A Look at SOS and the ACCT

[pfrduke]

Since the advent of the unbalanced schedule, I've looked annually at how each team's schedule stacked up. One of the more unique aspects of the method I use is to treat the conference as if it had 24 teams, rather than 12; that is each team has a "home" and "away" version, and for the teams you play once, you only get credit for the version you play (so, for example, Duke played the "home" version of Wake and the "away" version of Boston College). So let's look at that information first (all numbers are in points per hundred possessions):

Home Team	Off	Def	Margin
Duke		109.13	88.51	20.62
Clemson		107.80	89.75	18.04
North Carolina	105.24	89.69	15.54
Florida State	105.36	91.29	14.07
Virginia Tech	113.80	102.87	10.93
Georgia Tech	95.52	88.13	7.39
Boston College	111.24	109.72	1.53
Miami		103.14	103.11	0.03
Maryland	108.59	109.68	-1.09
NC State	109.58	111.63	-2.05
Virginia	90.41	96.71	-6.31
Wake Forest	90.72	112.25	-21.54

Road Team	Off	Def	Margin
Duke		109.46	96.95	12.51
North Carolina	104.67	99.81	4.86
Maryland	99.19	96.90	2.29
Virginia Tech	98.56	98.30	0.25
Virginia	102.52	104.19	-1.67
Boston College	104.90	107.51	-2.61
Miami		103.77	108.55	-4.78
Clemson		97.08	102.29	-5.21
Florida State	92.89	98.82	-5.93
Georgia Tech	98.67	112.15	-13.48
NC State	96.35	109.90	-13.55
Wake Forest	85.93	116.24	-30.31

To no one's great surprise, almost everyone's better at home than on the road - in most cases by a healthy margin. Only three teams - Duke, UNC, and Virginia Tech - were better than their opponents both at home and away. Maryland and Virginia were actually better on the road than at home, and Duke's road performance deserves a healthy amount of credit - better outside of Cameron than more than half the ACC was in their own stadiums, while Clemson had the most disparate home/road results (for the second season in a row - apparently Brownell couldn't cure the Tigers' road woes). Also, these numbers underscore again just how bad Wake was - the Deacs were worse at home than any other team was on the road. Yikes.

The strength of schedule is derived from figuring out the collective offensive and defensive ratings of the 16 teams you played, with your own performance factored out (so Wake's schedule doesn't look harder because it stank, and Duke's easier because it dominated). I figured out both the offensive and defensive degree of difficulty for each team. The disparities may look small, but keep in mind that the teams averaged just shy of 1100 total possessions in ACC play this season, so a difference of 2.00 in margin is 22 points over the course of the season.

Opponent offenses, from toughest to weakest:

			Opp Off
Duke			103.57
Florida State		103.42
Virginia		103.16
Miami			102.83
Wake Forest		101.99
North Carolina		101.95
Georgia Tech		101.94
Clemson			101.47
Boston College		101.22
Virginia Tech		100.99
Maryland		100.00
NC State		99.89

Opponent defenses, from toughest to weakest

			Opp Def
NC State		99.54
North Carolina		99.60
Boston College		100.12
Miami			100.32
Maryland		101.19
Clemson			101.72
Virginia		102.41
Virginia Tech		102.58
Duke			102.75
Wake Forest		102.96
Georgia Tech		103.65
Florida State		103.87

These two performances come together to make the opponent's scoring margin. A perfectly average schedule would be zero - anything positive is tougher, and anything negative is easier:

			O Marg
Miami			2.51
North Carolina		2.35
Boston College		1.09
Duke			0.82
Virginia		0.75
NC State		0.34
Clemson			-0.25
Florida State		-0.45
Wake Forest		-0.97
Maryland		-1.19
Virginia Tech		-1.59
Georgia Tech		-1.70

Virginia Tech was the beneficiary of an easy schedule (although no one had anywhere near as easy a schedule as Wake and VT last year). The Hokies only had to take on Duke, UNC, Florida State, and Clemson once each (although to their credit, they went 2-2 in those games), and played Virginia, Maryland, Wake, and Georgia Tech (4 of the bottom 5 teams) twice. Miami and UNC, by contrast, had the season's toughest schedules - both had to double dip against Duke, Clemson, and FSU; Miami's schedule ended up tougher largely by virtue of playing Virginia Tech in Blacksburg, rather than in Chapel Hill. Some of these results are skewed by just how bad Wake was - the teams that doubled up against the Deacs were NC State, FSU, Maryland, Virginia Tech, and Georgia Tech, and only NC State (which played Duke and UNC twice) ended up in the top half of schedule difficulty. Of course, Wake meant an extra free win for all of these teams, so that's probably appropriate.

So with all of this information, we can adjust performance to see how the teams would have performed against an average schedule. The unadjusted performance looks like this:

			Margin
Duke			16.64
North Carolina		10.28
Clemson			6.42
Virginia Tech		5.66
Florida State		4.00
Maryland		0.67
Boston College		-0.50
Miami			-2.38
Georgia Tech		-3.06
Virginia		-3.92
NC State		-7.85
Wake Forest		-25.97

Adjusted, we get a bit of movement - BC and Miami leapfrog Maryland, and Virginia jumps Georgia Tech and NC State:

			Margin
Duke			17.46
North Carolina		12.63
Clemson			6.17
Virginia Tech		4.08
Florida State		3.55
Boston College		0.60
Miami			0.13
Maryland		-0.52
Virginia		-3.17
Georgia Tech		-4.77
NC State		-7.51
Wake Forest		-26.94

Finally, based on the adjusted performance of the teams this season, here are the tourney odds. Duke comes out as a strong favorite (not quite as strong as last year, but still a heavy favorite). This is a good time for the following reminder - statistically, Duke was almost as strong in conference as last year's team; statistically, this year's UNC team was almost as strong in conference as last year's Maryland team. The profiles at the top of the conference are extremely similar this year to last year.

			Quarters Semis	Finals	Win
2  Duke			100.00%	93.85%	82.33%	60.50%
1  North Carolina	100.00%	87.00%	65.19%	26.82%
4  Clemson		100.00%	69.48%	24.20%	5.96%
3  Florida State	100.00%	55.49%	8.84%	2.77%
6  Virginia Tech	77.47%	39.32%	6.40%	2.04%
5  Boston College	97.91%	30.50%	6.34%	0.90%
9  Miami		61.58%	9.20%	3.28%	0.45%
7  Maryland		71.00%	5.24%	1.93%	0.38%
8  Virginia		38.42%	3.80%	0.98%	0.09%
11 Georgia Tech		22.53%	5.19%	0.32%	0.04%
10 NC State		29.00%	0.91%	0.18%	0.02%
12 Wake Forest		2.09%	0.02%	0.00%	0.00%

A couple thoughts. First, the odds are about 75% that one of Duke or UNC will be playing on Sunday, and 50% that both will match up. Duke's numbers are better than UNC's for a couple of reasons - first, because Duke played better in conference, and second, because Clemson and Miami are better statistically than their records - Clemson's a 3-seed that ended up 4th, and Miami is a 7-seed that ended up 9th. Both present above-seed threats to UNC. Also, five teams have essentially the same (or better) chance of winning the whole thing as Wake does of beating BC - they were really, really bad this year.

Finally, this will almost certainly be different from whatever odds Pomeroy runs later this week, because this takes into consideration only ACC play, while his will factor in non-conference games. Duke will still end up as a favorite, but it will be lower - my bet is that we'll end up with about a 50% chance of winning it all, Carolina between 25-30%, and everyone else scattered at 7% or lower.

[MChambers]

Thanks for doing this. It tends to confirm what I suspected. Hope it is borne out by the results in the tournament.

[kong123]

So, Kenpom says that Duke had the 10th toughest conference schedule out of 12 teams and you found a way to prove him wrong with his own numbers?

[hurleyfor3]

How did you compute the initial home/road breakdowns for each team? By hand? I don't see a way to get this info on Pom's Web site.

The strength of schedule is derived from figuring out the collective offensive and defensive ratings of the 16 teams you played, with your own performance factored out (so Wake's schedule doesn't look harder because it stank, and Duke's easier because it dominated). I figured out both the offensive and defensive degree of difficulty for each team. The disparities may look small, but keep in mind that the teams averaged just shy of 1100 total possessions in ACC play this season, so a difference of 2.00 in margin is 22 points over the course of the season.

So, for example, the rating for the "home Virginia Tech" doesn't include its victory over us when you compute our SOS -- you use only VPI's seven non-Duke home conference games. Right?

			O Marg
Miami			2.51
North Carolina		2.35
Boston College		1.09
Duke			0.82
Virginia		0.75
NC State		0.34
Clemson			-0.25
Florida State		-0.45
Wake Forest		-0.97
Maryland		-1.19
Virginia Tech		-1.59
Georgia Tech		-1.70

I generally suspect SOS is slightly negatively correlated within a conference, as Duke doesn't have to play Duke, and Wake doesn't get to play Wake. But as long as you adjusted for opponents' performance against yourself, I can't think of a reason to quibble (yet).

So, Kenpom says that Duke had the 10th toughest conference schedule out of 12 teams and you found a way to prove him wrong with his own numbers?

I think Pom's conference SOS numbers use the overall ratings of each conference opponent. I would guess Duke's rating here suffers because the rest of the ACC doesn't have a whole lot of good nonconference wins, whereas we do.

[JohnGalt]

So, Kenpom says that Duke had the 10th toughest conference schedule out of 12 teams and you found a way to prove him wrong with his own numbers?

10th of 12th is, perhaps, a result of not having to play themselves?

[kong123]

same could be said for UNC.

[pfrduke]

So, Kenpom says that Duke had the 10th toughest conference schedule out of 12 teams and you found a way to prove him wrong with his own numbers?

I'm not using his numbers, I'm using mine. They differ in three respects - first, I don't adjust for opponent; he does. That is, he uses an "adjusted" offensive and defensive efficiency that takes into account strength of schedule, I don't (because I'm not mathematically savvy enough to do it). Second, as I described in my initial post, I split the conference into 24 teams, rather than 12 - a home and road version of each team. So if you only play FSU in Tallahassee, for example, only FSU's performance as a home team is factored in to your strength of schedule. Third, I suspect (although am not certain) that his strength of schedule uses season long performance by the teams, including non-conference games, while mine uses in-conference performance only.

I'm sure my method is subject to criticism. Pomeroy's is, too - frankly, the fact that he has UNC with only the 6th toughest schedule in conference just seems wrong when, as you and I have both pointed out, they had to face Duke, FSU, and Clemson twice.

[pfrduke]

How did you compute the initial home/road breakdowns for each team? By hand? I don't see a way to get this info on Pom's Web site.

I keep track on my own throughout the season. It's my stat geek guilty pleasure. So I can break it down into home and away. The baseline method for calculating efficiency is the same. That being said, you could mine similar data from Pomeroy's site by pulling it from the team's Game Plan pages. There would be a fair amount of manual work involved, but the necessary information is there.

So, for example, the rating for the "home Virginia Tech" doesn't include its victory over us when you compute our SOS -- you use only VPI's seven non-Duke home conference games. Right?

Essentially, yes, although I do it cumulatively (that is, the opponent's performance in all 8 games (either home or road) go in to the mix, all 16 opponents' performances get added up, and then Duke's (for example) gets subtracted out). That's probably not a perfect way to do it - there should be some way to weigh the team's performance even in the games you play against them, but I'm not quite mathematically savvy enough to figure out how to do it.

[sandinmyshoes]

I'm not using his numbers, I'm using mine. They differ in three respects - first, I don't adjust for opponent; he does. That is, he uses an "adjusted" offensive and defensive efficiency that takes into account strength of schedule, I don't (because I'm not mathematically savvy enough to do it). Second, as I described in my initial post, I split the conference into 24 teams, rather than 12 - a home and road version of each team. So if you only play FSU in Tallahassee, for example, only FSU's performance as a home team is factored in to your strength of schedule. Third, I suspect (although am not certain) that his strength of schedule uses season long performance by the teams, including non-conference games, while mine uses in-conference performance only.

I'm sure my method is subject to criticism. Pomeroy's is, too - frankly, the fact that he has UNC with only the 6th toughest schedule in conference just seems wrong when, as you and I have both pointed out, they had to face Duke, FSU, and Clemson twice.

Thanks for all the info! As you say, most mathematical models are going to have weaknesses in this sort of thing. As noted, UNC didn't face FSU at FSU with their best player. On the otherhand, taking season's worth of games to project a tourney often fails to take into consideration how teams are "trending" right now, which I have to admit UNC is trending up. Never mind the good ol' human element that carried UVA to a title in 76.

But it's fun to have all these different angles to check out for curiosities sake.

[Kedsy]

Wow, thanks, this is so cool.

Interesting that the conference defenses we faced were the fourth worst. Obviously one reason for this is we don't face our own defense, but it still means that maybe our offense hasn't been tested so much.

[pfrduke]

Finally, this will almost certainly be different from whatever odds Pomeroy runs later this week, because this takes into consideration only ACC play, while his will factor in non-conference games. Duke will still end up as a favorite, but it will be lower - my bet is that we'll end up with about a 50% chance of winning it all, Carolina between 25-30%, and everyone else scattered at 7% or lower.

Pomeroy's are up on Basketball Prospectus, and as predicted, Duke is given a 54.5% chance of winning and Carolina a 30.5% chance of winning. As far as the rest of the conference shakes out, Maryland scores higher than BC and Miami in Pomeroy's odds, while Virginia checks in below Georgia Tech and NC State, but otherwise the order is the same.

[Reilly]

If I read the chart up above correctly:

pfr acc-only #'s give Duke a 60% of winning it all; UNC a 26% chance.
kenpom's #'s give Duke a 54% chance of winning it all; UNC a 31% chance.

Intuitively, just looking at the brackets, I like Duke's chances a bit better than UNC's chances, if I were to assign odds myself, but not to the tune of the disparity that either set of computer-generated numbers produces.

pfr, curious as to what your non-computer (but still analytic) sense is. That is, do you like Duke's chances better than UNC's? To the degree that the computers say?

[pfrduke]

If I read the chart up above correctly:

pfr acc-only #'s give Duke a 60% of winning it all; UNC a 26% chance.
kenpom's #'s give Duke a 54% chance of winning it all; UNC a 31% chance.

Intuitively, just looking at the brackets, I like Duke's chances a bit better than UNC's chances, if I were to assign odds myself, but not to the tune of the disparity that either set of computer-generated numbers produces.

pfr, curious as to what your non-computer (but still analytic) sense is. That is, do you like Duke's chances better than UNC's? To the degree that the computers say?

I think I end up in the same boat as you do - I like Duke's chances better than UNC's, both because I do think Duke is better at the end of the day and because I like our road better than Carolina's - I think they'll likely be playing a better team than we will at every round of the tournament. There's also something to be said for the mindset difference, given Carolina's disregard for the ACCT as compared to K's burning desire to win every tournament he's in - that counts for something in the earlier rounds, although I'm not sure it would be any factor in a Duke-UNC final. I'm not sure I'm quite as gungho on our chances as my numbers say, but mostly because I don't think we're as heavy a favorite in a Duke-UNC matchup as the numbers would predict. But Pomeroy's seem reasonable - calling the ACC championship a slightly better than 50/50 proposition for Duke seems about right, given that I do think we're very likely to make the finals, Carolina is less likely than us to make the finals, and we're more likely than not to beat UNC if we play each other.

I will say that part of my confidence comes from a firm belief that Kyle Singler won't keep playing this poorly on offense - that he's having a blip, and that he'll regress to his mean (regression in this case resulting in an improvement in play). If Kyle continues as he's going, I think our odds would drop below 50%, and there's a more meaningful chance that, for example, a hungry/desperate Virginia Tech team beats us in the semis.

[WakeDevil]

What are the odds that people will learn the difference between effectiveness and efficiency?

[ikiru36]

This analysis is awesome and probably provides as close to an accurate depiction of team strength based on an entire ACC unbalanced season's performance as is possible statistically. I'd also love for it to be proven accurate as a predictive device! :0)

Nevertheless, some teams are clearly playing much better ball now (UNC being an obviously prime example) than they were earlier in the year. Also, I don't think Duke has been quite as dominant in the last month as they were earlier. I would want recent performance weighted somehow before feeling that the model was likely to predict the tournament results with ideal accuracy.

Re: UNC, they seem particularly difficult to predict as their improved play of late has still included a number of so-so games in which they just squeaked by relatively lesser opponents (Clem, FSU and BC, all 2 pt. wins during February). Duke, by comparison, has been far more dominant in their winning efforts throughout the ACC season. Also, the recent Bullock injury, while not dramatically affecting their primary rotation, further reduces their backcourt depth which could be a negative during a game-a-day tournament.

In Duke's case, there's clearly been some improvement from many on the team over the course of the season. If that were maintained (Seth Curry's improvement in conjunction with Mason's consistent rebounding and flashes of quality play from Ryan and Miles) and Kyle were to simply recover his shooting stroke, Duke immediately becomes borderline-Elite again, even without KI. That's without even mentioning what Andre Dawkins could add if able to maximize his strengths and play closer to his seeming capabilities. Still that's a lot of "ifs" and that's why they play the games.

In any event, thanks again for sharing all the hard work you've done!

Go Duke!!!!!!!!!!!!! Go Blue Devils!!!!!!!!!!!!!!!!!!! GTHCGTH!!!!!!!!!!!!!!!!!!!!

[DukieinSoCal]

This analysis is awesome and probably provides as close to an accurate depiction of team strength based on an entire ACC unbalanced season's performance as is possible statistically. I'd also love for it to be proven accurate as a predictive device! :0)

Nevertheless, some teams are clearly playing much better ball now (UNC being an obviously prime example) than they were earlier in the year. Also, I don't think Duke has been quite as dominant in the last month as they were earlier. I would want recent performance weighted somehow before feeling that the model was likely to predict the tournament results with ideal accuracy.

Re: UNC, they seem particularly difficult to predict as their improved play of late has still included a number of so-so games in which they just squeaked by relatively lesser opponents (Clem, FSU and BC, all 2 pt. wins during February). Duke, by comparison, has been far more dominant in their winning efforts throughout the ACC season. Also, the recent Bullock injury, while not dramatically affecting their primary rotation, further reduces their backcourt depth which could be a negative during a game-a-day tournament.

In Duke's case, there's clearly been some improvement from many on the team over the course of the season. If that were maintained (Seth Curry's improvement in conjunction with Mason's consistent rebounding and flashes of quality play from Ryan and Miles) and Kyle were to simply recover his shooting stroke, Duke immediately becomes borderline-Elite again, even without KI. That's without even mentioning what Andre Dawkins could add if able to maximize his strengths and play closer to his seeming capabilities. Still that's a lot of "ifs" and that's why they play the games.

In any event, thanks again for sharing all the hard work you've done!

Go Duke!!!!!!!!!!!!! Go Blue Devils!!!!!!!!!!!!!!!!!!! GTHCGTH!!!!!!!!!!!!!!!!!!!!

Good points. And FSU likely would have beaten UNC with a healthy Singleton, like we had to face. There's no way to factor in important injuries with these stats. You could probably even make a stronger case for Duke.

And our superior numbers on the road compared to UNC is likely due to the experience on our roster compared to relative youth of UNC. I wouldn't be surprised to see UNC struggle away from home, ie. in the ACC and NCCAT.

[rasputin]

What are the odds that people will learn the difference between effectiveness and efficiency?

The same as the odds that people will learn the difference between irony and coincidence.

[kong123]

Good points. And FSU likely would have beaten UNC with a healthy Singleton, like we had to face. There's no way to factor in important injuries with these stats. You could probably even make a stronger case for Duke.

And our superior numbers on the road compared to UNC is likely due to the experience on our roster compared to relative youth of UNC. I wouldn't be surprised to see UNC struggle away from home, ie. in the ACC and NCCAT.

UNC lost 2 ACC games away from home this year and Duke lost 3 ACC games away from home.

[rsvman]

UNC lost 2 ACC games away from home this year and Duke lost 3 ACC games away from home.

Yes, but they required a last-second shot to win against a Florida State team that was without its best player. The argument here is that they would likely have lost they game had Singleton not been out with an injury. Obviously, that's not a certainty, and anything could've happened.

[ns7]

UNC lost 2 ACC games away from home this year and Duke lost 3 ACC games away from home.

Duke's efficiency margin on the road was significantly better than UNC's margin. Please read the first post.

Road Team	Off	Def	Margin
Duke		109.46	96.95	12.51
North Carolina	104.67	99.81	4.86