Post-Player Production of Past Champions: The Archetypal Approach (Part 2)

I'm back with Part 2 of my study on post-player production of national champions. If you have not read Part 1, it is not necessary to have read it in order to understand the concepts and/or analysis presented in this article. However, I feel it is a worthwhile read as a contrast to this article, and I may make a few fleeting references to Part 1 concepts in this write-up. Let's start at the same starting point as last article, and we'll move forward from there.

The table above is the National Championship Profile model with post-production filled-in and all other components left blank. The values are the same values from that article, but since these two articles are a rebuilding job, these values will be corrected at the end of this article. Also, the table only goes back to 2001 because of data reliability (I have data back to 1998, but I'm only confident in the data up to 2001, and it's the data which will be used in both articles). The archetypal approach is represented by the left column labelled POST, and it concerns the function of post-production as a part of the team's dynamic. In simple terms, we will be looking at the whole picture of the national champion and evaluating post production's share of the whole. Instead of the O (Offensive-oriented post-production), D (Defensive-Oriented post-production), or B (Both offensive and defensive post-production), new archetype names and labels will be created.

Similar to the first article, the hardest part of these write-ups is the organization/presentation of ideas. In Part 1, I originally wrote an article that felt more like a novel in length, so at the last minute, I decided to reorganize the paragraphs and the flow of ideas. This resulted in a three-day delay in submission, but it halfed the read time. Again with this article, the organization of ideas is a nuisance, but I think the easiest layout for Part 2 is to detail the parameters first, then unveil the archetypes with depth of analysis, and finally a general wrap-up to the concept with all remaining questions answered.

STEP 1: Parameters for Qualifying Players

Like I did with the taxonomical approach, I wanted to start the archetypal approach with an minimum level of participation or utilization. If a player doesn't measure above the utilization parameters, they are not counted as part of the team's rotation. I required qualifying players to meet two utilization parameters:

1. Play at least 10 minutes per game (I kept some players who averaged 9.8 MIN per game only because I'm not sure if it is a rounding error, and I kept one player on 2015 DUKE with less than 9.8 MIN per game because of a mid-season suspension to a rotation player and its effect on the MINs, FGAs and PTS per game), and
2. Have a shot distribution > X%, where X = (Rotation Position -1) x 0.4. If a player is ranked 7th in order of shot distribution, then his share of his team's shots should be greater than 2.4%, which can be calculated as (7 - 1) * 0.4. 8th would be 2.8%, or calculated as (8 - 1) * 0.4. 9th would be 3.2%, or calculated as (9 - 1) * 0.4. When I show the full ordered table in Step 3, you'll see more visually why this matters.

Shot distribution (ShDs) is just a shorter way to say the percentage of a team's shot attempts that a player takes. I also calculate Free Throw Distribution (FTDs) and Rebound Distribution (RbDs), which is the share of free throws and rebounds, respectively, that a player takes. These three metrics will play a critical role in defining archetypes and post-player function in these archetypes.

STEP 2: Team Archetypes and the Function of their Post-Production

In the original National Champion Profile article, I talked in the Intro about how 2021 BAY resembled the composition of 2019 UVA, but they were a more consistent variant of 2019 UVA in a weaker 2021 field. The resemblance of the two teams is why I added point guard production and post production to the National Champ Profile model. If I had went into far more detail like this reconstruction effort is doing, I probably would have made less errors in that model in the Final 2022 write-up. That is in the past, but I wanted to start with these teams as the first archetype, and by referencing my history on the subject, I wanted to document that I've been doing this well ahead of the ESPN half-time stats analysis.

Big 3 Archetype (B3): In the old notation, most of these teams were the D-archetype (Defensive-oriented post production). Now, they will be known as the Big 3 archetype, mainly because these teams have the same metrics in common with each other:

• With some player rearrangements (2014 CONN Daniels, 2016 NOVA Jenkins, and 2018 NOVA Bridges as SF instead of F), the Big 3 Scorers look like the PG-SG-SF roles and the remaining post-players as a Big 3 of their own in the post.
• The highest of the Big 3 scoring at least 15.5 ppg or at least 19.8% shot distribution.
• The lowest of the Big 3 scoring at least 11.8 ppg or at least 15.7% shot distribution.
  
• The drop-off in shot-distribution from third to fourth is at least 2.8% (2018 NOVA) but can be as much as 15.7% wide (2010 DUKE). Most of the 3rd-to-4th drop-off is in the range of 4.1-8.6%.
• The Big 3 Scorers all had 3P% >= 0.359, and for five out of six teams, they were also the Top 3 in FTDs.
  
• The Big 3 Post combine for approximately 18.5-22.3% of the ShDs (if we count 2018 NOVA as an anomaly), and this averages out to about 7% per post player.
  
• The Big 3 Post also combine for 3.0 - 7.5 ORBs per game, but no individual post-player averages more than 7.9 RBD per game.

Here are some other details about this archetype:

• All occurred from 2010 and later, which is one year after the 3-point arc was extended to 20'9". Also, five of the six occurred from 2014 and later, which is the year that the (horrible) Freedom of Movement philosophy was instituted. Imagine that, a rules philosophy dictating how a team should be built and how they should play in order to win the game.
• RbDs is not consistent among the six teams. For 2014 CONN and 2019 UVA, the Big 3 Scorers own a major share of the rebounds, which is counter to the other four teams in the group. For documentation purposes, I debated segregating these six teams into three archetypes along this discrepancy: 2010 DUKE and 2021 BAY as one, 2014 CONN and 2019 UVA as one, and 2016 NOVA and 2018 NOVA as one. I didn't like this approach because it gave the appearance as sorting by team/coach philosophy rather than metrics.
  
• 2014 CONN and 2018 NOVA are the obvious anomalies in this archetype. 2018 NOVA because they had the smallest 3rd-to-4th drop-off, which was a 2.8% difference compared to the other five teams in the group (4.1%, 4.9%, 7.7%, 8.9%, and 15.7%). Only one other team not in the B3 archetype had a 3rd-to-4th drop-off higher than 2018 NOVA (2017 UNC - 3.2%), and for reasons to be demonstrated in the next group, 2017 UNC and 2018 NOVA are not grouped together. There is a good chance, depending on who wins the 2023 title, that this group alone gets an overhaul in the off-season. 2014 CONN probably has the best match to the statistical mean of the B3 parameters, they don't match the statistical results of the group (RbDs is more guard-oriented, lacking a third post-player in the rotation, and highest BLK total by a longshot). If there was another group that 2014 CONN could belong, it would be the next archetype.

So, let's look at the next archetype group.

Go-To Player Archetype (Go2): In the old system, this group contains teams from all three labels (O, D, and B). Here's what these teams have in common:

• The leading scorer on the team took at least 23.7% of the team's shot attempts, and the next highest player took at least 6.5% fewer. The next-closest team to all of these parameters is 2014 CONN (as stated in the previous group) with only a 23.4% ShDs by the leading scorer and only a 3.8% drop-off from 1st-to-2nd.
• Three of the Go-To players were SFs and three were SGs (2014 CONN's Go-To was a PG).
• The Go-To player either had the highest FTDs on the team as well or had a 3PR >= 0.431 (the more jump shots a player takes, then the less likely they are to be fouled and get FTs).
  
• The two starting post-players on Go2 archetypes have at least 13.2 RBDs per game, with five of the six teams having one of those two starters with at least 8.2 RBDs per game. Looking closer at the 13.6 combined RBDs per game, at least 5.7 of these are ORBs. If the Go-To Player is taking more than 1/4 of the shots and missing more than 50% of their shots, there should be plenty of ORBs to go around. (Note: Since there is little difference in minutes played and shot distribution for 2003 SYR post-players, I just counted the post-production of the highest two producers).
  
• The next three highest in ShDs form a secondary Big-3 to the Go-To player, with the highest ranging from 14.5-18.5% ShDs and the lowest ranging from 11.8-14.6% ShDs. On every team in the Go2 archetype, one of the top in the secondary-3 is a post-player, and in four out of six teams, two of the secondary-3 are post players.
• Four of the six teams have post-production that could be described as a block-party, defensively speaking, as their total combined BLK is at least 3.7 BLK per game. Ironically, all four of these teams played before the Freedom of Movement rules philosophy, which turns legitimate blocked shots into fouls on the defender for the sake of artificially increasing box scores.

If there is one anomaly in this group, it would be 2003 SYR. For starters, it is one of three teams whose leading RbDs player is not a post-player (the other two are 2014 CONN and 2019 UVA). Unlike those two teams, the next three out of four in RbDs are post-players, so they can't be grouped with those teams. Likewise, 2003 SYR's Carmelo Anthony fits the description of a Go-To player, and they had a secondary Big 3, not a primary Big 3 like 2014 CONN and 2019 UVA. Their numbers could also be a function of being the only national champion on the list to play a zone as their primary mode of defense. The biggest differentiating factor is the ShDs drop-off from 4th-to-5th and from 5th-to-6th are the largest in the group, with 2003 UMD being the next closest to either of these drop-offs.

If there is another archetype that either of these two teams could belong, it would be the next one.

Two-Way Archetype (2W): In the old system, these teams could easily be classified as a B-archetype, although I think I settled on O-archetype for a few of them. Here's what these teams have in common:

• At least five players that each take at least 12.4% of their team's shots (in the case of 2012 UK, they have six players above the 13.8% mark in shot distribution, which almost breaks the bounds of mathematics to achieve and only the two NOVA teams come close to resembling it). With this many players getting this many shots, it is no surprise that each team has at least five players averaging 9.5 PTS per game and higher.
  
• Four of the five teams (2004 CONN) have each of their Top 4 in FTDs above 14.3%. Not to mention, three of their top 5 players in FTDs are post players (2012 UK is this exception).
• All five teams have their primary two post players collecting 40.5-54.9% of the team's rebounds. Not only is their top 2, but three of their top 4 in RbDs are post-players (again 2012 UK).
• All have two post players averaging at least 1.3 BLKs per game, and the entire post producing at least 3.2 BLKs per game.
• Four of the five teams have an even distribution of AST (only 2004 CONN having 11.5 AST concentrated to just two players).
  

The teams in this group are probably the most balanced teams to win a championship. The numbers show they can play offense and defense, both inside and outside, and with any player able to score, they should be able to take advantage of the opposing team's worst player. Both 2004 CONN and 2012 UK appear to be outliers in this group. For 2012 UK, it has a lot to do with being a 6-man rotation with a sparingly used post-player as a 7th in the rotation. It does a lot to explain why six players can achieve such a high threshold in ShDs. 2004 CONN is anomaly in its own right. They share similar stats with the Go2 archetype if not for the high ShDs of Okafor (2nd highest on team), only 2.0% less than Gordon. Likewise, 2002 UMD and 2003 SYR could be in this group if not for the wide drop-off in ShDs from 1st-to-2nd. 2004 CONN seems to have a Big 2 with a secondary Big 3 in ShDs (almost like a poker Full House Archetype), but this archetype is not shared by any other championship team. There are two other teams that are somewhat close to these metrics, but they do not share the same stat levels as 2004 CONN, or any team in the 2W archetype.

Let's look at these two teams and the next archetype.

5-Man Offense Archetype (5O): In the old system, these teams would have received the O-archetype. Here's what defines them, yet separates them from other archetypes:

• Five players that each take at least 13.8% of their team's shot attempts (1.4% higher than the 2W group) while each scoring at least 11.2 PTS per game (1.3 PTS per game higher than the 2W group) with one player scoring at least 20.8 (only 2004 CONN of the 2W group is close).
• Coincidentally (since two is a small sample size), both teams had their two primary post players collect 40.8% of their team's total rebounds. Both had four players each collect at least 1.7 ORBs per game, which amounts to an average of 6.8 extra shot attempts per game.
  
• Both teams only have one post player averaging more than 1.3 BLKs per game (unlike the 2W group which had two). The lack of interior shot blocking is compensated by five players averaging at least 1.0 STLs per game. With five extra shots coming in transition, it's easy to get at least 11.2 PTS per game while keeping your opponent off the scoreboard.
• Both teams have a concentrated distribution for AST, with the majority of AST shared between one or two players (2004 CONN of 2W had this trait and the ORBs trait, nothing else though).

With the exception of these schools being arch-rivals, the parameters and metrics tend to fit. In fact, only three national champs have players who PTS per game is more than their ShDs (as long as ShDs is greater than 6%), and two of those three teams are 5O-archetypes. Boozer took 13.8% of 2001 DUKE's shots but scored 14.0 PTS. Likewise, Tyler Hansbrough and Ty Lawson's PTS are above their ShDs figure. When PTS>ShDs, it suggest high efficiency in scoring (in other words, these players probably lead in points-per-shot-attempt among all players studied). Unlike their offensive prowess, they don't have the defensive stats to qualify as a 2W archetype, especially in BLKs. Likewise, they don't have a high enough difference in 1st-to-2nd ShDs (2.8 and 2.0, respectively) to qualify as a Go2 archetype. If there is one team in other groups that could resemble this 5-Man Offensive assault, it may be 2018 NOVA, but they lack the ShDs, FTDs and RbDs from post-production to resemble these two teams (probably a product of different eras of basketball).

Let's look at the last two teams and see what separates them from everyone else.

Post-Island Archetype (PI): They say that no man is an island, but these two teams had a center who  defy this wisdom. Here's what these two teams and their "island" have in common.

• A post-player who is 2nd in ShDs with at least 17.8% of the team's shot attempts, at least 25.7% of the team's FTDs, and at least 29.0% of the team's RbDs. If I remember correctly, the only other team that could qualify on this alone would be 2004 CONN (which is their 3rd possible group).
• Both teams also have all of their post-players in the Top 5 of their team's FTDs.
• Both teams also have all of their post-players in the top spots of RbDs (no post player is out-rebounded by a non-post player).
• The lack of shot-blocking is a peculiar feature, as neither center has more than 1.4 BLKs per game. This could be a product of their importance as an interior presence: By not taking risks of fouling, the BLKs stat is sacrificed in order to remain on the floor. (2004 CONN has BLKs).
  

Since 2005 UNC is the other team that features a player (Marvin Williams) with a higher PTS total than their ShDs, it is very likely they could transition to the 5O archetype (with some tweaking of the parameters of course). If another team were to win a national championship as a PI archetype, it would also make sense to move 2004 CONN to this group (with 2015 DUKE and the new team) and set tighter parameters to distinguish this group from all others (which means ensuring that 2005 UNC qualifies more as a 5O archetype than a PI archetype).

STEP 3: General Review of the Archetypal Approach

I would suppose that the best start to this review would be an overall view of the ShDs, FTDs, and RbDs to visualize how each archetype develops around these three parameters.

Each player is ordered highest-to-lowest (left-to-right) for each of the three parameters. To give perspective to post-production, post-players are marked with yellow boxes and small forwards are marked with green boxes. Notice how post-production is utilized by each archetype:

• B3: Post production is in the bottom-half of ShDs and FTDs, yet it is stretched across RbDs. In the B3 archetype, the post functions to defend the interior while claiming missed shots, both on offense and on defense.
• Go2: Post production is in the 2nd quarter (secondary to the Go-To player) and the 4th quarter of ShDs (reserves also taking on the supporting role), spaced throughout the FTDs, and heavily concentrated in the upper-half of RbDs. In the Go2 archetype, the post functions as a supporting role on offense (to take some of the scoring weight) while securing any misses by either team.
• 2W: Post production is two of the top 5 in ShDs, all in the upper 2/3 of FTDs, and mostly occupying the top spots in RbDs (usually one top spot occupied by the starting SF). In the 2W archetype, the post functions as 40% of the minutes/rotation and 40% of the scoring option (a balanced distribution), but still defend at a high level (BLKs not shown) and finishing off possessions with a rebound.
• 5O: Post production is two of the top 5 in ShDs, two of the top 5 in ShDs, and all in the tops of RbDs (especially when considered on the basis of per-minute played) with not as much help from the SFs. In the 5O archetype, the post functions as two-parts of a well-oiled, high-octane, 5-part scoring machine while dominating the glass on both offense and defense so that SFs can be more involved in the transition game rather than the half-court rebounding game.
• PI: Post production is occupies the 2nd spot in ShDs with very little drop-off from the 1st spot, takes 1/4 of the team's FTDs, and gets at least 10% more of the team's rebounds than the next post-player. In the PI archetype, the post functions as a one-man island (usually a center) whose presence on the floor dictates the team's will through high shot volume, high scoring potential (from the floor and the FT line) and high pursuit of missed shots.

Other details regarding post-production include

• Only two teams have a post-player as the top player in ShDs: 2009 UNC's Tyler Hansbrough and 2012 UK's Terrence Jones (big surprise that it isn't Anthony Davis).
• Two post-players in the top 3 of ShDs have only happened twice: 2002 UMD and 2005 UNC, both of which seem like eternities ago in college basketball (I wouldn't bet on a team in 2023 or the near future with this attribute).
• Only one team featured three post-players in the top 5 of ShDs (2005 UNC), and I would follow the same advice as the previous bullet point for this attribute.
  
• Two post-players in the top 4 of ShDs have happened four times, and three of these four were the Go2 archetype. Ironically, in the Go2 archetype, the Go-To player is not a post-player.
• Only three teams feature a top RbDs player that is not a post-player: 2003 SYR, 2014 CONN, and 2019 UVA. 2003 SYR's Carmelo Anthony was the prototypical Go-To player, so I wouldn't be worried about this one. 2014 CONN didn't have a post-player until the 5th spot in RbDs (a lot of this depends on how we classify 2014 CONN's DeAndre Daniels, which I felt was a struggle in both articles because of the various starting lineups of that team). 2019 UVA also didn't have a post-player until the 5th spot in RbDs, but this may have a lot to do with the pack-line defense.
• Only in the B3 archetype did post-play have no importance in FTDs, probably because it was all about the team's Big 3 scorers.
• Only two teams featured a 9-man rotation (according to the 10 MINs & X*0.4 parameters), whereas the rest were either 7- or 8-man rotation (although, you could potentially count 2001 DUKE and 2012 UK as 6-man rotations when basing it on the distribution of minutes played). When shots are distributed evenly, 9-man rotations would each get 11.1%, 8-mans would get 12.5, 7-mans would get 14.3%, 6-mans would get 16.7%, and 5-mans would get 20.0%. I found it interesting how close some of the actual cut-offs for ShDs mirrored these cutoffs for even distribution. Just look at each column in the ShDs in terms of how many are above and below these thresholds and the width of the margins on both sides of the cut-off points. It's why I stated that UK's 7-man rotation almost breaks the bounds of mathematics as six of their players were above the 13.8% level. In fact, their top five in shot distribution almost falls in line with the 6-man and 7-man even distributions. It is why I feel that I made a good choice in using ShDs as one of the factors in identifying a team's player rotation.
  

Larger Concerns for the Archetypal Approach:

1. This is a lot of detail for one component of one model for 6 wins in bracket prediction. In the 2022 Final Analysis, the NCP model looked at all of the components of 17 contenders. In some years, this count can be over 20 contending teams. To do this amount of work for this amount of teams in such a short time as BCW, it is akin to fitting a watermelon through the eye of needle.
2. The other pressing factor is the evolution of the game and its impact on the adaptability of the component (regardless if it is the Taxonomical Approach or the Archetypal Approach). As the game evolves with new (and sometimes stupid) rules and offensive/defensive philosophies, new archetypes will emerge. In 2010, this approach would have never identified DUKE as a national champion as the B3 archetype would not have existed at that time. The same would go for 2005 UNC and 2004 CONN. Likewise, at one point in the study, I identified eight different archetypes into which I could classify these 21 teams. In order to keep consistency with the Taxonomical Approach, I wanted to explain as much behavior as possible in as few labels as possible. Five archetype groups accomplishes what the eight did, so it seemed appropriate to go with this count (six taxonomies in the other article, even though it could have been more). To further this notion of malleability, I've stated that certain teams could be moved into another archetype and the metrical/statistical thresholds would only need to be altered slightly to differentiate between archetypes. This aspect alone gives more of a hindsight feel to the model even though it is being applied as tool for foresight.
   
3. In the Taxonomical Approach article, I raised about weighting in the model that I would like to address. If components of the NCP model counted as they currently existed, PG production, Taxonomical Approach, and Archetypal Approach would count as three weightings. In theory, the archetypal approach is the PG production combined with the taxonomical approach, sort of like fitting two puzzle pieces together. Should they count separately as three weights in the NCP model? Or should the two mirco-approaches (PG and taxonomical) be evaluated as validation/invalidation thresholds for the macro-approach (archetypal) and the whole puzzle count as one weight in the NCP model? In 2022, I kind of split the difference, counting PG as one weight and post-production (merging the two approaches into one measure) as another weight. In all honesty, I think only a full back-testing of the NCP model itself could answer which question is correct, so I'll stay with the same weightings as 2022 for now.

As always, thanks for reading my work, and like I said in Part 1, if you see any typos or any glaring misses, feel free to speak up in the comments section.

Post-Player Production of Past Champions: The Taxonomical Approach (Part 1)

The Championship Profile Model used to be a random assortment of models, checklists, and data scattered throughout various articles in the blog until Feb 2022 when I consolidated most of them into one tool. Over the off-season, I wanted to do an overhaul of it due to the various errors in data and calculations in last year's final article. In early December, I did an update to the Model (read it here), but I left one specific component blank with the intentions of standardizing that component. First off, it has been one of the most mentally taxing studies I have ever undertaken. The numerous ways I have attempted to quantify and qualify post-production only to abandon the attempt has felt like Sisyphean labor. It is a significant reason why it has taken until Feb to finish it. Second off, I am still unsure of its appropriate weighting in the model, and after Part 2 is published, you will understand what I mean by this (and I will discuss this problem in that article's conclusion). In the end, I ultimately decided to take the component (in its present form as analyzed in the two 2022 articles) and dissect it along its two primary methodologies. From these two methodologies, you will be able to see and understand my original intentions with the component: Post-player output and its importance to a national title. Thus, the two articles being written will feel and read like a walk-through of rebuilding this component.

Let's begin with the table above, and it should be a recognizable starting point. It's the NC Profile Model from the 2022 Final Analysis article with post-production filled-in and all other components left blank. The values are the same values from that article, but since we are rebuilding the component, these values will be corrected. Also, the table only goes back to 2001 because of data reliability (I have data back to 1998, but I'm confident in the data up to 2001 and it's the data which we will be using throughout both articles). The taxonomical approach is represented by the right column labelled PT / R*, and it concerns the statistical thresholds that post-production must achieve in order to be national championship quality. Thus, this approach will be similar to an archeological expedition, where we dig through a lot of data (our artifacts) and try to organize/sort them into their proper place (spoiler alert, it could get very boring).

STEP 1: Logical Foundations for a Post-Player Taxonomy

What do we know about post-players?

• Starts: Every team, champion or not, will 'regularly' start at least one post-player. You will hardly ever see five guards start every game or five post-players start every game. Some may regularly start two post-players. The obvious place to find a team's post-production is 'Games Started.'
  
• Blocks: If there is one category that post-players are nearly guaranteed to lead their team, it is blocks. Basketball is won and lost in the paint because that's where the easiest shots to make are located. If a team can get the ball into the paint, they have a high chance to score, so likewise, if a team can protect the paint, they can keep points off the board.
• Rebounds: Since post players are usually close to the basket, they are closest to a missed shot. While it is not always the case that post-players lead their team in rebounds, especially with the higher volume of 3-point attempts in today's game, rebounds -- especially the offensive variety -- will usually identify a team's post players.
• 3-point Rate: Speaking of 3-point attempts, post players typically have a low 3-point rate (3PR), which is the percentage of their shot attempts that come from the 3-point arc. More accurately said, post players will have a lower 3PR compared to the guards on their team. As we will see shortly, the post players on one national champion violated this theory.
• AST/TO: For a metric commonly associated with point guards, a negative AST/TO ratio (a ratio less than 1.0) can usually identify post-players. Logically, a post-player is more likely to draw the attention of the defense rather than run the offense, so it's more likely that post-players commit turnovers than passes leading directly to baskets. As we will also see, a few post-players on national championship don't conform to this theory.

Let's start with the first attribute as the foundation for our taxonomy and use the rest of the attributes as identifying and sorting. I've compiled a list of every starting forward and center on all national champions from 2001 to the present, as labelled by their team athletic website. First, you will notice that some guards are listed, and if you know your college player history, you should be wondering why they were classified as a guard in the first place. I have included them because I want them to be scientifically deduced by the metrics, not because of an unknown arbitrary classification system. Second, I tried to separate each championship team by its team-colors rather than an extra line or column (and in my opinion, knowing the team name and year isn't too essential for this exercise). For teams that share similar colors, like dark blue, or the back-to-back championships of FLA, I used alternate color schemes, but tried to use the same color throughout the table. (KU, DUKE and UK get their home-whites, and CONN and NOVA get grey since black text isn't easily visible when contrasted with their dark/navy blue).

Rather than attempt to identify the primary post player or the grouping of post players, the safest method would be to rule out the least likely candidate(s) to be the primary post player or post-grouping. The goal is to reduce all teams to two (or in rare cases, one) candidates (candidate) for post player. Again, if you know your college player history, you could probably do this exercise without the metrics, but for scientific purposes, I will use the metrics and explain the results. After the first few examples, I will begin to short-hand the analysis for the reader's sake in speed of reading it.

• Grey (2018 NOVA): Mikal Bridges is most likely the SF due to highest 3PR, highest A/TO, and fewest ORBs (the opposite of what we want to see in a post-player) and 2nd in BLKs and TRBs. He does not have a best in category for any, which would identify as a post-player.
• White (2015 DUKE): Justice Winslow is most likely the SF due to highest 3PR, highest A/TO, and fewest ORBs and TRBs, and tied for 2nd in BLKs.
• Grey (2014 CONN): Lasan Kromah is most likely a SF due to highest 3PR, highest A/TO, fewest ORBs, and fewest BLKs. Based on per minute data (not shown), Phillip Nolan played the same amount of mins as Amidah Brimah and half the mins as DeAndre Daniels, yet his metrics are less than the metrics of Brimah and mostly less than 50% of the metrics of DeAndre Daniels. Thus, Phillip Nolan is most likely a back-up/rotation post-player.
  
• White (2012 UK): Michael Kidd-Gilchrist, SF, highest 3PR, median A/TO, tied for last in ORBs, median TRBs, and fewest blocks.
• Grey (2011 CONN): Roscoe Smith, SF, highest 3PR, second-lowest blocks. Tyler Olander, back-up post-player, lowest in starts, TRBs, ORBs, BLKs.
• White (2010 DUKE): Brian Zoubek, back-up post player, lowest starts, highest A/TO.
• Light Blue (2009 UNC): Danny Green, SF, highest 3PR and A/TO, lowest ORBs and TRBs.
• Green & Orange (2007 and 2006 FLA, respectively): Corey Brewer, SF, lowest BLKs, ORBs and TRBS, highest A/TO and 3PR.
• Orange (2003 SYR): Carmelo Anthony, SF, highest 3PR and A/TO, lowest BLKs.
• Red (2002 UMD): Tahj Holden, back-up post player, fewest starts, highest 3PR and A/TO, lowest ORBs, TRBs, and BLKs.
• White (2001 DUKE): Mike Dunleavy, SG/SF, highest A/TO, lowest ORBs, not best in any category among four players, most unlikely to be primary post-player. Nate James, SG/SF, lowest BLKs and TRBs, while Boozer had highest DRBs (TRBs - ORBs) suggestive of post-defending.

With these players removed, let's take an updated look at our taxonomy.

STEP 2: Filtering Metrics and Categorizing Post-Player Roles

From this list, the first distinguishing factor I notice is 3PR, so I'll filter out the players with the highest 3PR among all candidates and define categories for them.

You will notice a few additional columns. The unlabelled column between ORB and TRB is DRB, which is TRB - ORB. The last unlabelled column is the ORB ratio (I did not label it because I didn't want it to be confused with OR%, which is one of the Four Factors of Efficiency). ORB Ratio is the percentage of a player's ORBs to their TRBs (or ORB / TRB). The unlabelled column to the right of the player is the player's taxonomical identity, so let me explain the notation.

• WF (Wing Forward): 3PR > 0.125 and BLK <= 0.7. A perimeter-oriented forward who has the size to score inside but also the shooting range to play on the perimeter allowing a bigger guard to take a smaller defender into the post.
  
• CF (Combo Forward): 3PR > 0.125 and BLK >= 1.4. A forward that can play inside and outside on both offense and defense.
  
• Of the 42 players under consideration, only eight have a 3PR that is 0.138 or higher. Of the eight players with a 3PR > 0.125, half have BLKs <= 0.7bpg and half have BLKs >= 1.4bpg. With this wide of a margin between the two, there is no need to over-analyze the data when the parameters kind of set themselves. I chose 0.125 for convenience since it is exactly 1 3PA out of 8 FGA. The next closest data value to the minimum parameter is 0.079, which is about 1 3PA out of 12 FGA.
• Looking at the other metrics, the taxonomy seems to fit. The 2P% of WFs is almost .100 higher than CFs, which leads me to believe their 3PR drag bigger/slower defenders out to the perimeter and score 2-pointers off the dribble rather than back-to-the-basket post-play. Likewise, the ORB of WFs are approximately 1.0 less than CFs, which leads me to believe that they spend more time on the perimeter than CFs, placing them further away from potential ORBs.
  
• Although eight is probably too small of a sample size to be practical, the results of the correlation coefficient on this group are interesting. Correlating 3PR to ORB, the value is -0.4445, which is expected but weak. As I've claimed, the more a player plays on the perimeter, then the more likely they are to attempt 3PAs than 2PAs and the less likely they will be in physical proximity to a missed shot. Thus, 3PR and ORB should be inversely related. Correlating 3PR to A/TO, the value is 0.7059, which is much stronger. By playing more on the perimeter, a player is more likely to pass the ball that leads directly to a basket, either by driving-and-passing or by direct-feed to the post. The player also likely has better passing and dribbling skills than the typical post player, making them a better fit to play on the perimeter than inside the paint.
  

The next taxonomies focus on points per game, or more accurately stated, the lack thereof. Basketball is won and lost in the paint, but these players won championships without proficient scoring in the paint.

Again, here's how I define the two new notations:

• RC (Rim-protecting Center): Pts < 7.0 and BLK > 1.2. These are better known as shot-blockers.
• PC (Paint-protecting Center): Pts < 7.0 and BLk <= 1.0. These players put a body on any opposing offensive player who enters the paint and their intention is redirect them away from the paint.
• Again, the parameters seem to set themselves. The highest point total in the RC and PC groups is 6.8ppg (the remaining 23 unidentified players all score more than 9.7ppg).
• In all honesty, I could have defined the BLK parameter as <=0.7 and >=1.0 and only one player would have changed roles. After deep thought, a 1.0bpg average is achievable by one game of 0 blocks and another game of 2 blocks, whereas a rim-protector/shot-blocker should theoretically get a block every game. 1.2bpg average has a lower chance (theoretically) of having a 0-block games than a 1.0bpg average. Also, the term 'prototypical shot-blocker' doesn't exactly describe 2021 BAY's Mark Vital, who happened to be the 1.0bpg player.
• On the surface, the metrics look a little less supportive of separate identities than the previous two, but there are some slight differences. First, the DRB per game of the PC group is roughly higher, as most PCs are >=2.4 DRB/gm whereas most RCs are <=2.4 DRB/gm. Second, the 2P% of appears higher for the PC group as four of six are >=0.567, whereas four of five RCs are below this threshold. I could also make the counter-argument that higher 2P% in both group are more related to the size of the player than the identity, so take this second assertion with caution.
• The correlation analysis is also interesting, but for the wrong reasons. For example, PTS and ORB correlate with a value of 0.5236 for all eleven players, and between groups, it is 0.4439 for RCs and 0.6266 for PCs. However, the same analysis for PTS and DRB shows values of 0.7150 for all eleven, 0.7354 for RCs, and 0.9125 for PCs. DRBs should not correlate with PTS better than ORBs since DRBs and PTS occur at opposite ends of the court. Looking at the correlation analysis between ORBs and A/TO, it shows values of 0.6419 for all eleven, 0.6697 for RCs, and 0.7197 for PCs. The fact that these correlations are higher than ORB-PTS correlations could suggest these type of players are coached to get ORBs in the hands of the guards/perimeter players to reset the possession. Again, interesting, but for the wrong reasons.
  

Now, the final 23 players are up for labeling, and let's see the results.

Here's how I defined the parameters of the last two identities and how to interpret them:

• OP (Offensive Post-player): PTS >= 9.7 and BLK <=1.2. In layman terms, the OP is a scorer/finisher on offense and a PC (paint-protecting post-player) on defense.
  
• 2P (2-Way Post-player): PTS >= 9.7 and BLK >=1.4. As the name would suggest, they can play both sides of the ball: Score on offense and rim-protect on defense.
  
• Although the parameters are identical to those of previous identities, I'm not sure if it is coincidence or if it is another case of the parameters setting themselves. For example, all OPs have A/TO between 0.531 and 0.846 except one: 2001 DUKE's Boozer. But this raises the question: Is his A/TO value the exception to the rule (identity) or is it the result of an external influence? I could make a case for the latter because he is the only OP paired with a CF, and in many games he was on the floor with four other players all of whom had 3PRs above 0.425. This lineup/rotation would boost his AST as he passes out of double-teams to the open shooter.
• On the same line of thought, 2Ps have essentially two ranges of values for their A/TO metric: Either range from 0.250 to 0.538 or from 0.942 to 1.278. For the 0.250 to 0.538 group, this equates to 4TOs per 1AST to 2TOs per 1AST. Thus, the 2P was either a finisher (focus on scoring, not passing, so low A) or a facilitator (focus on the highest percentage shot, so high TO, mostly >2.0 TOpg). All but one of these were paired with either an RC or a PC. For the 0.942 to 1.278 group, this again may be the result of an external influence, as all of these 2Ps were paired with another post scorer (WF, CF, 2P, or OP). The bifurcation of this group along the A/TO metric could potentially produce another taxonomical identity, but I'm not sure there is any additional predictive value gained in doing so.
  
• One noticeable pattern in this group is that all members have >=1.9ORBs. In the previous four identities, WF had 0/4, CF had 3/4, RCs had 1/5, and PCs had 3/6. Instead of the BLK metric, what if I categorized these players along PTS and ORBs and would it make a difference? In the WF/CF group, no player achieved >2.6ORB/gm. In the RC/PC group, only two out of 11 players achieved 2.6ORB/gm. In the table above, all players highlighted in red text have <=2.6ORBS. If you study the table along this parameter, you will see that it only aligns with one other metric: ORB-Ratio, which ORB is the numerator in the calculation, so it should be close to it. The correlation analysis also proves this lack of alignment, especially when seeing that DRB has higher correlations with TRB than ORB does.
  
• Up to this point, I've only pointed out one instance of what I thought could be an anomaly in the taxonomy, which was Mark Vital being either RC or PC (and for the most part, I believe it is correct to identify him as a PC). The only other potential anomaly that I see is 2012 UK's Terrence Jones as a CF. He gets this designation due to his 3PR of 0.138. I could just be picky, but the next closest to him is 2014 CONN's DeAndre Daniels at 0.284 3PR, more than twice of Jones. Excluding Jones, the remaining CFs and WFs have a 3PR in the range of 0.284 to 0.673, with the highest 3PR being five times that of Jones. If the threshold were raised to 0.250 3PR, then he would qualify as a 2P (PTS >= 9.7 and BLK >= 1.4). Ironically, his A/TO is 0.765, which is outside of the two ranges for the 2P group but splits the difference between them. More than likely, I would change the latter range to 0.765 - 1.278 because Jones aligns more with the traits of that group than the 0.284 - 0.538 group. For now, there's nothing really gained or lost by switching him from CF to 2P, and this will be understood later in the article.

For a quick recap:

• WF: 3PR >= 0.125 & BLK <= 0.7, and these parameters produced 4 results having 2P% > 0.583, 3P% between 0.283 and 0.386, ORB <=1.7, A/TO >0.940, PTS >= 10.3.
• CF: 3PR >= 0.125 & BLK >= 1.4, and these parameters produced 4 results having 2P% between 0.476 and 0.525, 3P% > 0.429 (for 3 of 4, 0.333 for other), ORB >= 2.3 (for 3 out of 4, 1.5 for other), and PTS >=10.7.
  
• RC: PTS < 7.0 & BLK > 1.2, and these parameters produced 5 results who have TRB <= 3.7 (for 4 out of 5, 5.7 for other), DRB <= 2.4 (for 4 out of 5, 3.0 for other), ORB <= 1.4 (for 4 out of 5, 2.7 for other), and 2P% <= 0.551 (for 4 out of 5, 0.663 for other).
  
• PC: PTS < 7.0 & BLK <= 1.0, and these parameters produced 6 results who have DRB >= 2.3 and 2P% >= 0.566 (for 4 out of 6, 0.422 and 0.487 for other two).
• OP: PTS >= 9.7 & BLK <= 1.2, and these parameters produced 10 results who have ORB <= 2.0, DRB >= 3.7, 2P% >= 0.540 (for 6 out of 10, the other four were 0.496, 0.503, 0.520 and 0.524), and AT/O <= 0.846.
• 2P PTS >= 9.7 & BLK >= 1.4, and these parameters produced 13 results who have ORB <= 1.9, DRB >= 3.9, 2P% >= 0.540 (for 10 out of 13, the other three were 0.498, 0.502 and 0.511), and A/TO between 0.250 and 0.538 or between 0.942 and 1.278.

STEP 3: Putting It All Together for the NCP Model

Since we have the parameters for identifying player roles and the likely metrics that role should produce, let's look at a finalized taxonomy before we discuss.

What else can we learn about the roles and post-production? Let's start with this breakdown:

• WF: Paired with CFx1 (2018), OP x2 (2022, 2005), and 2P x1 (2016).
• CF: Paired with RC x1 (2014), OP x1 (2001), and 2P x1 (2012).
• RC: Paired with PC x1 (2019), OP x1 (2003), and 2P x2 (2011, 2004).
• PC: Paired with PC x2 (2021, 2010) and 2P x1 (2015)
• OP: Paired with OP x2 (2017, 2009) and 2P x2 (2013, 2008)
• 2P: Paired with 2P x3 (2007, 2006, 2002)

Here's my thoughts:

1. 2Ps have a pairing with every identity, arguably most important identity. When paired with itself, it has won the most titles of any pairing, but none since 2007.
2. OPs have won a title with every pairing except PC. Although this rule could change, it does make logical sense considering that neither identity protects the rim.
3. PCs only win with PCs (both take up as much painted space as possible), RCs or 2Ps (if they can't keep opponents out of the paint, then they have rim-protection as a fail-safe). Rules #2 and #3 give a slight nod to the value of shot-blocking.
4. PCs have all six of their appearances since 2010 (one year after the 3-pt Line expansion). It is most likely a defensive philosophical shift with more area/space to defend.
   
5. WFs have three of their four since 2016 (the beginning of the PPB era). In the same mind as Rule #4, newer identities and newer pairings are very good reasons to do this overhaul and stay up-to-date on the ever-evolving profile of National Championship contenders.
6. WFs, CFs and RCs have never won a title when paired with themselves. If I had to guess, WFs because of no rim-protection, CFs because of lower 2P% (0.476 - 0.525), and RCs because their rim-protection doesn't compensate for lack points.

After all, you can't pick a perfect bracket if you can't pick the National Champion correctly. If you made it this far into the article, you're probably a champ in your own right. I also wouldn't be surprised --  from all of this data, all of this analysis, and having to re-organize and re-write the article -- if I over-looked a detail, typo'd the wrong number/digit, or left out one of the many insights I've had over the past three months. If you do see a typo or maybe an insight that could be added to the six rules above, feel free to leave a comment. As always, thanks for reading my work, and Part 2 of this study should be published around the same time next week.

2023 Quality Curve Analysis - February Edition

While most of the sporting world is moving on from American football (only the Super Bowl remains), the college basketball world is starting its push to the finish line. At the current moment in the college basketball season, most teams (referring to power conferences) have four weeks of regular-season conference play and one week of conference tournament play. Last week concluded the first pair of most rivalry games, and to my surprise, it didn't damage the quality curve as much as I thought it would. I already anticipated most of the high-seed teams to lose at least one game this week, and only IAST lost to a team outside the QC (yes, FLA, VT and OKST are in the QC if you are thinking about the losses by TENN, UVA, and TCU). While this fact is good for maintaining quality, it is not good for creating separation in quality, which is something that usually manifests in more saner tournaments. With further monologuing, let's see what the data shows.