2D Position Spectrum

[DSMok1]

I'm cross posting this from APBRMetrics since there isn't much activity on that board anymore.

As part of my work on revising Box Plus/Minus, I am investigating using a two-dimensional position spectrum rather than the conventional positions.

I started down this road with BPM 2.0 and I am moving further that direction with the next revision of BPM.

The two dimensions I am proposing are generally Size and Creation.

These generally line up with the first two components of various principal component analyses I have done or seen when evaluating types and roles of basketball players.

I am defining the size dimension based on on the percentage of the team's rebounds and blocks the player accumulates when they are on the floor. Defining everything in the context of the team allows the focus to be on the role of the player, hence the position of the player on that team. It also allows this approach to be flexible across any league.

I am defining the creation dimension based on the percentage of the team's points and assists the player accumulates when they are on the floor--with an added bonus for the points being efficient relative to the team's average true shooting percentage. This creation dimension does generally indicate a player is good on offense, in general.

For both of these dimensions I am adjusting for the variance of the two metrics being averaged. Assists and blocks are both having their variance divided by two because there is a much greater spread in those percentages. (This basically means I'm using z-scores of the two components, but informally.)

As always for percentages of team production, the league average is 20%.

I am then transforming the resultant percentages for each of these two dimensions into a one to five scale, capping outliers at 1.0 and 5.0 in that dimension. The exact capping bounds I have not nailed down yet.

Additionally, I am converting the resultant creation position to a letter for discussion purposes. A pure creator would be an A, with a secondary creator as a B, continuing on to E for the players with no creation ability.

Note that because of the way I am evaluating these, both of these dimensions do not have players evenly distributed on them. There are much fewer A creators then D or E creators. Similarly there are much fewer pure 5s in the size dimension than 1s and 2s.

Here is a visualization showing all of the players in the NBA over the last 43 years and where they would fall on this two-dimensional position spectrum:

https://public.tableau.com/views/ofNBAStats/Position2D?:language=en-US&publish=yes&:display_count=n&:origin=viz_share_link

Thoughts?

EDIT: A revised approach and visualization are below in the following post: https://forums.realgm.com/boards/viewtopic.php?p=110664979#p110664979

[eminence]

Did you experiment at all with defensive or offensive boards vs all boards? Or that may not be an option if you're working with more limited box-scores I suppose.

I think this creation metric will weight scoring a bit more heavily than I would mentally, but it's quite solid for how few inputs you're putting in.

Overall I like it a lot, anything in particular you were trying to decide on or wondering about?

[penbeast0]

Fun stuff. I see Manute (size without creation) and Harden (creation without size) as the primary multiple point outliers, though Westbrook has the single season outlier by far.

Jokic combines the two most successfully; Jason Collins has multiple seasons where he does nothing by these measures as much as anyone though those two aren't as clear as outliers go.

[DSMok1]

Did you experiment at all with defensive or offensive boards vs all boards? Or that may not be an option if you're working with more limited box-scores I suppose.

I think this creation metric will weight scoring a bit more heavily than I would mentally, but it's quite solid for how few inputs you're putting in.

Overall I like it a lot, anything in particular you were trying to decide on or wondering about?

Yes, I did look at regressions dividing out defensive and offensive rebounds. The separation did not improve fit when regressed on actual player size, which was mildly surprising to me.

The creation metric weights assists approximately 2.25x as heavily as points. When you think about it, some teams' offenses are more dependent on assists than others.

The goal is to characterize a player's role on the team--this will be useful when using linearly varying coefficient weights for the next version of BPM.

Here's an interesting comparison--San Antonio and Phoenix in 2007: https://public.tableau.com/shared/FKKNPBCP2?:display_count=n&:origin=viz_share_link

San Antonio has 3 B-level creators, while Phoenix only had 1 A-level and no B-level creators.

And as expected, Bruce Bowen shows up as a 1E--no size and no creation. Individual defense is not in the box score, unfortunately.

Shawn Marion is a 4D--plays big, limited creation, but not a zero offensively. Actually quite close to Ama're in this 2D spectrum--same "size" but Ama're with more creation.

Note: if there were a 3rd dimension/principal component, it would center on shooting, particularly 3pt shooting.

Fun stuff. I see Manute (size without creation) and Harden (creation without size) as the primary multiple point outliers, though Westbrook has the single season outlier by far.

Jokic combines the two most successfully; Jason Collins has multiple seasons where he does nothing by these measures as much as anyone though those two aren't as clear as outliers go.

Yes, those are the major outliers. Hassan Whiteside as well. Ridiculous block numbers...By my calculations, he was at 114% of Miami's blocks at his peak. Meaning he was basically blocking all the shots, and when he was off the floor they got very few blocks.

[MrVorp]

As someone who is currently trying to make a prior informed RAPM for the NCAA I think what you are doing is pretty smart. The problem that I am running into for the prior is that the linear coefficients don't really handle low usage players very well. As long as a player doesn't turn the ball over, which is obviously not hard to do if you barely touch the ball on offense, it's pretty hard to tank his offensive rating. It also tends to overrate players who get a lot of assists but don't have a ton of creation responsibilities, something I think BPM 2.0 does a good job of handling. From your results it looks like you did a good job of quantifying creation from the box score. Steve Nash still looks a tad underrated, but it may be impossible to properly portray his creation without using non-linear terms which I know you are against.

[eminence]

Did you experiment at all with defensive or offensive boards vs all boards? Or that may not be an option if you're working with more limited box-scores I suppose.

I think this creation metric will weight scoring a bit more heavily than I would mentally, but it's quite solid for how few inputs you're putting in.

Overall I like it a lot, anything in particular you were trying to decide on or wondering about?

Yes, I did look at regressions dividing out defensive and offensive rebounds. The separation did not improve fit when regressed on actual player size, which was mildly surprising to me.

The creation metric weights assists approximately 2.25x as heavily as points. When you think about it, some teams' offenses are more dependent on assists than others.

The goal is to characterize a player's role on the team--this will be useful when using linearly varying coefficient weights for the next version of BPM.

Here's an interesting comparison--San Antonio and Phoenix in 2007: https://public.tableau.com/shared/FKKNPBCP2?:display_count=n&:origin=viz_share_link

San Antonio has 3 B-level creators, while Phoenix only had 1 A-level and no B-level creators.

And as expected, Bruce Bowen shows up as a 1E--no size and no creation. Individual defense is not in the box score, unfortunately.

Shawn Marion is a 4D--plays big, limited creation, but not a zero offensively. Actually quite close to Ama're in this 2D spectrum--same "size" but Ama're with more creation.

Note: if there were a 3rd dimension/principal component, it would center on shooting, particularly 3pt shooting.

I'm not shocked, but was curious.

I really enjoy the Suns/Spurs example. Nash the creation core of the Suns, Duncan the size core of the Spurs. Both teams kind of platooning in the other area. You giving that made me realize there was a team filter, which is very very nice.

I appreciate that it's not overly complex in the assigned labels. First glances, I think it's doing a very good job of characterizing role.

Obviously can't separate the guys it doesn't try to separate down in the 2E, 1D, 1E corner, but I think we can safely assume most of those guys are on the court for their shooting, defense, or both (or coach has nobody else to play).

[DSMok1]

As someone who is currently trying to make a prior informed RAPM for the NCAA I think what you are doing is pretty smart. The problem that I am running into for the prior is that the linear coefficients don't really handle low usage players very well. As long as a player doesn't turn the ball over, which is obviously not hard to do if you barely touch the ball on offense, it's pretty hard to tank his offensive rating. It also tends to overrate players who get a lot of assists but don't have a ton of creation responsibilities, something I think BPM 2.0 does a good job of handling. From your results it looks like you did a good job of quantifying creation from the box score. Steve Nash still looks a tad underrated, but it may be impossible to properly portray his creation without using non-linear terms which I know you are against.

Re: prior informed RAPM--I've worked with that a fair bit. One thing you should consider is that a player with very low offensive involvement should have an intercept/prior well below 0, and that the threshold for positive efficiency is higher for a low load/usage player is higher (i.e. most shots are assisted so some of the credit should go to the assister.)

My 2D position scale is not intended to imply the goodness or quality or impact of the player, but rather their role. But as is clear, a high offensive load generally means the offensive player is "good at offense".

Steve Nash I have looked at many times over the years. The big issue is this: in the box score, all assists are counted equal. Whether they are a lob dunk, an open corner 3, or Rajon Rondo pitching it to Paul Pierce for a contested 18-footer. There is no way to differentiate those in the box score. I have accepted that Steve Nash is simply always going to be underrated by any pure box score metric.

[DSMok1]

I'm not shocked, but was curious.

I really enjoy the Suns/Spurs example. Nash the creation core of the Suns, Duncan the size core of the Spurs. Both teams kind of platooning in the other area. You giving that made me realize there was a team filter, which is very very nice.

I appreciate that it's not overly complex in the assigned labels. First glances, I think it's doing a very good job of characterizing role.

Obviously can't separate the guys it doesn't try to separate down in the 2E, 1D, 1E corner, but I think we can safely assume most of those guys are on the court for their shooting, defense, or both (or coach has nobody else to play).

I will note that league average actually falls just into the "D" category because the distribution is significantly skewed. So "D" isn't necessarily a bad offensive player, but just doesn't have a major role in creation. Again, a "D" player could be a great 3Pt shooter and end up very valuable from scoring efficiency and spacing gravity.

In other words--paging Kyle Korver at Atlanta! https://public.tableau.com/shared/K6XPW3PW6?:display_count=n&:origin=viz_share_link Somehow Atlanta was a very good offense with somewhat limited primary creators (Jeff Teague).

The other thing that really won't show up in these 2 role dimensions is individual defense. Rim protection will show up in Size to some extent, but individual defense will not. Marcus Smart shows up as a 1 in Size.

[Dutchball97]

This definitely looks like a big step in the right direction although I'm interested to see what modifiers you're thinking of for the different designations. Following BPM 2.0's logic in terms of position adjustments, smaller players get marked down because they tend to provide less value on defense but when looking at this new version we see 1E mainly being occupied by mid-sized defensive wings like Bruce Bowen and KCP, I feel like marking them down for their size to adjust for lack of defensive impact when they're already showing up so little on the boxscore is going to massively underrate these type of players.

Is the offensive role adjustment going to stay the same as well? Because that might cause some double up adjustments for players who do well in the creation department here.

[eminence]

I'm not shocked, but was curious.

I really enjoy the Suns/Spurs example. Nash the creation core of the Suns, Duncan the size core of the Spurs. Both teams kind of platooning in the other area. You giving that made me realize there was a team filter, which is very very nice.

I appreciate that it's not overly complex in the assigned labels. First glances, I think it's doing a very good job of characterizing role.

Obviously can't separate the guys it doesn't try to separate down in the 2E, 1D, 1E corner, but I think we can safely assume most of those guys are on the court for their shooting, defense, or both (or coach has nobody else to play).

I will note that league average actually falls just into the "D" category because the distribution is significantly skewed. So "D" isn't necessarily a bad offensive player, but just doesn't have a major role in creation. Again, a "D" player could be a great 3Pt shooter and end up very valuable from scoring efficiency and spacing gravity.

In other words--paging Kyle Korver at Atlanta! https://public.tableau.com/shared/K6XPW3PW6?:display_count=n&:origin=viz_share_link Somehow Atlanta was a very good offense with somewhat limited primary creators (Jeff Teague).

The other thing that really won't show up in these 2 role dimensions is individual defense. Rim protection will show up in Size to some extent, but individual defense will not. Marcus Smart shows up as a 1 in Size.

Is the average size in the 2nd category as well? Makes sense that the big majority of players will fall in categories 1-3 (E-C) and if you're a 4/5 that's pretty clearly a major part of your role on the court.

Shooting would make sense as the next possible dimension to add, I'm unsure if I'd like it more than this 2D version (at that point I might move back to a ### numbering system vs a #A system). Would probably have to see it. What inputs were you thinking? 3PM x FT% was the first one to come to mind to me that might work and wouldn't completely ignore long 2 shooters. Apologies to Bruce Bowen.

Can't really think of a 4th possible dimension that could even be approached (due to the difficulty of measuring man D as mentioned).

[DSMok1]

This definitely looks like a big step in the right direction although I'm interested to see what modifiers you're thinking of for the different designations. Following BPM 2.0's logic in terms of position adjustments, smaller players get marked down because they tend to provide less value on defense but when looking at this new version we see 1E mainly being occupied by mid-sized defensive wings like Bruce Bowen and KCP, I feel like marking them down for their size to adjust for lack of defensive impact when they're already showing up so little on the boxscore is going to massively underrate these type of players.

Is the offensive role adjustment going to stay the same as well? Because that might cause some double up adjustments for players who do well in the creation department here.

Good points. I will be reevaluating all of the weightings and variables within BPM.

I'm afraid Bruce Bowen is always going to be underrated because he just doesn't show up much in the box score.

[DSMok1]

Is the average size in the 2nd category as well? Makes sense that the big majority of players will fall in categories 1-3 (E-C) and if you're a 4/5 that's pretty clearly a major part of your role on the court.

Shooting would make sense as the next possible dimension to add, I'm unsure if I'd like it more than this 2D version (at that point I might move back to a ### numbering system vs a #A system). Would probably have to see it. What inputs were you thinking? 3PM x FT% was the first one to come to mind to me that might work and wouldn't completely ignore long 2 shooters. Apologies to Bruce Bowen.

Can't really think of a 4th possible dimension that could even be approached (due to the difficulty of measuring man D as mentioned).

Yes, average size is also in the 2nd category (average is 0.20 for both dimensions.) Size is actually an even more skewed distribution than creation. https://public.tableau.com/views/ofNBAStats/SizeDash?:language=en-US&:display_count=n&:origin=viz_share_link

My goal is primarily for the dimensions to describe role on the team so that the value of box score coefficients can be sensitive to the player's role.

I don't know if adding a 3rd dimension (shooting/spacing) would help much without adding more potential issues. It's also the most likely to be sensitive to league context, which will complicate matters.

[DSMok1]

One additional modification I am seriously considering--

Rather than looking at the arithmetic mean of the % TRB and % BLK (Normalized), I believe a geometric mean probably makes more sense. That requires players to have high values in both stats to have high overall values. In other words, Manute Bol, Jim McIlvaine, Reggie Evans, and Dennis Rodman would end up with smaller "size" metrics because their values are very lopsided. And on creation, players like Rajon Rondo and Earl Watson, and Ama're Stoudemire and Brook Lopez, show up a bit lower.

EDIT: that said, using geometric means does mess with low minutes players who have recorded 0 in one of the categories. So it may not be worth the tradeoff.

[DSMok1]

Here is an additional version of the 2D Position Spectrum dashboard that allows highlight by player, so you can see all of a player's seasons regardless of position highlighted at once:

https://public.tableau.com/views/ofNBAStats/Position2Dr1?:language=en-US&publish=yes&:display_count=n&:origin=viz_share_link

[OhayoKD]

the player on that team. It also allows this approach to be flexible across any league.

I am defining the creation dimension based on the percentage of the team's points and assists the player accumulates when they are on the floor--with an added bonus for the points being efficient relative to the team's average true shooting percentage. This creation dimension does generally indicate a player is good on offense, in general

https://public.tableau.com/views/ofNBAStats/Position2D?:language=en-US&publish=yes&:display_count=n&:origin=viz_share_link

Thoughts?

Not that I have looked too deeply into this, but perhaps there would be some benefit to applying some sort of penalty for individuals on teams with higher total assist totals?(though maybe that should be looked at relative to the league for historical purposes)

I'm sure there's a trade-off somewhere but it might be useful in distingiushing players who see higher assists because they are creating/drawing more attention vs those who are seeing higher assists because they're drawing less attention and the passes are accordingly easier:

Spoiler:

Are you under the impression that players can't rack up assist counts without being doubled? KD is like, the textbook example of that assumption being dumb...

KD's assists and ast% went up going to Golden State. Stockton literally built his whole legacy of passing, out of single-coverage, to a guy who didn't have any assist-cancelling moves. Extra defensive attention is important for creation, not assist-racking. While a teammate is more likely to score while more open, It's easier to pass by a single guy than multiple. And KD often sees his assisting go up when the opposing team isn't keying in.

In fact the very next postseason, with a Celtics team that was keying in, his raw assists barely went up while his ast% dropped from 26 to 22.

Great passers consistently see a trade-off as they can pass by multiple defenders consistently. KD sucks vs doubles so the opposite often happens...

yeah, if you have numbers showing 2012 KD as an ineffectual role player, it's definitely time to stop using those numbers.

Or maybe you should stop cherry-picking? I said "non-scoring" and even by box that's pretty indisputable:

Not shown by box is Kd being a tertiary ball-handler. Also not shown by Box is Miami focusing their attention on Harden. Also not shown by box is KD being a non-factor defensively. Let's see what happens to KD's epic scoring when he's asked to be a secondary as opposed to a tertiary on-ball guy:



Well, hmm, maybe KD ramped up his volume?



Volume does not go up, efficiency plummets...wanna direct me towards what numbers I should be looking at?

Bonus Round: What happens when KD gets back to being third in touches, third in passes attempted, and third in touches per-possession?

It's tough to distinguish between a Nash assist and a Durant assist without additional base inputs(as in different things being counted), but I feel this might help. There are potential trade-offs but given the relatively weak correlatoin with total assists and offensive rating, it might be worth it.

One additional modification I am seriously considering--

Rather than looking at the arithmetic mean of the % TRB and % BLK (Normalized), I believe a geometric mean probably makes more sense. That requires players to have high values in both stats to have high overall values. In other words, Manute Bol, Jim McIlvaine, Reggie Evans, and Dennis Rodman would end up with smaller "size" metrics because their values are very lopsided. And on creation, players like Rajon Rondo and Earl Watson, and Ama're Stoudemire and Brook Lopez, show up a bit lower.

EDIT: that said, using geometric means does mess with low minutes players who have recorded 0 in one of the categories. So it may not be worth the tradeoff.

That makes sense to me. IDK how exactly it would math out, but there might be a way to better approximate paint-protectoin(and to a large extent defensive value) by tying size and blocks to rebound totals. Both can be gamed by smaller players, but i'm guessing it's harder to game both.

Not a big sample, but even something crude like just adding rebounds and blocks make Draymond and Embid standout from their teammates closer to how they stand out if you were to look at synergy deterrence/rim protecting numbers

[DSMok1]

Not that I have looked too deeply into this, but perhaps there would be some benefit to applying some sort of penalty for individuals on teams with higher total assist totals?(though maybe that should be looked at relative to the league for historical purposes)

I'm sure there's a trade-off somewhere but it might be useful in distingiushing players who see higher assists because they are creating/drawing more attention vs those who are seeing higher assists because they're drawing less attention and the passes are accordingly easier:

It's tough to distinguish between a Nash assist and a Durant assist without additional base inputs(as in different things being counted), but I feel this might help. There are potential trade-offs but given the relatively weak correlatoin with total assists and offensive rating, it might be worth it.

Good points. Recall that what I'm doing here is in the context of the team--i.e. % of team's assists. I'm not sure if there's a reasonable way to differentiate between the two types of players directly from season-level box scores...

That makes sense to me. IDK how exactly it would math out, but there might be a way to better approximate paint-protectoin(and to a large extent defensive value) by tying size and blocks to rebound totals. Both can be gamed by smaller players, but i'm guessing it's harder to game both.

Not a big sample, but even something crude like just adding rebounds and blocks make Draymond and Embid standout from their teammates closer to how they stand out if you were to look at synergy deterrence/rim protecting numbers

Having looked at it further, this last sentence makes a lot of sense. I realized there was a lack of robustness in my original approach--averaging % of team's TRB and % of team's blocks doesn't work in some scenarios. Consider a team where they are mostly guards and get almost no blocks--if one player got a couple of blocks and ends up as 100% of the team's blocks--that is not at all the same "size role" as a twin-tower team where the biggest big gets 40% of the blocks. So I'm going to be pivoting toward giving TRB and BLK each a weight and then summing them and calculating the % of that summed value each player has.

[DSMok1]

In light of the discussion here and at APBR, I have revised my methodology significantly.

1. For the Size dimension, the new methodology is to take % of team's (TRB + 3*BLK). In other words, blocks are worth 3x rebounds. This was found by regressing on actual player size (height and wingspan), based on a measurement dataset. Using an additive approach makes this setup far more robust. Hassan Whiteside's 2015 season is still an outlier, but that can't be helped...
2. For the Offensive Creation dimension, I revamped the methodology and the regression basis. I compiled a large dataset from PBPstats.com to accurately measure creation--location of assists, self creation, and shooting vs. location were all included, along with team context. Using this superior basis (incidentally, Steve Nash had 4 of the top 6 seasons), I found a completely different approach to the offensive creation dimension was better.
   
   The new methodology is to take % of team's (AST + Pts scored above 0.85*TmTS%). In other words, the baseline is 85% of the team's true shooting percentage--points scored above this threshold are indicative of creation. Anything less is just...somebody shooting. This really highlights the importance of efficient scoring.

Using these revamped position dimensions, I plotted again the 2-Dimensional position spectrum. As before, the distribution is right-skewed, particularly for the size dimension.

Therefore, I set the position designations accordingly. I selected 10% intervals for the boundaries between positions. 10%, 20% (which is by definition average), 30%, and 40% are the separating points between the position designations (1,2,3,4,5) and (E,D,C,B,A).

For the continuous spectrum, the positions dimensions will be bounded by 5% and 45%, which correspond to the range 1.0 to 5.0.

https://public.tableau.com/views/ofNBAStats/Position2DRevised?%3AshowVizHome=no#3

Features of the visualization:

• Clicking on any point will provide a tooltip about that player-season and also highlight all other seasons by that player between 1990 and 2023.
• Filter by year, team, and by minutes played.
• Colors indicate the player's BPM (as currently formulated), but there is a drop down menu to select other variables for coloration

If you look at the boundary seasons (the "frontier"), you will see Hassan Whiteside, Greg Oden, Joel Embiid, Nikola Jokic, Russel Westbrook, and Chris Paul.

Interestingly, Magic Johnson (1991) is also in the top 5 Creation seasons. Recall this dataset only goes back to 1990.

Think about this "Offensive Creation" dimension as who the defense will prioritize to stop in their gameplan. Who they are most concerned about. Interestingly, Rudy Gobert's best seasons show up above league average creation (dimension 5C)--because his efficient rim scoring was a significant offensive weapon for his team.

[eminence]

Looks good again to me on first glance.

Are you planning on using the 'positions' as more of a categorical thing than a continuous spectrum (that's the impression I got, but not 100%)? If it's categorical I wouldn't be at all concerned about there being a few outliers like Whiteside.

[DSMok1]

Looks good again to me on first glance.

Are you planning on using the 'positions' as more of a categorical thing than a continuous spectrum (that's the impression I got, but not 100%)? If it's categorical I wouldn't be at all concerned about there being a few outliers like Whiteside.

It will be continuous but capped at the upper bound and lower bound (5% and 45%). Also important for small sample size robustness.

[DSMok1]

One of the veteran statisticians over on APBRMetrics pointed out that the approach I was using for creation here was actually measuring quality of creation (success in creation) rather than role.

I went back to the drawing board again to focus on shot attempts and attempting to exclude shooting efficiency where possible.

It looks like a formulation of % of team's (TSA + 5*AST) works well for offensive load/attempted creation.

Here is the Visualization with the revision made:

https://public.tableau.com/views/ofNBAStats/Position2DCreation?%3AshowVizHome=no#2

This should measure role specifically much better.