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

[fasbjd]

An additional thought or two:

 

Based on the above analysis, you can predict with over 85% confidence that the Final Four will be built from these 26 teams (all within the Final Four Arc):

Arizona, Arkansas, Auburn, Baylor, Boise St, Duke, Gonzaga, Houston, Illinois, Indiana, Iowa, Kansas, Kentucky, LSU, Memphis, Purdue, San Francisco, St. Mary's, Tennessee, Texas, Texas Tech, UCLA, UNC, Villanova, Virginia Tech, and Wisconsin.

 

Also with at least 85% confidence, you can predict the Finals will be made up of a combination of these 12 teams (championship-level aDE and aOE):

Arizona, Auburn, Baylor, Duke, Gonzaga, Houston, Illinois, Kansas, Kentucky, UCLA, UConn, and Villanova.

 

Finally, you can predict with 85% confidence that the national champion will come from these 4 teams (all within the Arc of Champions):

Baylor, Gonzaga, Houston, and Kansas.

 

Applying these to the brackets, this is what you find for each Region:

 

West:

Championship-grade team:

1. Gonzaga

 

Finals-grade teams:

1. Gonzaga

2. Duke

3. UConn

 

Final Four-grade teams:

1. Gonzaga

2. Duke

3. UConn

4. Arkansas

5. Boise State

6. Memphis

7. Texas Tech

 

East:

Championship-grade team:

1. Baylor

 

Finals-grade teams:

1. Baylor

2. Kentucky

3. UCLA

 

Final Four-grade teams:

1. Baylor

2. Kentucky

3. UCLA

4. Indiana

5. Purdue

6. San Francisco

7. St. Mary's

8. Texas

9. Virginia Tech

 

South:

Championship-grade team:

1. Houston

 

Finals-grade teams:

1. Houston

2. Arizona

3. Illinois

4. Villanova

 

Final Four-grade teams:

1. Houston

2. Arizona

3. Illinois

4. Villanova

5. Tennessee

 

Midwest:

Championship-grade team:

1. Kansas

 

Finals-grade teams:

1. Kansas

2. Auburn

 

Final Four-grade teams:

1. Kansas

2. Auburn

3. Iowa

4. LSU

5. Wisconsin

 

 

Looking at this, the East seems to be the deepest Region by far (lucky us!).  1 of the Sweet Sixteen teams from the East would have come from a 4-team grouping that included 2 FF-grade teams while 2 others (including IU's grouping) will have included 3 (in our case: IU, St.Mary's, and UCLA).  There is only 1 other grouping in all the bracket that has 3 FF-grade teams - interesting enough it is Gonzaga's which also includes Memphis and Boise State.  The West, South, and Midwest each have 1 additional grouping that includes 2 FF-grade teams.   All other 4-team groupings include only 1 FF-grade team.

The South Region looks to be the most top heavy with 4 Finals-grade teams.  Unfortunately for 1 seed Arizona, to reach the Elite Eight, they will be going through an 8-team grouping that includes 3 of them (Arizona, Houston, and Illinois).  The only other groupings in all the bracket that includes more than 1 Finals-grade team is the one the includes Indiana (Baylor and UCLA) and Gonzaga (Gonzaga and UConn).

Lace 'em up tightly, looks like it's gonna be a bumpy ride!

Edited March 21, 2022 by fasbjd

[5fouls]

1 hour ago, fasbjd said:

 

Final Four quality teams:

1. Baylor

2. Kentucky

3. UCLA

4. Indiana

5. San Francisco

6. St. Mary's

7. Texas

8. Purdue

9. UNC

10. Virginia Tech

 

Are these ranked in order?  🙂

[fasbjd]

They are listed alphabetically in each category with teams from the category above placed at the beginning of each new list.

 

As an aside, I changed the term from "Final Four-quality" to "Final Four-grade" since I didn't want to imply that I thought those 26 teams were necessarily the best 26 teams in the field.  These metrics don't directly take into account Wins/Losses which is why there can be such a discrepancy in seeding and these metrics.  For instance, IU's close losses to quality opponents can bolster their standing in these metrics but ultimately don't win you high seeds or championships.  It does, however, unveil the potential of the team to have success.  Those the term change.

[fasbjd]

Here is a Sweet Sixteen update of the Arcs graph with teams broken up by color according to their region:

 

One note of correction from the original graph - I had UNC and UConn labelled incorrectly.  Now in their correct position UNC sits just outside the FF arc.  Note also that these continue to reflect their pre-NCCA tourney stats.

As it stands currently, here's how the Regions sit:

 

West:

Championship-grade team:

1. Gonzaga

 

Finals-grade teams:

1. Gonzaga

2. Duke

 

Final Four-grade teams:

1. Gonzaga

2. Duke

3. Arkansas

4. Texas Tech

 

 

East:

Championship-grade team:

1. None

 

Finals-grade teams:

1. UCLA

 

Final Four-grade teams:

1. UCLA

2. Purdue

 

 

South:

Championship-grade team:

1. Houston

 

Finals-grade teams:

1. Houston

2. Arizona

3. Villanova

 

Final Four-grade teams:

1. Houston

2. Arizona

3. Villanova

 

 

Midwest:

Championship-grade team:

1. Kansas

 

Finals-grade teams:

1. Kansas

 

Final Four-grade teams:

1. Kansas

 

The West looks like the deepest region with all 4 teams FF-grade or better and the South remains the most top-heavy with 3 remaining Finals-grade teams.   In the East, of the 9 available FF-grade teams, only 2 advanced to the Sweet Sixteen and they no longer have a Championship-grade team.  The Midwest has become the Kansas regional with no other FF-grade teams remaining.

 

A point to ponder is that the teams lying outside the FF arc seem to be the teams playing some of the best basketball!  It will be interesting to see if this is sustainable as their season-long metrics suggest that it may not...or will it just be a year that busts the Arcs!

 

 

[fasbjd]

In anticipation of the Final Four, here is an update of the Grid.  UNC made the Final Four while starting just outside the Final Four Arc.  Kansas is the only Champs Arc team standing but Duke and 'Nova both sit just outside the Arc.  UNC's success will help refine the FF arc while a win by 'Nova or Duke may do the same to the Champs Arc.  That said, I've been working on a much more robust project using the larger volume of data available via KenPom (after this year there will be 20 years of Tempo-free data available).

 

KenPom-driven Arcs:

As you can see, there is a massive amount of information in there.  With that, the new Arcs were derived - some basic principles guided their creation.  First, the grid is divided into 7 sectors - just as there are 7 "finishing spots" in the NCAA tourney - Champs, Runner Up, Final 4, Elite 8, Sweet 16, Round 32, and Round 64 (note that the First Four games are essentially ignored with losses counting as R64 losses).  Secondly, it is known that Seeding has a strong correlation with the way teams finish (in part due to the fact that, in general, better teams get better seeds and in part due to the inherent advantage seeding gives via the bracketing process).  In creating the sectors, I wanted to make a system that has at least as strong a correlation and after several versions, this one does.  There is a really strong correlation between seeding and the sectors but it's not a perfect correlation (with 2 3-seeds, 2 4-seeds, 1 5-seed - Houston will be a second - and 1 10-seed [Witchita St in '17] among the 1 Sector crowd) which allows it to be paired with seeding to have even stronger predictive power.  And finally, Sector 1 size is ~6% of the total teams which is around the number of total 1-seeds (6.3% versus 6%) which I think allows for better direct comparison between the 2 groups.  

 

As far as some preliminary information from the above data, here are some Sector Facts (using '02-'21 data):

 

Along with the aforementioned seeds, Sector 1 has included 55 1-seeds and 19 2-seeds.  It accounts for 73.7% of the championships and 57.9% of teams playing in the Finals.  That's despite only accounting for just over 6% of the teams.  Sector 1 teams have a 17.5% chance of winning the title (versus a 1-seeds 17.1% chance).  If you are a 1-seed in Sector 1, your chances go up to 23.6%.  As can be seen above, all of this year's Sector 1 teams have been eliminated.  This includes 1-seeds Gonzaga and Arizona (gone in the Sweet 16) and Baylor (gone in R32).  The final Sector 1 team was Houston who made the Elite 8 (well outperforming their 5-seed, which would average only 1.12 wins/tournament).

 

This year, 3 of the 4 Final Four teams come from Sector 2.  Sector 2 accounts for 15.8% of the championships and typically only about 1/3 of the Final Four.  Sector 2 has been made up of predominantly 2-seeds (44) such as is the case with 'Nova and Duke.  It's also housed 16 1-seeds (like Kansas this year) along with 33 4-seeds, 14 5-seeds, 11 6-seeds, and a handful of 7/8/9-seeds and 1 11-seed.  A Sector 2 team has a 2.6% chance of winning it all and 13.2% chance of making the Final Four.  Interestingly, of the 16 1-seeds in this grouping, none have won a title and only 1 made the Final Four.  5 other 2-seeds in this sector have made the Final Four with 3 playing for the title and 1 ('04 UConn) winning it all.

 

Skipping to Sector 4, you will find the UNC Tar Heels.  This is also where IU sat (red circle).  About 9% of the Final Four participants have come from this sector with Butler in '11 (who was also an 8-seed) as the only one to make the Finals.  None have won a title.  It's predominantly made up of 7 through 11-seeds and on average  a Sector 4 team will win 1.46 games/tourney (again this is discounting First Four wins).

 

Lastly, regarding Sector 7.  It's predominantly populated with 15 and 16-seeds (about 3/4 of the teams) but has had seeds as high as 10 and 11-seeds.  Just like the 16-seeds, prior to St.Peter's (circled in white), it never had a team go further than the Sweet 16 (twice: Florida Gulf Coast '13 and Oral Roberts '21).  On average a team in this Sector wins 0.05 games/tourney.

 

This is a not-so-brief introduction to this new Grid as well as some fun facts from the database I've created.  Will continue to add posts related to data from these as time goes on.

 

Wonk On!

 

Edited April 2, 2022 by fasbjd

[FKIM01]

Yikes...TLDR.  You are one dedicated basketball fan or else you do this for a living!

That said, I applaud your efforts for those who care as much as you do.

Signed, casual IU fan.

[Drroogh]

I wonder how this fits in the Arc of Champions? Once again @fasbjd thanks for the work!

[fasbjd]

On 12/2/2022 at 1:02 PM, Drroogh said:

I wonder how this fits in the Arc of Champions? Once again @fasbjd thanks for the work!

A little late in responding and things have changed a bit in the last few games but for some prospective, here is where IU sits on the Arc graph as of 12/12:

Now this is comparing our current standing with the final standings of prior years, so not quite apples to apples, but it gives some general assessment of where things stand.

Our current location in the grid puts us in the 2B area:

For reference, in the 14 post-seasons accounted for ('08-'22), there have been 113 tournament teams that plot into this area.  Of those, there were 2 champs (1.8%), 7 teams in the title game (6.2%), 14 in the Final Four (12.4%), 32 in the Elite Eight (28.3%), and 65 in the Sweet Sixteen (57.5%).   Teams in this area have an average win total 0f 1.96 games in the tournament, average tournament seeding of 3.7, and performance-wise fall between the success of 2 and 3 seeds. 

[5fouls]

If I'm reading the chart correctly, Defense is good enough, offense needs to get better.  

[fasbjd]

5 hours ago, 5fouls said:

If I'm reading the chart correctly, Defense is good enough, offense needs to get better.  

I think that is accurate.  Here is another version of the graph that is a bit fairer of a comparison and hopefully makes that clearer:

 

First I'd like to explain the difference in the graph here and the one above (as you can see our positioning is a little less favorable in this one).  The most important change is that this graph represents the Pre-tourney data, so a more useful comparison.  The biggest change in our position, though, is due to this graph point is from Bart Torvik's T-rank where the prior was from KenPom.  While similar, T-rank uses a different adjustment for SOS.  The data used in building the Arcs (all those data points) were also from T-rank.  I had switched to T-rank as it led to a graph with stronger correlation to tourney results.  It also has the advantage of ease of separating data on the website, and is also free to use.  (I had forgotten I had switched when I made the first graph, so my bad.). Lastly, this graph does away with the A/B/C boxes.  This was also done because correlation analysis showed it, while being as strongly correlated with results as Tournament seeding, actually reduced the correlation coefficient of the Arc sectors alone.

 

Now in regards to were we currently stand, as you can see, we sit just outside the #2 arc.  The 3 Sector has had 206 teams in the 14 tournaments represented and of these teams has had 1 champion (0.5%), 3 teams play in the final (1.5%), 8 in the Final Four (3.9%), 18 in the Elite Eight (8.7%), and 47 in the Sweet Sixteen (22.8%).  Teams in this Sector average 0.94 wins/tournament with an average seeding of 6.4.  Before getting TOO worried about our current position, keep in mind that with only 10 games in, we only have a small fraction of the final set of data.  As such, outliers carry a heavier impact on the efficiency averages and we currently have clear one-game outliers for both the offense (Rutgers game) and defense (Arizona).  Without the outliers, the aOE rises 2.2 points and aDE drops 1.8 points - that positioning is the second "X" on the grid.  Now those games obviously happened and cannot be ignored, but given the smallish collection of data it is fair to assume that where this team properly sits is somewhere between these two Xs.

 

Finally, in regards to what 5Fouls said, looking at this graph it is fair to say our defense as it stands currently has been championship-worthy where our offense still needs improvement.  While our defense is not as strong as the average championship D (represented by the yellow circle), it is better than a majority of the championship teams (represented by the yellow/white diamonds) - 8 of 14 had worse aDE.  Every championship team, however, had a better offense with the championship average aOE being far better than our current aOE (the two closest teams being the '13 Louisville team who had a punishing defense and the '14 UConn cinderella team that won it all as a 7 seed).

Edited December 13, 2022 by fasbjd