Counting the Baskets

A Little More Green Space

(The Celtics Have More Shooters Than They Started with Last Year)

The clock is ticking down on the NBA off season and cap space and roster spots are drying up like the California reservoirs.  That means that the odds of significant changes to the Celtics roster before the start of the season are also shrinking.

So, I thought I'd apply my shooting style analysis to what we're currently working with in terms of the Celtics roster.  I did something similar for the Celtics last year in a post that ended up being titled, "No Threes for Us, We're Celtics."

Long distance shooting isn't the only valid playing style, but a number of  studies have indicated that having long distance shooters on the court is helpful to offensive efficiency even beyond the extra point on the three.  The general thought these days is that an effective line up needs to have mixture of shooting styles with at least a few players able and willing to shoot from three. 

There has actually been a significant turn over in the Celtics back court since the start of last year, and we've gained a year of data on last year's rookies.  In addition, there's also been an evolution in Jared Sullinger's case in his first year under Brad Stevens with a not always successful addition of the three point shot to his arsenal.  So that's no longer an exactly accurate description of the roster.

Quickly, the following table shows the results of a statistical data mining technique to group data with similar cases called Cluster Analysis on the shooting styles of players.  The Clusters were run separately on front court players and back court players to give a better opportunity to finely analyze playing styles.

First the guards and wings:

In contrast to last year there are three back court players that qualify as Stretchers based on their shot selection, where Keith Bogans, who effectively ended up not playing at all last year, was the lone Stretch player in the back court.

In addition, there are the incoming rookies Marcus Smart and James Young.  Smart took over 42% of his field goal attempts from three, and 35% at the rim, according to Hoop-Math. Though his conversion rate on threes was only 29.9%  Young even more clearly has Stretch potential with 52% of his shots from three and only 22% at the rim.  Young had a decent 34.9% conversion rate, but the Celtics front office seems to think that number is below his expected long term shooting ability.

The front court also has a couple of players who adopted a 'Stretch' shooting mix, though the percentage of threes taken for a big to be considered a 'Stretch' player is lower than for guards and wings.

Sullinger, Kelly Olynyk and Vitor Faverani all took enough shots from three under Stevens to rate as Stretch Bigs, while Brandon Bass remained a mid-range specialist.

Of course, shooting and making the three are not the same thing, though there is a relationship. In order for a shooter to provide effective spacing he has to be guarded, meaning the defense has to want to discourage him from shooting.  The final column on this table with the points per shot from three gives a very rough idea of the player's immediate 'stretch potential' based on their shooting percentage from three last year. (I actually have another project in development looking at predicting three point shooting year to year, if I ever get around to completing it).

 

Shot Selection Avery!  Based not only on last year, but over his career as a 36.6% shooter from three Bradley has the best potential as a Stretch shooter, which would not only increase his efficiency but add provide more space for other player's to get to the basket. 

Chris Johnson, Marcus Thornton and Jeff Green under performed their long term three point shooting, so should be added as potential Stretch threats.  Although Green is probably more valuable as a Slasher over the long term, but in certain line ups he could take the Stretch role.

Phil Pressey needs to be able to shoot an NBA three to remain in the NBA beyond this year.

And the same for the front court.

Obviously, Olynyk looks like the most legitimate Stretch big threat on this team, while there's probably only one more year on the Sullinger from three experiment unless he starts hitting at a higher rate. I also wouldn't mnd seeing Bass expand his range at leas to some corner threes if he sticks around. It would be good for both his trade value and next contract if it works.

There isn't really a knock down shooter on this roster, but there are at least a couple of willing and marginally capable three point shooters, which is at least a step in the right direction. (Now if only Avery would take two steps back).

Curse of the Mid Range Shooter

(And The Shooting Competence Curve)

Last October I unveiled my Scoring Versatility Index at Hickory High.  The idea at the time was to create an index that graded a player's efficiency scoring in a variety of ways including from different spots on the court and from the line, with the theory that a player efficient from more locations would be harder to guard.  

The immediate problem that I found was that as one carves up the court into smaller pieces one creates more data sets with smaller sample sizes, and the less reliable data.  It is a problem, as I have noted, with the shot chart era in general.  Carving up the court into pretty pictures can sometimes give us pretty unreliable impressions. Looking to account for this has been an interesting challenge and lead me to a few somewhat unexpected directions.

Players with only a few shots from any zone will have averages unreflective of their 'true' talent level, and, in fact, with three point shots the inherent high variability it takes a fairly large number of shots to determine true talent with any confidence.  

Statistics and a couple of assumptions can help us out here.  Over a given period players will shoot above or below their 'true' ability based solely on random variance (compounded, perhaps, by opponent variation, injuries, confidence levels and so on).  It's a tried and true assumption that after these streaks, over the longer term the player's shooting percentage will revert or regress toward their 'true' average, with reversion taking longer with a higher variability.

That leaves open the question of what the player's true shooting ability.  

My assumption also was that a player that rarely takes a three point shot is likely to be  a 'replacement' level three point shooter rather than an average one.  That's convenient for estimating the Versatility Index as crediting every player with average percentages with few if any shots would not help in measuring difference in scoring versatility.  When I looked at the data is also happened to be true.

Using the NBA.com shot zone data I charted each of the NBA's five shot zones with each player's shooting percentage against the number of shots taken in that zone. (The zones are the restricted area, paint outside of the circle, mid-range, corner three and above the break three).  For the three jump shooting zones in the mid range and the threes the pattern was pronounced, players who shoot more mid range jumpers, for example, make them at a higher rate.

The number of attempts from the mid range conveys two pieces of information, the amount of time the player is on the court and the degree of comfort the player and his coach have in him shooting in the mid range, ie whether that is one his spots.  Contrary to some opinions coaches have some idea who their better players are and players have some idea where they shoot better. The same is true of corner and above the break three point shots. 

Curses and Blessings

The problem, for mid range shooters, is that even for good mid-range shooters the shot isn't terribly efficient.  That can be seen in the image below along with the increasing expected competence with more attempts via a logarithmic trend line.  

Only the most efficient mid range shooters like Chris Bosh and Dirk Nowitzki approach league average efficiency  as measured by eFG% (the dotted line) from mid-range.  Players like Carmelo Anthony, DeMar DeRozen and LaMarcus Aldridge last year were fairly good (and liberal) with a not good shot.

Via Ian Levy's work on Xpps, the average point per shot for a mid-range attempt is .793, or an eFG% of 39.6%.  The competence curve on mid range shots last year indicates that players who attempted fifty to sixty mid-range shots were more likely to average near 36%, while players with just over 150 attempts the expected competence is closer to league average and high volume mid-range shooters the curve rises to only 42% to 43%.

In contrast, most of the more prolific shooters of the above the break on the three hit for above average efficiency.  And we also see the same increasing competence curve, leaving players on the right side of the image taking a allot of an efficient shot and being pretty good at it.

 

All of the most prolific shooters of above the break threes hit is with above league average efficiency, with only Kobe Bryant and Goran Dragic, last year, hanging around league average on those shots.  The curve indicates that a player taking 50 above the break threes as an expected eFG% of about 44% on those shots, higher than the more prolific and skilled mid range shooters.  The players higher on the competence curve shooting above the break threes show an expected eFG% of aproximately 58%.

Summing Up

To be clear, the train of causation here is primarily that players are taking the shots they are more comfortable, and skilled at, more often.  And that those shots are more likely to be within the flow of the offense than Chris Anderson's random above the break heaves or DeAndre Jordan's stray fifteen footer.

On the mid range shots, hitting a higher percentage is certainly better than shooting many and hitting fewer.  In addition, part of the impetus for the Scoring Versatiliy Index was the idea that being efficient from more spots on the court puts more pressure on the defense than a specialist like Kyle Korver or DeAndre Jordan.  

Currently two of the NBA's most efficient offenses, the Houston Rockets and Portland Trailblazers, featue very different ideas about spacing with the Rockets focusing entirely on three point shots and the Blazers featuring a mix that includes Aldridge's  mid range game in addition to highly efficient three point shooting.  So clearly an effective mid range game can be a part of a larger efficient scheme, if only to open the floor to other, better shots.

 

The Value of Line Up Stretch

This post originally appeared at Hickory-High.com on 11/06/2013

The value of the three-pointer is a staple of basketball analytics. It is often referred to as 'advanced,' but really it is mostly the result of pretty simple algebra, a team has to hit 50% more two point shots to get the same number of points as they would get off of three point shots. Away from the rim, most players struggle to do that.

Of course, there is more to it than that, all kinds of nuances can effect the percentages of any shot. Defenses can do the same math and prioritize guarding the three point line. When misses do happen there are different expected percentages of offensive rebounds. It is easier to for the opposing team to score off of defensive rebounds, which add up with more misses from distance. Driving to the rim results in more free throws, which is a very efficient way to score.

Then there is the issue of 'spacing,' simply for its own sake. Kirk Goldsberry, in a Sloan paper, estimated the scoring area in basketball is 1280 square feet based on where the vast majority of shots are taken. From a geometry stand point taking shots from further out increases the percent of that area the five defenders have cover and increases the space between defenders, opening lanes to the basket. As Houston GM Darryl Morey or any old time basketball hand would probably tell you, driving to the rim and spacing are complimentary. Players need space to open lanes and drive to kick it back out.

A while ago I ran a number of K-means Cluster analyses based on shot type using data from the suddenly defunct, HoopData. The analysis grouped Guards, Wings and Bigs based on where they shoot in relation to the basket. The analysis grouped both the guards and the wings into groups of Stretch and Slasher types, scoring from the three point line and at the rim respectively. Meanwhile, Bigs fell into three clusters, Bigs that shot almost exclusively at the rim, those with more varied offensive games and stretch bigs, who added a three point shot.

For example, Stretch Wings averaged 56% of their shots from three point range and 19% at the rim, while Slashing Wings averaged 21% from three and 35% at the rim, according to my analysis.  The numbers for Stretch and Slashing guards were both very similar. The cluster analysis allows me to group player types together to look for patterns in the data, for example, I found some interesting patterns in terms of style of play with Stretch back court players and wings have higher eFG% percentages, but Slashers get more offensive rebounds and more free throws. Again, I will use the Wings as my example.

Group	COUNT	Avg TS%	Avg eFG%	Avg ORB%	Avg DRB%	Avg AST%	Avg TOV%
Slash Wing	39	52.7%	49.1%	5.84	16.09	10.79	11.95
Stretch Wing	25	53.7%	51.2%	3.20	13.08	10.03	11.15
Grand Total	64	53.1%	49.9%	4.81	14.91	10.50	11.64

But to take the analysis to the next step I wanted to look for an independent value of spacing, and its limits. I think that is another value of using categorization, Stretch players are measured as players that take more three point shots, not necessarily make them at a higher rate (though there is a correlation there too). The methodology adopted was both to chart the Stretch players in five man line ups against offensive rating (ORTG) and, secondly, to calculate an expected ORTG, (points per one hundred possessions) based on the individuals in a line up and compare it to the actual ORTG generated by that five-man lineup, then add Spacing configurations to the mix. (Similar to an analysis done here by Jacob Frankel using a different definition of stretch.)

I used line up data from the last two years, courtesy of NBA.com's media stats site. The chart below uses a cut off of five-man lineups that played at least 250 minutes together in the either of the last two years, however, I ran the same chart multiple times with different minute filters and got largely the same results.  With the five man line up at this cut off, Tyson Chandler, Carmelo Anthony, Jason Kidd, Raymond Felton and J.R. Smith had the highest ORTG with 119.4 points per 100 possessions, and Brandon Knight, Jason Maxiell, Greg Monroe, and Rodney Stuckey had the lowest at 93.6 points per 100 possession.

 

I used a polynomial line to visualize the trend.  Consistently, with different minute filters the trend showed an increase in offensive rating going from 0 Stretch players in a line up to 1 and 2, and then flattened.  The same pattern was seen with Wing and Guard Stretch players only, as well as, using effective field goal percentage. Then I ran the expected ORTG for each line up against the actual ORTG the line up had, with the 250 plus minute filter the R^2 was a decent 0.434.  The chart below shows the number of Stretch shooters in each line up against the residual error on the expected ORTG.

Again the same pattern can be seen with an increase in the offensive rating with two stretch players on the court and a then leveling off indicating diminishing returns to spacing.  Using that information I made a 'dummy' variable for each lineup that had two or more Stretch shooters and ran that variable in a step wise regression along with the Expected ORTG and linear count of Stretch shooters.  In every minute filter the Dummy Stretch came out as the most significant contribution in addition to the Expected ORTG. The result of the model run with the 250 minute filter indicated that the value of having at least two Stretch shooters on the floor is 2.44 points per hundred possessions.

	Unstandardized Coefficients		Sig.	95.0% Confidence Interval for B
Variable	B	Std. Error		Lower Bound	Upper Bound
(Constant)	13.29	12.53	0.29	-11.74	38.31
Expected ORTG	0.83	0.12	0.00	0.60	1.07
StrechersDummy	2.44	0.89	0.01	0.67	4.21

 

The results were similar with other filters on minutes, with the independent value of having two Stretch shooters in a line up centered just above two points per hundred possessions.  It might not seem like a lot, however, this value represents the value above the simple algebraic shooting percentage multiplied by three points. And two net point per game equal about 5 wins over the course of the season.

Can Asik and Howard Work Together? Maybe!

(The Non-Negative Value of Negative Spacing)

There's a well known bias in academic publishing that favors papers that find statistically significant results over any study that doesn't. That is unfortunate, because sometimes it is as important to find evidence to rule out relationships or causation as to find evidence to support them.

Of course, blog posts don't go through a committee or reviewers; but there is still a natural bias I think to report research that finds significant relationships. This isn't going to be one of those posts.

OK, throat clearing over, I have been doing a whole series of posts on shot location in the NBA here and at Hickory-High. The last one looked at the independent value of of having 'Stretch' shooters on the floor in addition to the improved efficiency of the three point shot. In that study I found that having at least two Stretch shooters on the floor appeared to improve a line up's offensive efficiency as measured by points per 100 possessions (ORTG), but adding an additional Stretch shooter did not aid offensive efficiency.

In my shot location Cluster Analysis series I found three groups of Big players; players who shot almost exclusively from arms reach of the basket, stretch Bigs that shot three point shots and Hybrids that had a mid range game.

This is how the shot selection and statistics looked for each type:

		AVG Att at the Rim	% Att at 3-9 ft	% Att at Mid Range (10-15)	% Att at Long Two(16-23)	% Att of Three Pointer
At the Rim Big		67.31%	21.24%	3.58%	7.62%	0.36%
Hybrid Big		40.31%	16.47%	10.94%	29.88%	1.96%
Stretch Big		26.10%	9.32%	5.83%	19.36%	38.91%

 

The 'At the Rim' shooters displayed almost no spacing value, and the majority of Bigs fell into the middle category.

In terms of interior spacing, there has also been a good deal of discussion about the viability of line ups with two bigs with limited jumps shots, such as Dwight Howard and Omer Asik in Houston. Both scored as 'At the Rim' shooters, and have displayed limited range on their jump shots.

Given that, I decided to add to the spacing analysis with some negative space analysis of Bigs. I coded every 'At the Rim' big as a negative -1, then added all of the negatives together, finding this distribution for Line Up combos over the last two years:
.

Statistics
RimBig	Count	Offensive Rtg	TmTOV	AST Ratio	Net Rtg
2 Negative Spacers	8	103.04	16.33%	17.59	3.53
1 Negative Spacer	50	104.42	15.62%	17.85	2.72
No Negative Spacer	36	104.76	14.50%	18.95	3.51

 

There were only eight line ups with 2 Negative Spacing Bigs that played over 200 minutes together in the last two years, indicating coaches certainly believe in interior spacing's value.

In the examples found there was little absolute degradation in offensive rating for the handful of line ups the featured 2 Negative Spacers without a distance or mid-range game. In fact the Net offense rating minus defense rating of the 2 Negative Spacers line ups were better than the 1 Negative Spacer line ups and virtually identical to the no Negative spacer line ups.

Looking at the difference between expected offensive rating ORTG based on the average of players in the line up and the actual ORTG achieved, there was also little evidence of a negative spacing effect.  There was no statistically significant effect from having negative spacing in the front court in any filter of minutes played together.

In fact one of the line ups that worked well last year and continues this year, is the starting Toronto line up with Jonas Valanciunas and Amir Johnson, who no one comments on because they play in Canada.  That line up had an average ORTG but a very good defensive rating for a Net of +12.9 per 100 possessions over 354 minutes last year.

Returning to Dwight Howard and Omer Asik playing together, this study found no negative effect of playing two Negative Spacers on the floor together.   All that suggesst that Asik/Howard could work together. However, even without an independent effect from negative spacing bigs, Howard and Asik had the lowest ORTG of the Rocket's current starting line up last year, both being below the league average.

And to date it hasn't worked that well in Houston.  Part of the issue is that Asik just isn't playing well so far, his eFG% through six games is down ten points to 45.5% and his turn over percentage is up to 28.8% from 18.8% last year.  But neither can be blamed on Howard, as Asik's eFG% is higher and TOV% is marginally lower when on the court with Howard according to NBAWowy.

It also appears that having Asik and Howard on the court is clogging the lanes for their teammates. Harden, Parsons and Lin are all taking a lower percentage of their shot attempts at the rim when the Asik/Howard tandem is on the court than when it is not, again via NBAWowy.

Player	% of Shots 0-3 feet WITH Asik/Howard Combo	% of Shots 0-3 feet WITHOUT Asik/Howard Combo
James Harden	20.8	33%
Chandler Parsons	34.6	60%
Jeremy Lin	33.3	39%

 

In fact, so far the team as a whole has taken a higher percentage of their shots inside three feet when the Asik/Howard combo is not on the court than when they are.

Part of the problem in addition to opponents sagging off of them may be contained in the high turnover and low assist numbers for both Howard and Asik, neither of whom are particularly good interior passers, and that's generous for Asik.

But the evidence I found suggests that line ups with two space clogging bigs can work, whether Asik and Howard will work is too early to tell.

(Note light editing added 11/9/13 for clarity)

Should Brad Stevens Start Jordan Crawford Over Avery Bradley at Point Guard?

(I can't believe I am writing this)

To the surprise of no one, on the Sports Hub yesterday, Danny Ainge confirmed that, Rajon Rondo is likely to miss the first part of the season.

Given that Rondo is both the best player on the team and the only natural Point Guard with NBA experience, I have been thinking about how the C's should start the season's back court line up, as I suspect has Brad Stevens and his staff.  The issues in picking a replacement back court also ties in nicely to some work I have been doing on shot creation and shot location in the NBA., in terms of finding the most complimentary mix of ball handing, passing, floor spacing and defense.

The shot creation pieces are particularly relevant to playing at the Point and the skills the Celtics will need to replace while Rondo recovers.  The Point on offense is probably the best defined position of the five cardinal positions.  He handles the ball, sets up his team mates, and gets his own shot when needed.

To take those skills in reverse order, most Point Guards ranked as what I called Shot Creators in my cluster analysis with only a quarter rating as Spot Up Guards, who score disproportionately off of getting assisted, including Avery Bradley.  In fact, of all the players defined as a Point Guards by Hoop Data with more than two hundred minutes played last year, Bradley ranked 11th from the bottom last year, or the 12th percentile, in his propensity to get his own two point shot. (Two point shots are the most telling since so few three point shots are unassisted, players with a good handle and a nice three stroke get artificially lowered in their shot creation when threes are included).  Rondo, on the other hand, rated highly, creating 77% of his own two point shots, putting him in the 73% percentile.

Bradley also rates low in getting assists.  Third from the bottom on that same list with 11.6%. Only Royal Ivey and the remains of Derek Fisher scored lower.  By contrast, Rondo led all NBA Point Guards with a 49.3% assist percentage, and Jordan Crawford, playing the two had a 19.4% assist rate in his time with the Celts last year, and higher in DC.

Ball handling is harder to measure directly.  Certainly the eye test says to most observers that Bradley looked uncomfortable as a ball handler last year, looking to rid himself of the ball as soon as possible to the nearest guy with a green jersey.  We can also probably look at the numbers above to make some inferences that Bradley wasn't comfortable with the ball in his hands

Bringing the shooting guards into the list; here are the Celtics guards in terms of getting creating their own shot, assists and turnovers, the signature stats for Point Guards.

	Pct Two Point Offense Assisted	Total Field Offense Assisted	AST Pct	TOV Pct
Avery Bradley-BOS-2013	49.68%	62.88	11.60	12.60
Courtney Lee-BOS-2013	52.13%	65.73	11.70	13.00
Jordan Crawford-BOS-2013	29.03%	46.64	19.40	15.50
Jordan Crawford-WAS-2013	20.93%	41.01	25.50	14.90
Keith Bogans-BKN-2013	54.18%	86.70	8.10	14.40
Marshon Brooks-BKN-2013	33.57%	39.99	14.60	15.50
Rajon Rondo-BOS-2013	23.22%	24.01	49.30	22.60
Phil Pressey- MO- 2013	4.72%	19.54	37.80	23.20

I included rookie Phil Pressey here, even though I do not have his shots assisted data from the NCAA as of now. (Update, per commenter Adrien, I have added Pressy's numbers from Hoop-Math). Apparently there was no else on the team with the slightest ability to throw a pass in Missouri last year.  Jordan Crawford's numbers look like a combo guard, he gets his own shots (not always to his advantage) and assists at a high rate with a higher assist percentage than turnovers.  Bradley, Lee and Bogans look like spot up Shooting Guards, not Point Guards, with Brooks playing the role of slashing Two Guard.

Last year the Celtics were able to pair Lee and Bradley as defensive pit bulls despite their ball handling and distribution weaknesses primarily because of Paul Pierce's ability to play Point Forward.  That's a luxury they won't have this year.  Some of this may sound like I am picking on Bradley's game, but I am not.  His defense is amazing, as is his effort.  He's just not a Point Guard, and playing him as one does him no favors.

As I wrote above, in addition to ball handling duties floor spacing and defense have to be considered in matching up a line up.  Offensive spacing does not just come from the back court, but the front court doesn't have any spacing specialists like a Kyle Korver or Dorrell Wright (unless they put Bogans in as a Small Forward).

 

Player- Team- Yr	Pct of Shots at Rim	Pct of Shots from Three	Three Point Percentage
Avery Bradley-BOS-2013	30.04%	26.46%	31.7%
Courtney Lee-BOS-2013	32.75%	30.59%	37.2%
Jordan Crawford-BOS-2013	26.46%	37.57%	33.7%
Jordan Crawford-WAS-2013	15.99%	34.62%	33.7%
Keith Bogans-BKN-2013	7.02%	86.67%	34.3%
Marshon Brooks-BKN-2013	35.60%	17.34%	27.3%
Rajon Rondo-BOS-2013	40.44%	11.11%	24%
Phil Pressey- MO- 2013		38.2%	32.4%

In terms of shot selection, Bogans is the only pure Stretch Guard taking nearly 90% of his shots from three, with Crawford rated on the borderline of being what my analysis considered a Stretch Guard.  In actual efficiency only Lee had a three point field goal percentage above the average for a Guard of 36.3% last year, though Bradley was down considerably coming off of the double shoulder surgery.  Defenses are likely lie well off both Rondo and Brooks outside the arc.

Putting it together in terms of combos, if we want to have one Shot Creator and one Stretch Guard on the court most of the time, our options look something like this without Rondo:

 

Creators	Stretch	Rim Attack	Defense
Crawford	Lee	Brooks	Bradley
Pressey	Crawford	Lee	Lee
Brooks	Bogans	Crawford	Bogans
Bradley	Bradley	Bradley	Pressey
Lee	Pressey	Pressey	Crawford
Bogans	Brooks	Bogans	Brooks

 

Not all of the those divisions are equidistant (Bradley and Lee's defense is probably significantly better than the next Guard available).  But then it's Steven's job to balance those trade offs setting his line ups for the first month.

Location Visualization

Below is the latest and greatest visualization for shot location, percentages based on percent of all shots taken at the rim or from three.. It defaults to show Wings, but you can change the filter for the Guards types and by year.  One can also see the Bigs, if you include everyone, but (spoiler alert!) they don't shoot many threes so there's less to see.

 

Learn About Tableau

Guard Location Viz

Below the break is a visualization of Guards' shot location broken out by my cluster analysis groups, Slashing Guards and Stretch Guards based on their percent of attempts at the rim versus from three...

No Threes for Us, We're Celtics (Keith Bogans Excepted)

I have been doing a series of studies on shot location in the NBA, breaking it down for guards, wings and big men. Naturally I could not help looking at how this applied to the Celtics.

Briefly, the series looks at shot location by position in the NBA with the help of a statistical technique called clustering, which looks for grouping patterns in data. (You can read about here if you are so inclined, but it's really not necessary).  The analysis gave a some nice intuitive results with 'Good' cohesion that showed that, yes, there are fairly distinct groups of Slasher Guards and Wings as well as Three Point Specialist Guards and Wings. For the front court players I found three groups, guys who only shoot at arms length from the rim, hybrids that add a mid range game and Stretch Bigs.

The study is primarily intended to look at big groups in terms of analysis. But, it is interesting to see how it applies to individual players and rosters plus it provides a nice test of reasonableness bfore I go further.  All that said and done this Celtics group is not a very stretchy roster, based on shot location last year. (For now I am ignoring the rookies).

The analysis rated only one of the current roster members as a 'Stretch' at their position, and that was Jeff Green because the HoopData.com data listed Green as a Power Forward.  Of course, this year Green will play more of his time at small forward, so I changed his position and reran the Cluster analysis where Green was rated as a Slash Wing.

For reference, the Slash Wings average 35% of their shots at the rim and 21% from three, while the Stretch Wings took 19% of their shots at the rim and 56% from three point land.

PlayerName	Pos	Pct Shots at Rim	Pct Shots 3-9 Ft	Pct Mid Range (10-15)	Pct Shots from Long Two (16-23)	Pct Shot from Three	Group
Jeff Green	SF/PF	38.61%	11.93%	5.23%	19.97%	24.26%	Slash Wing
Keith Bogans	SF	7.02%	1.75%	0.00%	4.56%	86.67%	Stretch Wing
Gerald Wallace	SF	45.43%	7.31%	.91%	9.13%	37.12%	Slash Wing

 

Crash is a slasher and that's a good thing given his poor three point shooting.  When Green is considered a small forward he also rates as a Slasher.  These numbers are based on his overall shooting tendencies, but looking at NBA WOWY Green shot a lower percent of his shots from three without Pierce on the court last year than with Pierce on the court, indicating he is likely remain a Slash Wing.

Hoop Data also listed Bogans as a small forward last year.  I kept him there because he may see more time there than in the crowded back court, especially if Wallace or Green miss any time.  In any case, Bogans is pretty much exclusively a three point shooter at this point.

Next let's look at the Guards. The break downs on the Guards were similar to the Wings.  Slashing Guards took 33% of their shots at the hoop and 23% from three, while Three Point Specialist took 19% at the rim and 49% from downtown.

PlayerName	Pos	Pct Shots at Rim	Pct Shots 3-9 Ft	Pct Mid Range (10-15)	Pct Shots from Long Two (16-23)	Pct Shot from Three	Group
Avery Bradley	PG	30.04%	4.71%	4.71%	34.08%	26.46%	Slashing Guard
Courtney Lee	SG	32.75%	6.27%	6.47%	23.92%	30.59%	Slashing Guard
Jordan Crawford	SG	26.46%	12.17%	8.99%	14.81%	37.57%	Slashing Guard
Marshon Brooks	SG	35.60%	20.43%	10.53%	16.10%	17.34%	Slashing Guard
Rajon Rondo	PG	40.44%	11.33%	6.44%	30.67%	11.11%	Slashing Guard

 

No secrets here.  The Celtics guards, as a group, are Slashers.  Jordan Crawford was the only Guard on the fence of Stretch Shot selection last year. Let that sink in...

In addition, only Courtney Lee  at 37.8% hit from three was above the league average for Guards of 36.3% per the NBA Geek.  A Rondo and Brooks back court would have spacing issues, to say the least, as they were justifiably shy shooting threes hitting only 24% and 27% respectively.  Bradley also struggled with his threes last year, though he had been much better the year before his shoulder surgeries.

Finally the bigs.  

PlayerName	Pos	Pct Shots at Rim	Pct Shots 3-9 Ft	Pct Mid Range (10-15)	Pct Shots from Long Two (16-23)	Pct Shot from Three	Group
Brandon Bass	PF	26.67%	8.83%	18.38%	45.77%	0.00%	Hybrid Big
Jared Sullinger	PF	49.55%	17.27%	5.91%	25.00%	2..27%	Hybrid Big
Jeff Green	SF/PF	38.61%	11.93%	5.23%	19.97%	24.26%	Slash Wing
Kris Humphries	PF	48.03%	15.46%	12.50%	23.36%	0.00%	Hybrid Big

 

Brandon Bass is interesting because he's close to being a Stretch Big without ever shooting from beyond the arc once. The Celtics also have rookies Kelly Olynyk and Vitor Faverani joining the front court this year, both of whom have some range, though I don't see Faverani as a true Stretch Big.  They also have the option to go small with Green or Wallace at the Four, though it's not an option I love, so forget I said it.

I don't really have the data at this point to indicate the actual importance of 'stretch' in offensive efficiency.  But, it looks as though the Celtics may be preparing to give it an interesting test, especially in the back court.  So, that's kind of cool, right?

Are Stretch Bigs A Good Idea?

Ok, I am not really going to answer that definitively. But, at first glance, it doesn't look it.

This is the third in my series on shot location in the NBA. The first two looked at guards and small forwards.  In this one I grouped Centers and Power Fowards together as 'bigs.' I used a Two Step K-Means cluster anaylsis to group Bigs based on their shot locations, without regard to shot making.

The idea of the 'stretch big' or stretch 4 is actually what first got me thinking about the project. Also the arguments over the value of guys like Tyson Chandler who almost never shoot from more than a few feet away from the basket and the ability of Omer Asik and Dwight Howard to play together.

The cluster analysis creates as many groups as seem to be present in the data, for both Guards and Small Forwards the analyses came up with two in each, one group centered around three point shooters and the other around shots at the rim. For both I named the two groups Slashers and Stretches.

For Bigs I came up with three groups that I am calling At the Rim Bigs, Hybrid Bigs, Stretch Bigs, at least until I think of better labels. This is the first analysis where mid-range shots and long twos were a significant factor in grouping players, because some of the bigs basically don't take any.

 

Here's how the clusters settled out in shooting location:

 

	COUNT	AVG Att at the Rim	AVG Att at 3-9 ft	AVG Att at Mid Range (10-15)	AVG Att at Long Two(16-23)	AVG Att of Three Pointer
At the Rim Big	35	67.31%	21.24%	3.58%	7.62%	0.36%
Hybrid Big	90	40.31%	16.47%	10.94%	29.88%	1.96%
Stretch Big	26	26.10%	9.32%	5.83%	19.36%	38.91%

 

The 'At the Rim Bigs' on average shot over 67% of their attempts within two feet of the basket, and over 87% within nine feet.  Don't bother guarding these guys at the elbow.

The best way to think of the Hybrids are as bigs with a little mid-range and long two game. The defining characteristic of the of the Stretch Big is the three ball.

Below I have some of the more prominent Bigs picked out by sorting for top ePts (effective field goal percentage times shots).  I had to add a couple at the end of the list just to get another At the Rim Big onto the list other  Dwight Howard.

 

PlayerName	Pct of Shots at RIm	Pct of Shots Lng 2	Pct Shots from 3	Group
LaMarcus Aldridge	24.12%	42.94%	1.18%	Hybrid Big
Blake Griffin	42.31%	26.15%	3.08%	Hybrid Big
David Lee	44.29%	25.00%	0.71%	Hybrid Big
Al Jefferson	27.33%	38.00%	1.33%	Hybrid Big
Brook Lopez	45.00%	20.71%	0.00%	Hybrid Big
Al Horford	37.14%	37.14%	0.71%	Hybrid Big
Ryan Anderson	22.31%	16.15%	53.08%	Stretch Big
Carlos Boozer	37.86%	26.43%	0.00%	Hybrid Big
DeMarcus Cousins	42.86%	28.57%	2.14%	Hybrid Big
Chris Bosh	31.67%	40.83%	8.33%	Hybrid Big
David West	27.69%	31.54%	2.31%	Hybrid Big
Tim Duncan	36.15%	35.38%	0.77%	Hybrid Big
Zach Randolph	43.85%	21.54%	2.31%	Hybrid Big
Dwight Howard	68.00%	4.00%	1.00%	At the Rim Big
Roy Hibbert	40.00%	14.55%	0.91%	Hybrid Big
Kevin Garnett	21.82%	48.18%	1.82%	Hybrid Big
Derrick Williams	38.00%	23.00%	26.00%	Stretch Big
Jeff Green	40.00%	21.11%	25.56%	Stretch Big
Tristan Thompson	50.00%	6.67%	0.00%	At the Rim Big
Dirk Nowitzki	10.00%	39.23%	22.31%	Hybrid Big
Nikola Pekovic	67.27%	3.64%	0.00%	At the Rim Big

 

Besides the fact that At the Rim Bigs don't, as a rule, seem to shoot much, a couple of things are kind of interesting. Two of the three stretch Bigs are pseudo-bigs, Jeff Green and Derrick Williams, both of whom should see a lot of time at the three this year.  Green because of the trade of Paul Pierce, and Williams because of the expected return of Kevin Love.

Also, Dirk just missed the Stretch category.  In fact, when the cluster was limited to two groups, he was the only player to switch groups becoming a Stretch with the Hybrid option eliminated.

Outside of volume of scoring the At the Rim Bigs dominate most of the efficiency stats.  They score more efficiently, in contrast to the Wings and Guards, where the Stretch groups scored more efficiently.  The At the Rim Bigs also rebound more and block more shots.  The Stretch Bigs lead in assist percentage and lowest turnover percentage.

Row Labels	Count	Av TS%	Av eFG%	Av ORB%	Av DRB%	Av AST%	Av BK%	Av TOV%
At the Rim Big	29	54.9%	53.53%	11.89	21.68	5.45	3.96	15.83
Hybrid Big	78	52.8%	49.12%	10.07	20.37	8.47	3.04	13.23
Stretch Big	24	52.4%	49.68%	5.95	16.76	8.65	1.77	11.17
Grand Total	131	53.2%	50.20%	9.72	20.00	7.84	3.01	13.43

 

The advanced one number player metrics for the most part value the At the Rim big guys more than the other Bigs groups.  The stretch Bigs are not well liked by the player metrics.  As with the guards, I am using Nathan Walker's xRAPM projection and a three year average Wins Produced per 48 from Arturo Galleti, while Win Shares and Daniel Myers' ASPM is a two year average weighted by minutes.

Row Labels	Count	Avg Proj xRAPM	Avg Wghtd 2 Yr ASPM	Avg WS/48	Avg WP 3 yrs
At the Rim Big	29	0.77	0.09	0.117	0.144
Hybrid Big	78	0.29	0.05	0.114	0.099
Stretch Big	24	-1.11	-1.42	0.080	0.058
Grand Total	131	0.14	-0.21	0.108	0.102

 

Since I combined the Centers and Power Forwards, it was worth it to look the two cardinal positions separately. There are some differences between the positions, especially the relative lack of Stretch Centers, which appears to be a good thing because the stats of the two I found weren't very good. The ratio of At the Rim and Hybrid Bigs is significantly closer.

The At the Rim Centers lead in most efficiency categories, including a gaudy 55.44 average effective field goal percentage.

Positon

Center

 

Row Labels	Count	Av TS%	Av eFG%	Av ORB%	Av DRB%	Av AST%	Av BLK%	Av TOV%
At the Rim Big	19	56.3%	55.44%	11.89	21.07	5.34	4.27	15.91
Hybrid Big	36	52.5%	48.98%	10.52	20.85	8.40	3.46	14.29
Stretch Big	2	53.4%	51.40%	5.10	17.00	12.55	1.45	14.90
Grand Total	57	53.8%	51.22%	10.78	20.79	7.53	3.66	14.85

 

The metrics all agree, Stretch Centers are a bad idea.  Though the fact that one of them is Byron Mullens doesn't help.  Nor does it that other, Boris Diaw isn't really a Center.

Position

Center

Row Labels	Count	Avg Proj xRAPM	Avg Wghtd 2 Yr ASPM	Avg WS/48	Avg WP 3 yrs
At the Rim Big	19	0.97	0.48	0.127	0.150
Hybrid Big	36	0.35	0.09	0.110	0.092
Stretch Big	2	-1.80	-2.02	0.065	0.010
Grand Total	57	0.48	0.14	0.114	0.108

 

The At the Rim power forwards are less dominant in scoring efficiency, but still dominate the boards and blocks.

Position

Power Forward

 

Row Labels	Count	Av TS%	Av eFG%	Av ORB%	Av DRB%	Av AST%	Av BK%	Av TOV%
At the Rim Big	10	52.1%	49.90%	11.90	22.84	5.65	3.38	15.67
Hybrid Big	42	53.1%	49.24%	9.69	19.96	8.53	2.68	12.33
Stretch Big	22	52.3%	49.53%	6.02	16.74	8.30	1.80	10.83
Grand Total	74	52.7%	49.41%	8.90	19.39	8.07	2.51	12.33

 

The metrics for the Power Fowards are very close between the Hybrid Bigs and At Rim Bigs, the Stretch Bigs still don't fare well:

Position

Power Forward

	Values
Row Labels	Count	Avg Proj xRAPM	Avg Wghtd 2 Yr ASPM	Avg WS/48	Avg WP 3 yrs
At the Rim Big	10	0.38	-0.64	0.098	0.134
Hybrid Big	42	0.24	0.01	0.117	0.106
Stretch Big	22	-1.05	-1.36	0.082	0.062
Grand Total	74	-0.12	-0.49	0.104	0.096

 

The next step, eventually, is to look into whether Stretch has an independent effect on offensive efficiency. The basic idea will be to look at line up Stretch against expected efficiency.

Two Ways to Wing It

In my last post I looked at shot selection and Guards.  This time I am going to look at Wings, AKA small forwards.

Again, I used a two step Cluster analysis based purely on shot locations without regard to how good the player was at making shots from any particular spot.  I only used players that played more than 150 minutes in the 2012-2013 season to limit complete noise.  At some point I will probably need to redo the cluster analysis with more years of data if I ever want to do more analysis with it.  But, like the Guard analysis this one gave me some interesting starter results.

Just like the Guards, Wings can be said to fall into clusters of players who try to get to the rim, Slash Wings, and three ball shooters, or what I am calling Stretch Wings. For the most part the cluster analysis output was pretty intuitive. Here are a couple prominent Slash Wings and Stretch Wings selected by top ePTS (Effective Field Goal percentage times shots).

PlayerName	Pct of Shots at Rim	Pct of Shots From 3	Cluster
LeBron James	40.59%	19.41%	Slash Wing
Kevin Durant	25.29%	24.12%	Slash Wing
Carmelo Anthony	29.55%	28.18%	Slash Wing
Paul Pierce	24.29%	35.71%	Slash Wing
Chandler Parsons	38.33%	43.33%	Stretch Wing
Thaddeus Young	50.00%	0.83%	Slash Wing
Danilo Gallinari	25.83%	42.50%	Stretch Wing
Nicolas Batum	20.91%	55.45%	Stretch Wing
Kyle Korver	3.75%	70.00%	Stretch Wing
Martell Webster	23.75%	53.75%	Stretch Wing
Jimmy Butler	40.00%	21.67%	Slash Wing

 

LeBron shot over 40% of his shots at the rim in the regular season according to HoopData, no wonder Popovich tried to pack the paint during the finals. Durant is also more of a Slasher than one might think, though clearly less than LeBron.  Durant took 25% of his attempts at the rim and 24% behind the arc.  By contrast Martell Webster, Kyle Korver and Batum shot over 50% of their attempts for three. Paul Pierce is probably the closest to switching clusters, which may actually happen next year as he gets a year older and is a little less able to convert at the rim.

The amount of 'stretch' appears to be pretty consistent between Guards and Wings.  Stretch Wings shot an average of over 50% of their shots from outside the arc, very close to the Three Point shooting Guards.  Slash Wings took 34% of their shots at the rim, just like the Slasher guards.

	COUNT	AVG Att at Rim	AVG Att at 3-9 Ft	AVG Att of Mid Range (10-15)	AVG Att of  Long Two (16-23)	AVG Att of Three Pointer	AVERAGE of eFG
	382	33.13%	12.15%	7.42%	23.30%	23.35%	48.12%
Slash Wing	51	34.97%	11.12%	7.70%	24.14%	21.35%	49.71%
Stretch Wing	31	19.45%	4.60%	3.18%	15.21%	56.03%	51.27%
Grand Total	459	32.50%	11.58%	7.20%	22.90%	25.11%	48.48%

 

There were also similarities in the non-shooting statistics the Stretch Wings had significantly better effective field goal percentages and better true shooting percentages, though difference isless dramatic because Slash Wings get to the line more often. The Slash Wings had better rebounding numbers particularly on the offensive end.

 

	COUNT	Avg TS%	Avg eFG%	Avg ORB%	Avg DRB%	Avg AST%	Avg TOV%
Slash Wing	39	52.7%	49.1%	5.84	16.09	10.79	11.95
Stretch Wing	25	53.7%	51.2%	3.20	13.08	10.03	11.15
Grand Total	64	53.1%	49.9%	4.81	14.91	10.50	11.64

 

As far as the advanced 1 number metrics go all of them liked the Slash Wings just a bit more, but overall they were fairly even. As with the guards, I am using Nathan Walker's xRAPM projection and a three year average Wins Produced per 48 from Arturo Galleti, while Win Shares and Daniel Meyer's ASPM is a two year average weighted by minutes.

	COUNT	Avg Proj xRAPM	Avg Wghtd 2 Yr ASPM	Avg WS/48	Avg WP 3 yrs
Slash Wing	39	0.17	0.07	0.102	0.109
Stretch Wing	25	-1.00	-0.70	0.090	0.105
Grand Total	64	-0.29	-0.23	0.097	0.108

 

Of course, the fact that both LeBron and Durant fall into the Slash Wing cluster helps the group scores on the player metrics.

I think both the Guards and the Wings look like there are probaby two fairly distinct styles of back court play.  One leaning on shooting ability and stretching defenses, the other more on raw athleticism.

Next I will write up my findings on the Bigs.  The Bigs are interesting since the Cluster analysis indicated three clusters, that I dubbed At the Rim, Hybrids, and Stretches.