The Arc of Champions (or who's gonna win it all)

[fasbjd]

There are many analytical ways to evaluate sports teams.  One way in basketball is to look a the number of points the offense scores per 100 possessions versus the number the defense gives up (offensive and defensive efficiencies) which can then be adjusted to the strength of the opponent.  You can use the numbers to come up with a differential or you can chart them on a graph.  When graphed with adjusted offensive efficiency (aOE) on the horizontal axis and adjusted defensive efficiency (aDE) on the vertical one, you get a graph in which the closer you are to the lower right corner, the better your team is as a whole.  Wonk nerds have made such charts, plotted past NCAA champions, and have found a strong clustering of champion teams within an arc on the bottom right of the chart (what wonk Andy Wittry called the Championship Arc).  In the chart below, this area is represented by the yellow with champions since '02 represented by golden triangles.  As can be seen, there are a few outliers ('03 Syracuse who rode 'Melo to the title, '11 UConn who did the same with Kemba, and '14 UConn who won it all as a 7 seed).  These represent ~15% of the winners but a large majority fall within the arc.  

With this knowledge, I graphed the current position of the top 25 teams (plus our Hoosiers) to see how they stack up (if you're interested in how past Hoosier teams stack up, I will be doing a chart of them in the knowledgebase soon).   A few observations:

• There are two clear favorites, one a little surprising.  No one, I think, will be surprised to see Gonzaga in a prime position but Houston clearly has a team that looks capable of making a push.  
• Just outside the periphery lies some expected contenders in Duke, Baylor, and Arizona.  
• The closest Big10 contenders (Purdue, Iowa [both troubled by suboptimal defenses] and Illinois [better defense, suboptimal offense]) form their own arc well outside the contention area.  
• Indiana's defense is strong enough to fall within the Championship Arc...if their offense was ~7.8 points better per game.

 

[BruceDouglas]

Houston's analytics are a little suspect as they lost 2 of their best players midway through the season. Credit to them for continuing to play well but given they are in a weaker league I'm not so sure they are a real contender. It's unlikely they will get a protected seed which will also make their path tougher.

Edited March 5, 2022 by BruceDouglas

[fasbjd]

2 hours ago, BruceDouglas said:

Houston's analytics are a little suspect as they lost 2 of their best players midway through the season. Credit to them for continuing to play well but given they are in a weaker league I'm not so sure they are a real contender. It's unlikely they will get a protected seed which will also make their path tougher.

Good point - I looked at their numbers following the loss of Mark and Sasser and they are a little worse (aOE from 118.2 to 117.4 and aDE from 89.4 to 90.3).  The "adjustment" in the efficiency score is meant to account for the strengths/weakness of their opponent.  Below shows where their position shifts to in games missing those guys - laying right on the arc and still in second best position.

 

Edited March 5, 2022 by fasbjd

[fasbjd]

Added results heading into conference tournaments.  Also tweaked the graph so that the NCAA champion's positions represent their standing prior to the NCAA tourney (parred it down to the '08 to present due to data availability).  With these changes, an additional (injury-ridden) team ,Baylor, is poised right on the arc with Arizona just outside.

 

I looked at the sets of teams that fell within the Arc since 2008, some thoughts:

 

• A total of 71 teams in the 13 represented tourneys fell within the Arc - Indiana was present once, 2013

   

• Of the 71 Arc teams: 
  15.5% won it all
  22.5% made the finals
  36.6% made the Final Four
  62% made the Elite Eight
  80.3% made the Sweet Sixteen
  97.2% made the round of 32

   

• If this year stands as it is with only 3 Arc teams, it would tie for the least amount of Arc teams for a season with '21 (all three went to the Final Four) and '14 (when 7 seed UConn won it all)

   

• '09 had the most Arc teams in the tournament at 9, including champion Duke, runner-up Wisconsin, and Final Four participant Kentucky

   

• Seasonal stats for Arc Teams: 
  Most Final Four teams: 4 ('08)
  Least Final Four teams: 1 ('18, '16, '13, '14, '11)
  Most Elite Eight teams: 5 ('19, '12)
  Least Elite Eight teams: 2 ('18, '14)
  Most Sweet Sixteen teams: 7 ('19, '15)
  Least Sweet Sixteen teams: 3 ('21, '18, '16, '14)

 

Edited March 7, 2022 by fasbjd

[5fouls]

I absolutely love this stuff.  Thank you for bringing it to the board.

[KoB2011]

2 hours ago, fasbjd said:

Added results heading into conference tournaments.  Also tweaked the graph so that the NCAA champion's positions represent their standing prior to the NCAA tourney (parred it down to the '08 to present due to data availability).  With these changes, an additional (injury-ridden) team ,Baylor, is poised right on the arc with Arizona just outside.

 

I looked at the sets of teams that fell within the Arc since 2008, some thoughts:

 

• A total of 71 teams in the 13 represented tourneys fell within the Arc - Indiana was present once, 2013

   

• Of the 71 Arc teams: 
  15.5% won it all
  22.5% made the finals
  36.6% made the Final Four
  62% made the Elite Eight
  80.3% made the Sweet Sixteen
  97.2% made the round of 32

   

• If this year stands as it is with only 3 Arc teams, it would tie for the least amount of Arc teams for a season with '21 (all three went to the Final Four) and '14 (when 7 seed UConn won it all)

   

• '09 had the most Arc teams in the tournament at 9, including champion Duke, runner-up Wisconsin, and Final Four participant Kentucky

   

• Seasonal stats for Arc Teams: 
  Most Final Four teams: 4 ('08)
  Least Final Four teams: 1 ('18, '16, '13, '14, '11)
  Most Elite Eight teams: 5 ('19, '12)
  Least Elite Eight teams: 2 ('18, '14)
  Most Sweet Sixteen teams: 7 ('19, '15)
  Least Sweet Sixteen teams: 3 ('21, '18, '16, '14)

 

This is really fascinating, and I’m saying this knowing full well the team I think will win it all isn’t on the arc, but it also highlights why I think people are wrong when they talk about how deep the field of potential champions are this year.

I think the reason the top 10-20 seems so deep is that most of them are so flawed so there isn’t much separation but I do think a few teams stand out at the top. It’ll be fascinating to see where things end up as we revisit this throughout conference and then NCAA tournaments. 

[Bustout]

This is awesome - but is Houston a bit misleading since they really haven’t beaten anyone?  

[5fouls]

1 hour ago, Bustout said:

This is awesome - but is Houston a bit misleading since they really haven’t beaten anyone?  

Pretty sure the Effeciency Ratings factor in strength of opponent.  

What it tells me is it makes sense we were able to beat Purdue and Ohio State.  Despite being weaker offensively, we were much stronger defensively.  Also helps explain why we should/could have beat Wisky.  They have an advantage offensively, but we have a very similar advantage defensively.

It also points as to how tough Illinois would be for us if we did beat Michigan.  They are the B1G team closest to the arc.

[fasbjd]

On 3/8/2022 at 10:44 AM, Bustout said:

This is awesome - but is Houston a bit misleading since they really haven’t beaten anyone?  

As 5Fouls alluded to, these efficiencies are adjusted according to the competition. 

To give an example, for our game versus Purdue, we gave up 69 points and scored 67 points on a 65 possession game.  That would equal an Offensive Efficiency of 103 and Defensive Efficiency of 106.  But, Purdue has the most efficient offense in the country and a middling defense.  For that game, our adjusted Defensive Efficiency was 88.5 and adjusted Offensive Efficiency was only slightly altered at 106.3.  For Purdue, the opposite is true.  Their Offensive Efficiency was 106 and Defensive Efficiency was 103.  But IU is a significantly better defensive team than offensive team.  So their adjusted Offensive Efficiency for that game had a significant bump to 119.3 (still on the lower end for them) and adjusted Defensive Efficiency saw a less significant change to 97.1.

[Proud2BAHoosier]

On 3/7/2022 at 3:37 PM, 5fouls said:

I absolutely love this stuff.  Thank you for bringing it to the board.

Makes my head hurt....  🤪

[Bustout]

10 hours ago, fasbjd said:

As 5Fouls alluded to, these efficiencies are adjusted according to the competition. 

To give an example, for our game versus Purdue, we gave up 69 points and scored 67 points on a 65 possession game.  That would equal an Offensive Efficiency of 103 and Defensive Efficiency of 106.  But, Purdue has the most efficient offense in the country and a middling defense.  For that game, our adjusted Defensive Efficiency was 88.5 and adjusted Offensive Efficiency was only slightly altered at 106.3.  For Purdue, the opposite is true.  Their Offensive Efficiency was 106 and Defensive Efficiency was 103.  But IU is a significantly better defensive team than offensive team.  So their adjusted Offensive Efficiency for that game had a significant bump to 119.3 (still on the lower end for them) and adjusted Defensive Efficiency saw a less significant change to 97.1.

Got it.  Thanks!

[5fouls]

@fasbjd

I'm curious as to whether you will be able to make one of these for the full field once it is announced?  

Thanks!

[fasbjd]

That’s the plan.  I’ve been populating one w/ teams that are in / likely in and let’s just say, it’s very busy in the area around / above where IU falls.

[fasbjd]

Here is the graph with all 68 teams - obviously very busy but some key developments:

1.  Following adjustments for conference tourney - there are now 4 teams in or at the Arc (Zags, Houston, Kansas, Baylor) with Arizona just outside.

2. Outside those 5 teams, there is a strong grouping of 4 more teams as the 2nd tier (Duke, UK, 'Nova, UCLA)

 

 

Here's a graph highlighting IU, Wyoming, and St Mary's.  IU and St Mary's appear pretty closely matched (advantage Gaels) with Wyoming as the outlier

All three teams are relatively evenly matched offensively (all within ~1 point): St Mary's 109.3, Wyoming 108.9, IU 108.2

Defensively is where we see the separation:  St.Mary's and IU are within 1 point from each other (St.Mary's 89.9 vs IU 90.9) where Wyoming is 6-7 points worse (97.4)

 

 

Edited March 14, 2022 by fasbjd

[SawatchHoosier]

Looking at the numbers it appears the committee valued Offensive Efficiency more than Defensive efficiency for at large teams.

Edited March 14, 2022 by SawatchHoosier

[fasbjd]

Another interesting take on this graph:  

Below you will find the pre-tourney aOE X aDE positions of the Final Four participants since 2008 (gold diamonds = champions, silver diamonds = runner-ups, bronze diamonds = other Final Four teams).  With these teams, a new arc can be formed that would encompass over 94% of the Final Four teams since '08:

Now here is this Arc added to the current crop of teams:

 

Interesting group of teams, isn't it!  25-26 teams, including our Hoosiers, fall within the Arc (+/- Loyola Chicago).  Bear in mind that over the 13 seasons compiled, there have been a LOT of teams that fall within this range so being in it doesn't mean you are likely to make the Final Four (for instance, Oklahoma falls right on the Arc and they are definitely not going to the Final Four)...but being outside does mean you are quite unlikely to do so (<6% chance)...so I'd prefer to be in it!  More food for thought.

 

 

Edited March 14, 2022 by fasbjd

[5fouls]

6 hours ago, fasbjd said:

Another interesting take on this graph:  

Below you will find the pre-tourney aOE X aDE positions of the Final Four participants since 2008 (gold diamonds = champions, silver diamonds = runner-ups, bronze diamonds = other Final Four teams).  With these teams, a new arc can be formed that would encompass over 94% of the Final Four teams since '08:

Now here is this Arc added to the current crop of teams:

 

Interesting group of teams, isn't it!  25-26 teams, including our Hoosiers, fall within the Arc (+/- Loyola Chicago).  Bear in mind that over the 13 seasons compiled, there have been a LOT of teams that fall within this range so being in it doesn't mean you are likely to make the Final Four (for instance, Oklahoma falls right on the Arc and they are definitely not going to the Final Four)...but being outside does mean you are quite unlikely to do so (<6% chance)...so I'd prefer to be in it!  More food for thought.

 

 

IU is in the Final Four Arc.  I like it!

[fasbjd]

One thing to notice from this graph is the differences defense makes in making the Final Four versus winning it all.  A punishing defense is enough to get a team into the Final Four despite a pedestrian offense - the dotted line on the left is the aOE of 100 mark.  This year there were 224 teams that had a aOE of at least that.  So the old adage is correct: defense does win championships - at least Regional championships.  However, no team has been able to win it all without an aOE of at least 112.6.  This year, that includes just 41 teams.

On the other hand, a potent offense does not have the same ability to, alone, take you to the Final Four - there just aren't teams sitting above the Champions Arc.  Except for VCU in 2011, no team since '08 has made the Final Four with a pre-tourney aDE greater than 96.6 (by the way, VCU played amazing defense during the tourney) - which is about the top 1/3 defensive teams this year.  Villanova in '18 was able to wean it all with an aDE of 95.2 - this year that limits it to the top 42 teams.

The take-away is that to get into the Final Four, you need a top third defense - with the best defenses overcoming even relatively bad offenses.  But only teams that are in the top 10-12% in both, have a realistic chance at winning it all.

 

Edited March 15, 2022 by fasbjd

[5fouls]

Who are the two Champions sitting outside the main Arc?

[fasbjd]

2 minutes ago, 5fouls said:

Who are the two Champions sitting outside the main Arc?

They are both UConn - '11 with Kemba and '14 who won it as a 7 seed

[CincyHoosier]

On 3/7/2022 at 4:33 PM, fasbjd said:

Added results heading into conference tournaments.  Also tweaked the graph so that the NCAA champion's positions represent their standing prior to the NCAA tourney (parred it down to the '08 to present due to data availability).  With these changes, an additional (injury-ridden) team ,Baylor, is poised right on the arc with Arizona just outside.

 

I looked at the sets of teams that fell within the Arc since 2008, some thoughts:

 

• A total of 71 teams in the 13 represented tourneys fell within the Arc - Indiana was present once, 2013

   

• Of the 71 Arc teams: 
  15.5% won it all
  22.5% made the finals
  36.6% made the Final Four
  62% made the Elite Eight
  80.3% made the Sweet Sixteen
  97.2% made the round of 32

   

• If this year stands as it is with only 3 Arc teams, it would tie for the least amount of Arc teams for a season with '21 (all three went to the Final Four) and '14 (when 7 seed UConn won it all)

   

• '09 had the most Arc teams in the tournament at 9, including champion Duke, runner-up Wisconsin, and Final Four participant Kentucky

   

• Seasonal stats for Arc Teams: 
  Most Final Four teams: 4 ('08)
  Least Final Four teams: 1 ('18, '16, '13, '14, '11)
  Most Elite Eight teams: 5 ('19, '12)
  Least Elite Eight teams: 2 ('18, '14)
  Most Sweet Sixteen teams: 7 ('19, '15)
  Least Sweet Sixteen teams: 3 ('21, '18, '16, '14)

 

With less teams inside the arc (and the ones that are right on the border except Zags) you could argue it makes the field more wide open. 

[fasbjd]

On 3/15/2022 at 11:32 AM, fasbjd said:

One thing to notice from this graph is the differences defense makes in making the Final Four versus winning it all.  A punishing defense is enough to get a team into the Final Four despite a pedestrian offense - the dotted line on the left is the aOE of 100 mark.  This year there were 224 teams that had a aOE of at least that.  So the old adage is correct: defense does win championships - at least Regional championships.  However, no team has been able to win it all without an aOE of at least 112.6.  This year, that includes just 41 teams.

On the other hand, a potent offense does not have the same ability to, alone, take you to the Final Four - there just aren't teams sitting above the Champions Arc.  Except for VCU in 2011, no team since '08 has made the Final Four with a pre-tourney aDE greater than 96.6 (by the way, VCU played amazing defense during the tourney) - which is about the top 1/3 defensive teams this year.  Villanova in '18 was able to wean it all with an aDE of 95.2 - this year that limits it to the top 42 teams.

The take-away is that to get into the Final Four, you need a top third defense - with the best defenses overcoming even relatively bad offenses.  But only teams that are in the top 10-12% in both, have a realistic chance at winning it all.

 

Excuse the self quote, but I wanted to followup this thought with a little more robust data.  The above Final Four Arc includes teams with an aOE as low as 103.4 and teams with an aDE as high as 96.6.  In the Championship Arc, the lowest aOE is 112.6 and highest aDE 95.2.  

For the seasons '08-'22, an average of 145.6 teams/season (or 41.8%) had an aOE of 103.4 or better while only half that amount, 70.1 (20.1%) had an aDE of 96.6 or lower - in other words, defense alone eliminates over 80% of teams from Final Four contention.

For the same seasons, an average of only 30.6 (or 8%) had a championship-level aOE of 112.6 or better while 51.1 (14.6%) had an aDE of 95.2 or better - only a handful of teams have the offensive chops to win it all.

Now, most teams that make the Final Four are very strong on both sides of the ball, but not in equal proportions.  Of the Final Four teams, ~85% have a championship-level defense (aDE 95.2 or better) while ~73% have championship-level offense (aOE 112.6 or better) - essentially, an average of one Final Four team / season will fail to have an adequate offense to win it all.

It appears the lack of offensive punch is most greatly exposed in the championship game itself as a slightly higher percentage of inadequate offenses (28%) were able to advance to the finals versus percentage of inadequate defenses (25%) - essentially 3/4 of each will be eliminated though.

This information is probably too late to help with filling out the brackets, but I find fascinating nonetheless.

Edited March 16, 2022 by fasbjd

[BeerBQ]

Awesome work!

 

What are you using to build these?

[fasbjd]

1 hour ago, BeerBQ said:

Awesome work!

 

What are you using to build these?

The data comes from Bart Torvik’s site.  https://www.barttorvik.com/teamcast.php?&team=Indiana&year=2022

The graphs are made on good ‘ol Apple Numbers.

[Drroogh]

27 minutes ago, fasbjd said:

The data comes from Bart Torvik’s site.  https://www.barttorvik.com/teamcast.php?&team=Indiana&year=2022

The graphs are made on good ‘ol Apple Numbers.

So glad to have you back, come tourney time especially! Don't make yourself a stranger again!! Your analytics have always been appreciated! 

Not just your analytics though, but as a true Hoosier fan!

Edited March 16, 2022 by Drroogh