) 52.7 (34) 19.9 (89) 30.9 (215) 28.5 (74)
2005 116.2 (14) 53.2 (33) 18.5 (31) 30.6 (215) 27.3 (92)
2006 111.5 (40) 55.0 (10) 19.6 (77) 26.0 (310) 29.9 (30)
2007 113.3 (46) 54.9 (13) 21.8 (202) 28.1 (306) 29.7 (46)
You need not be good at all four factors in order to have a good offense, but, obviously, the more diversified your strengths, the better.

Herb Sendek's offenses relied on a high eFG% and a low TO%, eschewing offensive rebounds, and that worked out fine. But we lost one of those staples this season (the low TO%) and didn't make up for it by improving our offensive rebounding. Although this year's offense looks like it's in the same ballpark as the last three, it really isn't. Pomeroy's adjusted numbers give more weight to a team's most recent performances, so State's late-season surge provided a jolt that is misleading (particularly in comparison to last year's offense, which slumped at the end). We spent the majority of this year with an offense ranked in the 70s (still not bad, but not close to recent years, either).

The Wolfpack offense in conference play (conference rank in parenthesis):
          OE (Rk)       eFG% (Rk)    TO% (Rk)       OR% (Rk)     FTR (Rk)
2005 112.0 (4) 54.1 (3) 19.4 (7) 30.5 (10) 30.6 (4)
2006 110.2 (4) 55.6 (1) 20.2 (4) 27.2 (12) 33.5 (2)
2007 101.1 (11) 53.1 (1) 22.5 (11) 26.2 (12) 25.6 (8)
A few weeks ago, the Tobacco Road Report noted:

[T]he Wolfpack haven't won a conference game when they had less than a 55 percent EFG.

That's our offense summed up in one line. Fifty-five percent isn't merely good shooting, it's great shooting. If we were anything less than great, we lost. Next year, it's all about finding a second leg to stand on, be it through a significant improvement in either TO% or OR%, or, more likely, an incremental improvement in both.

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Thursday, March 22, 2007

Wolfpack Women, Tempo-Free Style

I have laid this out to look like one of Ken Pomeroy's scouting reports.

Raw Tempo: 71.8

Offense Defense
Raw Efficiency 93.2 79.6

Effective FG% 44.9 40.3
Turnover Pct. 23.0 25.9
Off. Rebound% 36.1 30.8
Free Throw Rate 20.1 26.4

3-Point FG% 31.3 30.0
2-Point FG% 44.4 38.9
Free Throw Pct. 69.6 69.5
Block Pct. 6.1 9.4
Steal Pct. 10.9 10.7

3FGA/FGA 19.3 23.3
Ast/FGM 52.3 54.4


                  %Min     ORtg   %Poss   %Shots   eFG%     OR%     DR%   FTRate
K. Whittington 73.1 91.6 21.9 21.8 42.2 12.2 24.9 36.2
S. Fields 71.8 93.3 19.1 20.1 44.0 1.3 8.2 32.9
A. Key 71.6 101.4 18.7 18.9 48.6 3.5 5.8 23.9
M. Dickens 66.1 87.6 20.1 18.2 43.8 6.8 12.0 32.3
K. Brown 53.3 104.1 15.2 18.2 48.8 5.4 7.2 16.4
G. Goring 40.7 102.0 25.8 27.8 53.0 13.1 20.4 25.2
S. Reaves 31.5 100.9 16.3 13.5 62.5 11.5 15.1 42.0
N. Gartrell 29.1 80.1 22.5 25.1 33.4 4.4 10.4 28.5
A. White 22.4 75.9 19.7 17.5 38.9 1.7 8.1 22.2
S. Beal 15.8 72.7 18.4 18.0 35.6 5.9 11.5 20.3


                  AstR     TO%   %Blks  %Stls  Pts/40
K. Whittington 7.7 20.5 4.3 3.5 14.2
S. Fields 13.6 21.4 0.1 1.7 13.7
A. Key 20.9 22.8 0.7 2.3 13.3
M. Dickens 15.8 27.3 1.8 1.5 12.0
K. Brown 8.0 15.6 1.1 2.1 12.1
G. Goring 9.6 19.4 6.2 0.9 20.4
S. Reaves 3.5 29.4 1.7 2.0 12.4
N. Gartrell 10.1 19.2 0.0 1.1 13.1
A. White 14.9 35.0 0.0 4.0 10.4
S. Beal 8.2 29.4 1.7 2.6 9.2

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Monday, March 05, 2007

Shot Attempt Differential

I had been updating my conference-only stats earlier today when I noticed something disturbing...

NCSU FGA: 819
Opp FGA: 972

Borrowing from some of Ken Pomeroy's work, I'm going to look at shot differential in conference play for all of the ACC schools. To calculate the differential for each team, I'm going to take the shots portion of the possession equation (FGA + (0.475 x FTA)), divide that by total possessions and then multiply by 100. That gives me the shot differential per 100 possessions. A positive number means a team had more attempts than its opponents, while a negative number means a team's opponents got more shots at the basket.

Conf games only:
                    Shot_Diff
1) Miami 8.4
2) Clemson 7.1
3) UNC 5.3
4) Ga Tech 5.1
5) Duke 1.8
6) Wake 0.0
7) FSU -0.8
8) Maryland -0.9
9) Va Tech -3.3
10) Virginia -3.8
11) Boston College -5.1
.
.
.
12) NC State -14.7

-- Miami is interesting. They had 989 FGAs in conference play, compared to 817 for their opponents (opponents shot 174 more free throws). But the Hurricanes shot so poorly and their opponents shot so well that the Canes made a grand total of six more field goals (411 to 405) than their opponents despite the 172 extra attempts.

-- Clemson used theft to build its advantage--the Tigers were +55 in the turnover department.

-- Wake Forest had exactly as many field goal attempts (900) and free throw attempts (377) as its opponents. Weird.

-- When you consistently get pounded on the glass and don't force turnovers, you get the deficit that's staring at NC State. If you'd prefer the number in per game terms rather than per 100 possessions, here you go: -9.8 shots per game. Talk about diggin' yourself a hole.

NC State committed 58 more turnovers than its opponents did, so that's part of it. The rest can be attributed here:
        OR%    OR
NCSU 26.2 124
Opp 39.3 225
We're both the worst offensive rebounding team and the worst defensive rebounding team in the ACC. That's kinda not good.

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Sunday, March 04, 2007

Final Adjusted Conference Standings

(Previous adjusted standings.)

In the table below, teams are ordered by their expected conference records, which are derived from each team's offensive and defensive efficiency in conference play. Expected W-L records are calculated using the pythagorean theorem, and you can read all about it here.

EFF Margin = OFF EFF - DEF EFF
ExpW-L = Expected Win-Loss Record
ActW-L = Actual Win-Loss Record

Conference Games Only
Rank TeamGamesOFF EFF (Rk)
DEF EFF (Rk)
EFF MarginExpW-LActW-L
1 UNC16112.5 (1)
95.7 (1)
16.814-211-5
2 Maryland16106.4 (6)
100.3 (3)
6.111-5
10-6
3 Duke
16103.9 (8)
98.8 (2)
5.110-68-8
4 Virginia
16103.5 (9)
101.4 (4)
2.19-711-5
5Boston College
16109.7 (T2)
108.0 (9)
1.79-710-6
6 Georgia Tech
16107.4 (5)
105.9 (6)
1.59-78-8
7 Florida State
16109.7 (T2)
109.0 (10)
0.78-87-9
8 Virginia Tech
16107.8 (4)
107.3 (8)
0.5
8-810-6
9Clemson
16102.3 (10)
103.8 (5)
-1.57-97-9
10NC State
16101.1 (11)
111.4 (11)
-10.34-125-11
11 Miami16105.8 (7)
117.0 (12)
-11.24-124-12
12Wake Forest1695.1 (12)
106.7 (7)
-11.63-135-11

-- On Miami's defense...

Canes beat writer Omar Kelly had a Q&A with Frank Haith during which he (Kelly) asserted the following:

Your team has been one of the top defensive squads in the ACC the past two seasons, but this year there has been a significant drop off.

One of the top defensive teams in the ACC. Ha! Haith didn't disagree with that notion, though. (And why would he? "Actually, Omar, I can't teach defense for the life of me. Our team defense resembles a jelly doughnut: inviting on the outside with a delicious creamy center inside. I should probably be fired.")

They're committing the cardinal sin of college hoops analysis: looking at PPG and failing to account for tempo. Miami is one of the slowest teams in the conference every year. In conference play over the last three years, the Hurricanes have ranked 10th, 10th, and 12th, respectively, in defensive efficiency. If you cruise around Ken Pomeroy's stats page, you'll see their full season numbers have been no better.

Take note, you would-be coaches: the best way to create a reputation as a teacher of good defense is to install a methodical offense. Look at those Princeton guys! 52.5 PPG allowed; they must have an awesome defense! They do not. What they do have is some good names: Strittmatter, Buffmire, and my new favorite college hoops name, Kyle Koncz. Tyler Hansbrough got Koncz-ed on the nose earlier today.

Sorry. What was I talking about?

-- NC State, last three seasons (speaking of overrated defense...):
         OE (Rk)       DE (Rk)     ExpW-L   ActW-L   Poss/G
2005 112.0 (4) 110.5 (11) 9-7 7-9 63
2006 110.2 (4) 107.3 (9) 9-7 10-6 69
2007 101.1 (11) 111.4 (11) 4-12 5-11 67
Not a whole lot changed for the defense this year, as we're mired near the bottom of the league in defensive efficiency as per usual. The difference has been offensively, where production fell off a cliff.

-- (10) NC State vs. (7) Duke on Thursday. Tough break for us, but there are a few reasons to think positively. Assuming Gerald Henderson remains suspended, more minutes are going to have to go to McClure/Thomas/Zoubek, and all three of those guys are very turnover-prone. Maybe we can count on a few more unforced errors from the Dukies. Which would be good since we don't go through the trouble of forcing any ourselves. There's also the Engin Atsur factor; Engin didn't play in the first meeting and we were helpless against their clutch-and-grab defense. (Kudos, Coach K, to the defensive niche you've crafted for yourself with your tireless bullying of officials. Playing Duke is like playing the New Jersey Devils.)

But Henderson's absence isn't likely to damage Duke's interior defense, and there's our problem. We shot 33.3% on twos in the first meeting.

So Duke is the bad part of the Pack's tournament draw, but the rest is all good, baby. Virginia is the fraudingest fraud that ever frauded its way to the two-seed, and Virginia Tech, well, you know.

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Monday, February 26, 2007

The Price Of Turnovers

Last week, Big Ten Wonk examined how effective B10 teams are when they don't turn the ball over. Which team scores the most points on possessions that don't end in a turnover? Letting no good idea go unborrowed, I crunched the same numbers for ACC teams.

Possessions are calculated like this: FGA + (0.475 x FTA) - OReb + TO
By just subtracting turnovers from each team's possessions total, then, we're left with turnover-less possessions.

Points per turnover-less possession (conference games only):
Boston College    1.40
North Carolina 1.39
Georgia Tech 1.37
Florida State 1.36
Duke 1.35
NC State 1.32
Virginia 1.31
Maryland 1.31
Virginia Tech 1.29
Miami 1.26
Clemson 1.25
Wake Forest 1.24
So every time the Wolfpack turns the ball over, it costs us 1.3 points. Every time Gavin dribbles the ball off his foot and out of bounds, 1.3 points go down the tubes. Every time Gavin has a lazy pass intercepted, that's 1.3 points we can never get back. Every time-- Okay, okay.

(By the way, Gavin, you owe us 66 points for your 51 turnovers in ACC games. You can't really pay us back, though...does anyone know the points/wind sprints exchange rate?)

All of this leads to another question: whose overall offensive efficiency is helped/hurt the most by turnovers?

The next table is sorted by turnover rate in conference play. The second column (TOLeP_Rk) is each team's rank in points per turnover-less possession (TOLeP being my awkward abbreviation for turnover-less possessions). The third column (OE_Rk) is each team's rank in offensive efficiency (points per possession, which includes turnovers).

Conference games only:
                   TO%   TOLeP_Rk   OE_Rk
Virginia Tech 15.8 9 3
Miami 17.0 10 6
North Carolina 18.9 2 1
Clemson 19.9 11 11
Florida State 19.9 4 4
Maryland 20.1 8 7
Virginia 20.5 7 9
Boston College 21.0 1 2
Duke 22.8 5 8
Georgia Tech 22.8 3 5
NC State 23.0 6 10
Wake Forest 23.0 12 12
Take turnovers out of the equation and Virginia Tech's offense is revealed as one that's actually quite pedestrian--relative to the rest of the ACC, anyway. The 1.29 points per turnover-less possession scored by the Hokies is just 9th-best in the league. But because the Hokies take care of the ball better than anyone else, their overall offensive efficiency is very good: 3rd-best in the ACC.

It's a similar story for Miami: nothin' special on turnover-less possessions--Miami is the worst shooting team in the conference--but ball security allows them to have an offense that ranks in the conference's top half.

On the flip side, there's NC State. Turnovers have made what is an otherwise decent offense into one of the worst in the league. And this is only tangentially related, but you want to know how much we suck at the secondary offensive factors--how much they drag us down? We're #1 in effective field goal percentage in conference play...and 10th in offensive efficiency. Thanks to turnovers and anemic offensive rebounding, the best shooting team in the ACC has one of the three worst offenses in the ACC.

Wake Forest and Clemson: well, they aren't any good regardless of whether or not they're turning the ball over. If you want to look at the glass as being half full, you can say that although Wake turns the ball over more than anybody else, it costs them fewer points (per turnover) than anybody else. So there is that.

"Talking out of turn...that's a paddlin'. Looking out the window...that's a paddlin'. Staring at my sandals...that's a paddlin'. Turnin' the ball over...ooh, you better believe that's a paddlin'."

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Thursday, February 15, 2007

Looking At The Adjusted Conference Standings

In the table below, teams are ordered by their expected conference records, which are derived from each team's offensive and defensive efficiency in conference play. Expected W-L records are calculated using the pythagorean theorem, and you can read all about it here.

EFF Margin = OFF EFF - DEF EFF
ExpW-L = Expected Win-Loss Record
ActW-L = Actual Win-Loss Record

Conference Games Only
Rank TeamGamesOFF EFF (Rk)
DEF EFF (Rk)
EFF MarginExpW-LActW-L
1 UNC11112.1 (2)
91.3 (1)
20.810-18-3
2 Duke12104.1 (7)
96.5 (2)
7.68-4
6-6
3 Boston College
12113.3 (1)
107.0 (7)
6.38-49-3
4 Virginia Tech
11107.5 (4)
105.7 (6)
1.86-58-3
5Virginia11103.5 (8)
101.8 (T3)
1.76-58-3
6 Clemson11103.2 (9)
102.6 (5)
0.66-55-6
7 Maryland11102.2 (10)
101.8 (T3)
0.46-55-6
8 Florida State
12109.7 (3)
110.3 (10)
-0.66-65-7
9Georgia Tech
11106.5 (6)
107.2 (8)
-0.75-65-6
10NC State
11101.3 (11)
112.1 (11)
-10.83-83-8
11 Miami11106.7 (5)
119.5 (12)
-12.82-93-8
12Wake Forest1293.9 (12)
108.0 (9)
-14.12-103-9

(The conference average is about 105 for OFF EFF and DEF EFF.)

You can see the tiers breaking down like so:

North Carolina


Duke
Boston College

Virginia Tech
Virginia
Clemson
Maryland
Florida State
Georgia Tech

NC State
Miami
Wake

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Friday, January 26, 2007

Dishin' It

I was updating my tempo-free statistics this afternoon and thought it'd be interesting to take a look at how some of the ACC's point guards are faring. I've got a bunch of numbers here, including (just for the hell of it) per game and per minute stats that do not adjust for pace.

In conference games only:
                 AstRate  Ast/Gm  Ast/40  Ast:TO   TO%    TO/Gm  TO/40

Tyrese Rice 34.4 6.3 6.8 1.9:1 20.8 3.3 3.6
Sean Singletary 33.2 5.8 7.0 1.3:1 26.3 4.3 5.2
JR Reynolds 28.8 4.7 5.7 1.3:1 19.9 3.7 4.4
Isaiah Swann 28.4 4.2 6.3 2.1:1 23.1 2.0 3.0
Ty Lawson 26.6 4.2 7.2 1.1:1 35.9 3.7 6.3
Ish Smith 25.3 3.1 5.2 .76:1 37.0 4.1 6.9
Eric Hayes 23.4 3.3 5.2 1.8:1 25.1 1.8 2.9
Jamon Gordon 22.7 3.8 4.5 1.1:1 23.9 3.5 4.1
J. Crittenton 22.1 4.2 4.8 1:1 27.3 4.0 4.6
Anthony Harris 21.6 3.1 4.4 1.4:1 20.5 2.3 3.2
Greg Paulus 20.1 3.3 4.3 1.1:1 27.0 3.0 3.9
Gavin Grant 19.2 3.0 3.4 .75:1 24.5 4.0 4.6
AstRate = Estimates the percentage of teammates' made shots the player assists on while he is on the court. For example, we see above that when Greg Paulus is on the floor, he assists on one out of every five shots his teammates make.
Ast/40 = Assists per 40 minutes. Equalizes for playing time but not for pace. (Player's Assists / Player's Minutes Played) x 40
TO/40 = Turnovers per 40 minutes.

-- It's not really fair to lump Gavin with these guys, but I wanted an NC State representative and Atsur hasn't played enough minutes to qualify.

-- I would like to direct you to Ishmael Smith's unfortunate line. His assist rate is good, but the turnovers, oh, the turnovers. Six-point-nine per 40 minutes. Making matters worse, Smith is shooting 40.9% (eFG) in conference play.

-- In general, the freshmen--Lawson, Smith, Hayes, Crittenton--are struggling to hang onto the ball. Lawson and Smith in particular are finding out how tough this league can be on young point guards. Lawson at least redeems himself with efficient scoring.

-- Which ACC forward has the best assist rate? Ben McCauley: 20.9%. He edges out Josh McRoberts (18.5%).

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Tuesday, January 23, 2007

The One Where We Think Happy Thoughts

If, in these trying times, you are searching for a reason to be optimistic--and who isnt?--then I present you with the matter of Virginia's road woes.

Yes, Virginia hasn’t won a road game outside its own state the past season and a half and the Cavs have lost 23 of their last 27 road games dating back to the 2004-05 season.

But coach Dave Leitao clearly gets irritated when the topic comes up. Following Sunday’s home win over Wake Forest, Leitao was reminded of this week’s two road games and his team’s 0-3 road mark this season (losses at Purdue, UNC and BC).

[snip]

“I know the reasons why. It’s more upstairs. We’ve got to prepare ourselves to play through everything, through the crowd, through the opponent and through runs and just maintain our poise, our focus and our energy. If we do that, I am confident whether it’s Wednesday or whenever, we’ll win some games.”

Just how bad were the Cavaliers on the road in conference play last season? Really, really bad. Were I Dave Leitao, I'd be irritated too. Also, I'd wear my suit inside out. Because I have to change our mojo somehow. Time for the rally...er, pants! Here's how ACC teams fared on the road in 2006, sorted (worst to best) by efficiency margin:

Team           OFF_EFF    DEF_EFF    EFF_Margin

Virginia 87.3 108.3 -21.0
Olé! 106.1 120.8 -14.7
Maryland 89.8 102.2 -12.4
Clemson 92.4 102.4 -10.0
Ga Tech 101.8 110.5 -8.7
Miami 103.2 110.3 -7.1
Va Tech 102.5 107.5 -5.0
Florida State 103.9 108.7 -4.8
Boston College 106.7 106.6 +0.1
NC State 107.2 106.9 +0.3
Duke 115.0 104.9 +10.1
North Carolina 112.6 100.4 +12.2

[EFF Margin is OFF EFF - DEF EFF.
For reference, the conference average offensive and defensive efficiency in 2006 was 104.7.]

As you can see, Virginia was in its own suckosphere. I mean, the Cavs were way out there. Even Wake Forest and its comically bad road defense offered no match.

87.3 points-per-100-possessions? It's like they would forget how to run their offense. The defense wasn't good either, but at least they were only a few points off the conference average at that end. Were there Virginia fans who sat through all eight road games, and if so, have their eyes stopped bleeding yet?

En route to a 1-7 road record, Virginia lost five games by double-digits. Their lone road win: an ugly, low scoring affair in Blacksburg. They weren't good that day; they were out-sucked.

It's too early to know if the pattern will hold with the 2007 Cavs, but the numbers they've posted in their first two road games aren't exactly encouraging. I have to think their road offense will be much better this year...it has no where to go but up. And fortunately for the Wahoos as it pertains to Wednesday, NC State's defense at home has been a joke. It's the movable object and the stoppable force! Who will succumb?

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Monday, January 15, 2007

Some Early In-Conference Statistics

Now that we're a quarter of the way through the conference slate, it's time to look at a few numbers. These are up-to-date through the games played yesterday and include conference games only.

                  2FG%   3FG%   3FGA/FGA

Duke 59.4 35.6 30.8
Georgia Tech 59.1 42.6 34.9
NC State 56.5 37.5 32.9
Wake Forest 54.7 31.2 36.0
Clemson 51.9 37.5 30.0
League Average 50.6 35.4 30.6
North Carolina 49.0 26.8 26.8
Boston College 48.7 34.8 29.7
Virginia 48.6 33.8 42.3
Florida State 45.9 35.6 26.9
Virginia Tech 45.9 42.4 19.6
Miami 45.4 36.8 30.9
Maryland 43.4 31.0 24.6


Effective FG%

Georgia Tech 60.8
Duke 57.5
NC State 56.4
Clemson 53.2
Wake Forest 51.9
League Average 51.3
Boston College 49.8
Virginia 49.5
Virginia Tech 49.4
Miami 48.4
Florida State 47.9
North Carolina 46.7
Maryland 44.2


Opponents' Effective FG%

Virginia 42.8
Maryland 46.9
Miami 48.3
North Carolina 48.9
Boston College 49.2
Virginia Tech 51.2
League Average 51.3
NC State 52.0
Georgia Tech 52.1
Duke 54.1
Florida State 54.7
Wake Forest 55.0
Clemson 60.3


Offensive Efficiency (Pts Scored per 100 Possessions)

Georgia Tech 115.5
Clemson 114.1
Boston College 112.9
North Carolina 112.6
League Average 105.9
Virginia Tech 105.2
Miami 104.7
Duke 104.3
NC State 103.8
Wake Forest 99.0
Maryland 98.2
Virginia 98.0
Florida State 97.2


Defensive Efficiency (Pts Allowed per 100 Possessions)

Boston College 97.7
North Carolina 98.4
Duke 98.7
Virginia Tech 100.1
Virginia 102.2
Maryland 103.7
League Average 105.9
Wake Forest 107.7
Miami 108.8
Clemson 110.5
NC State 111.4
Georgia Tech 112.4
Florida State 114.2


Efficiency Margin (Off Eff - Def Eff)

Boston College 15.2
North Carolina 14.2
Duke 5.6
Virginia Tech 5.1
Clemson 3.6
Georgia Tech 3.1
Miami -4.1
Virginia -4.2
Maryland -5.5
NC State -7.6
Wake Forest -8.7
Florida State -17.0


Turnover Percentage

Virginia Tech 13.1
North Carolina 16.6
Clemson 16.9
Miami 19.4
NC State 20.2
Boston College 20.5
League Average 20.9
Virginia 21.5
Wake Forest 22.6
Florida State 23.8
Maryland 23.8
Georgia Tech 25.7
Duke 26.4


Opponents' Turnover Percentage

Clemson 27.3
Virginia Tech 24.8
Duke 23.0
Wake Forest 21.5
Florida State 21.4
League Average 20.9
Maryland 20.5
Boston College 20.5
Miami 19.8
Georgia Tech 19.6
NC State 18.8
North Carolina 17.9
Virginia 14.5


Offensive Rebounding Percentage

North Carolina 45.9
Boston College 43.1
Clemson 42.1
Maryland 38.6
Georgia Tech 37.9
Miami 35.9
Florida State 35.7
League Average 35.6
Virginia 32.8
Wake Forest 32.4
Duke 28.9
Virginia Tech 25.5
NC State 21.2 (Rebounds are overrated anyway...)


Defensive Rebounding Percentage

Duke 79.1
North Carolina 72.7
Wake Forest 69.7
Boston College 69.5
Virginia 68.7
League Average 64.4
Virginia Tech 63.0
Miami 62.6
Clemson 61.6
Georgia Tech 60.4
Florida State 58.2
NC State 57.6 (I'm telling you. Overrated. Please, take them all, [Opponent].)
Maryland 54.4

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