Tag Archives: Miami Heat

Career shot and point distribution charts: Ray Allen

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Lately I’ve been getting back to looking at shot and point distribution charts, ones of players still in the Finals and a few other greats over their entire careers. The charts are the ones I’ve used for players and teams in previous posts, tracking shots on NBA.com from the restricted area, in the paint non-restricted area, mid-range, corner 3, above the break 3, and free throws, but I’ve recently added a few more charts to the mix. This post is basically a trial version of them with Ray Allen’s being the ones tested, and if it turns out all right I might turn it into a blog series over the off-season.

There will probably be some tweaking to do, but for now I plucked Allen’s yearly numbers from NBA.com which somehow has shooting stats and charts starting not at 2001 but 1997, though I don’t consider the ones from ’97 to be all that accurate thanks to the shortened three-point line back then. We get to work with every other season of Allen’s career, though, and maybe other notable players from the late-90s to today.

In past posts, I included GIFs and/or screenshots to show changes in charts from each season, player or team, and while I’ll use each of those for this post I’ll also use galleries so readers can cycle through charts at their own pace. The galleries also provide a little animation between each season to help show shifts in shooting and scoring.

Hopefully all of that isn’t confusing, but I can be pretty lazy with explaining things. For those who haven’t looked at these kinds of charts before, maybe just looking at them is easier to understand anyway.

Allen’s attempts over his career from both the field and the free throw line were what I looked at first, and below is an example of the four different charts I made for that section. This one is from 1998’s available stats:

1998 rayface

My apologies if screenshots look a bit blurry. They look much sharper when clicking to enlarge.

The first 3 charts are mostly similar with FGA distribution missing free throws, of course, but that one and attempts per 36 minutes compliment Allen’s first chart (attempts per game) best in his later years when his minutes and total attempts decline.

The last chart, attempts per 36 minutes compared to the player average, is something I’ve recently been playing with, though it doesn’t adjust for pace. In 1998, Allen took nearly six mid-range shots per 36 minutes, but compared to every other player’s numbers it was more standard than his attempts from the corner three, where he took twice as many attempts/36 minutes as the average player. This is a pretty common theme over Allen’s career.

Below are the rest of Allen’s attempts in a photo gallery. It should be on auto play, so I guess in way it’s still a slow-moving GIF, but it can be paused any time:

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Where Allen shoots from each location has obviously changed over the years, once heavy on mid-range shots and almost always making a ton of either above the break threes or corner threes compared to the player average.

Below are the differences between his second and 18th season of his career (1998 and 2014):

1998-2014 rayface

Allen still takes a similar amount of above the break threes per 36 minutes as he did in 1998, but now he attempts about 3.5 times as many corner threes, half the free throws and shots in the paint (outside the restricted area), a third from mid-range, and about three-fifths as many around the rim. It also shows how three-happy the league has become with Allen’s above the break 3s/36 minutes more standard now than compared to the late-90s.

Some of Allen’s changes are consistent with how his FGA distribution has changed with each team. Below is a GIF putting his combined point distributions for each team together (click to enlarge):

Allen on Make A Gif

Along with the roster around him, age most likely contributes to Allen’s shift in FGA and FGM distribution. With the Heat, it also changes a bit when he’s in lineups with or without LeBron James:

ray w-o lebron

 

I also looked at Allen’s biggest changes in FGA distribution from season to season, basically by a simple subtraction of percentages. I took 1998’s percentages and subtracting them from 1999’s, for example, then made every change in percentage positive and adding each location’s numbers up.

This is what each season looks like, sorted by biggest total changes to smallest:

ray fga change overall

Visually, that looks correct when looking how the largest and smallest changes stack up (as usual, click to enlarge if you’d like):

ray fga change large 2010-11

Allen took more of his attempts from mid-range in 2011 despite having a fourth straight decline in usage rate, but he also took a higher percentage of his attempts from the corner three and, as shown much further down in this post, he was way more accurate there than in 2010.

Mid-range and non-restricted area paint attempts are the biggest differences in 2004 and 2005, but everything else looks the same otherwise. When comparing changes in Allen’s FGA distribution in 2003 before and after the trade that sent him from Milwaukee to Seattle, his chart hardly moves and would be the lowest compared to season-by-season changes, totaling to a 6.53% change. (Threes were a different story. More on that later.)

Simply subtracting doesn’t take into account the shots Allen takes least (depending on the season, either corner threes or in the paint non-RA shots) and most (either shots around the rim or above the break threes). It’s often a bigger deal if a player or team takes five percent more of field goal attempts from the corners than around the rim, and I tried a couple ways to balance for that but hit snags since they’d be hopeless if Allen (or any other player, or team) took zero percent of their shots from one of the five locations. Also, I’m terrible at math and maybe over-thought the whole process, so if there’s an easy way to calculate that stuff I’d love to hear it since I’m looking into shooting and scoring by teams over each season, among other post ideas.

To go back to mid-range and other two-point shots, though, it may or may not be surprising that Allen took as many as he once did, though that can be said about the league as a whole. Mid-range shots made up a great chunk of Allen’s shots for a long time, and about 20 percent of his attempts as a member of the Heat still come from that area of the floor, but that’s down from what was anywhere from 25 to over 40 percent as a Buck, Sonic, or Celtic.

Looking at his shot charts at NBA.com that split into several locations, less of his twos come from the wings now than they did as a Sonic or Celtic, but there’s still a similar amount from the baseline where, for most of his career, Allen took the most of his jump shooting twos.

Below is a breakdown of Allen’s 2PA distribution according to spots on NBA.com’s shot charts. I gave locations names that are hopefully self-explanatory, but can be found here just in case:

2pa dist

As usual, click to enlarge. Very helpful!

Allen’s baseline shots are the standard ones from being run off the three-point line and getting separation off screens, but quite a few come from trying to get space off the dribble when the shot clock is winding down. He doesn’t get all that far, painful to watch when he was once so good at attacking off the dribble (one example here), but he doesn’t need much space to get his beautiful shot off anyway.

Even if Allen seems to struggle a bit more in getting to the rim off the dribble, he’s still having career-lows or near career-lows in attempts/36 minutes from all the 2PA locations on NBA.com’s shot charts all while having a career-high in corner three-point attempts/36 minutes and percent of his FGA being corner threes. His mid-range shots/36 minutes have gone from around or above league-average in his first 15 charted seasons to two-thirds and nearly half the average in 2013 and 2014, respectively, and he shot nearly three times as many corner threes per 36 minutes as the average player this season. The leaders from the corners each season often take four to five times as many as the average player, though, sometimes even more when looking 10+ seasons back. James Jones led all players this year by taking 5.8x corner threes/36 minutes, but in 2005 Donyell Marshall took 7.1 times as many, then followed it up with 6.0x and 5.8x as many while Cleveland in 2006 and 2007, respectively. Fun times.

To touch on free throws, Allen’s charts almost always show him above the player average in free throw attempts/36 minutes during his prime which, like his attack off the dribble, feels underrated considering his status as a killer shooter.

I found his free throw and three point rates to be pretty interesting, even though they seem common in both his age and that when the free throws lower the threes often rise:

ft and 3p rates

I’ll touch more on threes later when chiming in on some thoughts on Allen’s scoring distribution, which I looked at in a similar way to shot attempts but with some tweaks. Below is a gallery visualizing four scoring stats from 1998 to 2014, but with some changes in charts from attempt distribution:

  • Points per game from the six spots on the floor.
  • Effective field goal percentage from all but free throws.
  • Point distribution but this time including free throws, unlike in the first gallery of graphs.
  • How Allen’s points/36 minutes from each spot measure up with the league average (per player).

Anyway, flip through the charts if you’d like:

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There are some hopefully cool things to look at. Going back to mid-range shots, below is a similar graph like before but covering 2PM distribution:

2pm dist

And a gallery comparing 2PA and 2PM distribution. Flip flop if you’d like:

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Season by season, Allen’s changes in point distribution from largest to smallest are a bit different from changes in FGA distribution, where the largest for that was from 2010 to 2011 and the smallest from 2004 to 2005:

ray point dist change overall

Understandably, the smallest change in point distribution was in Allen’s second season with the Heat. The largest change was not after a trade in 2003 or 2007 or going from the Celtics to the Heat in the summer of 2012, but from his seasons as a Buck in 2001 and 2002. 

Again, with simple subtraction, that all looks correct visually:

ray pt dist big and small

From 2001 to 2002, Allen scored less from the free throw line but upped his three point rate from .357 to .460. He took 3.67 times the average player’s corner 3s/36 minutes, ranking tenth minimum 1,000 minutes. For above the break threes (he attempted 3.32x the player average), he was only behind Antoine Walker (3.64), Jason Williams (3.70), and Tim Hardaway (4.22).

No shame in falling just behind those three players in anything related to threes, and Allen’s got pretty nuts when flipping through the 1998-2003 section of the scoring gallery shown above. Maybe suspected from the 2002 charts: Allen placed in the top 10 that season in both threes attempted and made for both the corner and above the break three. It started a string of top 10 finishes in the latter location:

ray 3pa-36 min leg avg

I thought Allen’s threes deserved a gallery of multiple charts, featuring both three-point attempt and made distribution from the five spots available on NBA.com’s shooting charts, another with accuracy from those locations, and a line chart tracking the shooting swings each season.

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1998, 2002, and 2010 look almost perfectly balanced in attempt distribution from each spot, while some weirdly (for a right-handed shooter, anyway) show a great deal of threes from the right wing. Also, to go back to the graph of his shots with and without LeBron on the floor, it’s no surprise to see Allen taking more of his threes from the corner as a member of the Heat. Last year he teed off from the left side, but this year it’s from the right. Attempts from straight away are just about gone and weren’t ever a big deal anyway.

Below is a GIF of Allen’s combined distributions during his Buck, Sonic, Celtic, and current Heat career. The differences in attempted and made threes are pretty minor (click to enlarge):

A4ZqD7 on Make A Gif, Animated Gifs

Followed by that GIF are threes in 2003 before and after the trade that sent him from Milwaukee to Seattle. Quite a change midway through the season:

ray 3pa dist mil-sea 2003

Again, it’s kind of weird to see a right-handed shooter take a bunch of his attempts from the right wing, but Allen went through shifts from just about everywhere but from straight away. Shots from the corners and from straight on barely changed, at least in attempt distribution.

Lastly, Allen’s assist percentage on threes over the last two seasons are some of his highest ever. Among other notes, the right corner was a flat 100 percent for six straight seasons with 114 assisted threes during that stretch:

ray 3 ast%

Allen’s long been one of my favorites to watch from the times his NBA Live ’98 player torched me to how unfair he can make Miami’s offense just by standing in a corner. His charts were a test to see how they look in a blog post and if readers would be curious about ones for other players. A lot of other greats over the years have some cool charts, or maybe I’m biased because I was so curious about them to begin with. Probably the latter.

Some other thoughts:

  • I could’ve added playoff shooting and scoring, but was worried it would clutter this post even more.
  • Clutter…were there too many charts? A lot of them were player dependent, though. As much as I’d like to, I’d probably refrain from 3pt charts for someone like Tim Duncan. Maybe throw in a game of Solitaire instead.
  • The charts obviously don’t tell everything, like I can’t even put together SportVU-related shooting charts because the numbers don’t add up to Allen’s total points. I could try fooling around with them for other players, though, and see if something’s presentable.

Oh well. Curious what others think of this post and if any tweaks could’ve been made. This is definitely a trial version of posts I had in mind for other players and was also a post meant to shake off a ton of rust over the last few weeks.

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East vs. West Week 23: Counting down to the last of the 450 games

Another week, another updated week-by-week breakdown:

The most exciting non-conference game of the week had to go to Minnesota traveling to Miami and winning in double overtime, much of it thanks to Kevin Love’s ridiculous shot making and Ricky Rubio carving up a hyper Heat defense. LeBron James and Chris Bosh weren’t too bad for the Heat, though, among other players. Dwyane Wade didn’t play because of a lingering hamstring injury.

Houston also lost their last two non-conference games, falling to the Nets and Raptors. Aside from all but guaranteeing the Rockets the fourth seed in the West, it also meant that San Antonio clinches the best record against the East at 24-6 while the Lakers and Kings are tied for the worst at 12-18 each. Neither hold a candle to Milwaukee’s 3-27 record in non-conference play, however, and the Bucks, 76ers, Magic, Celtics, and Pistons are collectively 100 games under .500 against the West, a combined record of 24-124 with the 76ers and Pistons finishing up the season with Memphis and Oklahoma City, respectively.

Maybe that’ll lead to an uptick in the West’s point differential, which I also updated from last week’s post. It hardly changed, but probably worth noting where it ranks in non-conference play since 1997 anyway:

Lastly, here’s the 212,749,834,9a8,943,f92th reminder about the West’s possible record-breaking winning percentage: They’d have to finish their last five games 4-1 to tie 2004’s 63.3 winning percentage and win all five to break it.

Below are those final non-conference games this season:

The last three games look very winnable for the West while the first two are something of a toss-up. Maybe they’ll split? Miami and Minnesota will be playing the tail-end of back-to-backs, however, with the first games against Brooklyn and San Antonio, respectively. Not the easiest two consecutive games for either team, especially when Minnesota has been without Nikola Pekovic, Kevin Martin, and about half the roster recently.

Updated point distributions in graphs

About a month ago, I fiddled around with graphs visualizing how many points a team scores from specific shot locations. While it was something I enjoyed working on, there wasn’t a whole lot of space to include both GIFs and pictures while looking at the difference between a squad’s offense and defense. Back then, I went with GIFs but now I’ll include some photos of the graphs with updated percentages.

I also left off effective field goal percentage this time around so I wouldn’t flood a post with a ton of huge pictures. What’s left is a percentage of points a team scores at six areas on the floor: restricted area, in the paint (non-RA), mid-range, corner three, above the break three, and free throws.

In the future I’ll experiment more with these types of graphs, but for now these are the ones for each team over the entire season, both on offense and defense. They’ll probably appear blurry but clicking on the picture, then zooming in helps a ton.

Also, below the picture are links to team graphs for offense only and defense only. Enjoy, hopefully:

offense-defense

Offense-only graphs.

Defense-only graphs.

Similar to what I mentioned in the first post, the graphs for the best and worst offenses and defenses just aren’t the same as one another. Take the Heat, Clippers, and Mavericks as the top three offenses, for example. Thanks to LeBron James, Dwyane Wade and Chris Bosh, Miami scores a ton of their points in the restricted area — 36.5 percent, to be exact and fourth-highest in the league. Meanwhile, the Clippers are near the middle in point distribution from a few locations, but with the help of Blake Griffin they get just under one-fifth of their points from the free throw line. Dallas, with a nightmare of a scorer to gameplan for in Dirk Nowitzki, is weirdly balanced in all locations as they don’t appear too high or low in any of them.

Defenses are more similar as Indiana and Chicago both concede a bunch of points from mid-range. The Spurs and Warriors, in third and fourth place in defensive efficiency, respectively, have similar mid-range portions of the graph but allow more points in the paint (non-RA) region than the top two teams. Overall, it would seem like offenses would want their offenses to shift as far to the left side of the graph as possible and the opposite for defense.

I’ll actually admit these graphs are slightly misleading, one reason being that corner threes don’t jump out in them but are nonetheless important to team success. Attempts per location looked about the same and points per location was slightly different when comparing offense to defense. In the future, though, I’ll sort by the latter stat but I had a really weird time calculating it last night and this morning and ran out of time to put those graphs together.

Lastly, below are two tables of the top and bottom five teams in point distribution for each shot location. One table is for offense and the other for defense, starting with the former:

All stats, including ones used for tables and graphs, are according to NBA.com. 

Solid final quarter of season a common trait among champions

Every team has a peak and valley during their season, even the 76ers who started the season 3-0 but are now dealing with a winless five-week stretch. For a team looking to grab a top-3 pick in this year’s draft, that’s probably the right time to find their high and really, really low points of the season. As for the title contenders it should be the opposite, though a few teams are going through some recent woes whether it’s from a difficult stretch of games (Miami dealing with Joakim Noah and Boris Diaw), adjusting after a trade (Indiana with Evan Turner and other problems) or whatever else factoring into a slump (it’s all Russell Westbrook’s fault!).

History has shown that it’s fine to experience those downswings as long as they don’t carry too deep into March or April. Over the past 30 years, 26 of the eventual champions played .600 ball or better in the final quarter of the season. Also worth noting is that, with the help of Basketball-Reference, 26 of the last 28 champions finished the same stretch of games with a positive net rating.

Below are the last 30 champions with their records, offensive and defensive efficiency, and net rating over the final fourth of the season. Highlighted are the outliers. All stats are according to Basketball-Reference:

The outliers:

1995 Houston Rockets

Hakeem Olajuwon missed eight of the final 20 games with the Rockets going 3-5 over that stretch. Clyde Drexler played out of his mind during Dream’s absence, averaging a stat line of 30.0/9.3/5.5/2.4/0.9. He also made over 30 percent of his threes, something not totally guaranteed throughout his career.

In the 12 games Olajuwon played, Houston squeaked out a positive net rating of 0.1. Also, Zan Tabak played in only eight of the last 20 games. Absolutely has to be noted.

Orlando finished 9-11 as well, though they had efficiency splits of 114.2/112.3/+1.9. Long live the mid-90s Magic jerseys and Penny Hardaway.

2006 Miami Heat

Dwyane Wade missed three games while Shaquille O’Neal missed five. Each sat out the last two games, paving the way for a Michael Doleac-Wayne Simien-Antoine Walker-Dorell Wright-Jason Williams starting lineup. Miami lost both. Fun times.

Dallas also finished 11-9 that season and Dirk Nowitzki played 81 games, so what might be their best excuse? Their schedule wasn’t the greatest as they played the Cavaliers, Clippers, and Kings each twice and the Jazz, Nets, Nuggets, Pistons, Spurs, Suns, and Wizards each once. That’s not exactly the most murderous row of opponents but a mix of title contenders and playoff-worthy teams jousting for seeding nonetheless. Also mixed in the final 20 games were the Hornets with a rookie Chris Paul, the Magic with a young Dwight Howard, and the Warriors who…they stunk down the stretch, sure, but we all know what happened next year. Regardless, that’s 19 of the final 20 games. Joe Johnson and the Atlanta Hawks were the other squad Dallas faced (and defeated).

2010 Los Angeles Lakers

Andrew Bynum missed the last 13 games of the season while Kobe Bryant missed four. Pau Gasol was awesome down the stretch, though, averaging a line of 24.2/12.9/3.8 with 2.2 blocks.

2012 Miami Heat

A lockout-shortened season where resting core players was rarely a bad move. LeBron James, Wade, and Chris Bosh made only 31 appearances out of a possible 48, making way for front courts of some combination of Eddy Curry, Dexter Pittman, Udonis Haslem, James Jones, and Shane Battier. Arguably more fun times than 2006.

It might seem standard for solid teams to play any fourth of the season with a positive net rating, but that’s not exactly true. Using the net ratings from NBA.com, below are 10 notable teams of the last 15 seasons that dipped into the negatives over the final quarter:

Sure, a lot of those teams were pseudo-contenders. The 2001 Sixers, for example, were never going to win four games against a Lakers squad that mowed over their first three opponents with an offense-defense efficiency line of 113.0/96.3/+16.7, but maybe sputtering down the stretch contributed to those teams not being among the league’s elite during their respective seasons. As for the 2010 Lakers and 2013 Spurs, they clearly stand above the eight other teams in terms of talent and confidence they’d make a deep run in the postseason.

Some team over the next five weeks is bound to hit a rough patch. Maybe they’ll right themselves in time for what should be a hell of a postseason, but they could also end up as a team to write off whether it’s in April, May, or possibly even June. Below is a breakdown of the remaining schedules for a mix of title contenders and ones I don’t think will go that far in the playoffs, but included them anyway just because. Each team also has their own sheet with their last 20 games, including the (color-filtered) difficulty of their opponents. It’s a fricken rainbow.

Every team seems to have a few games in a row against teams competing (or about to compete) for lottery balls, though teams out West appear to have more daunting schedules overall.

There’s always the chance for an outlier like four of the last 30 seasons, though, but the Clips at least look well on their way to fit the minimum requirements to be labeled as a contender. That’s at least in regards to finishing steady.

But to include one last table, ending the last quarter of the season over .600 and with a sexy net rating doesn’t always guarantee making the deepest of runs in the playoffs. Below is a table of the best nets in the final fourth of seasons since 1997, according to NBA.com:

If that final table makes a team finishing hot suddenly worrisome, it probably shouldn’t. When looking at net ratings provided by Basketball-Reference in the very first table, champions often had very respectable ones. Chicago’s from 1996 is unreal.

Anyway, a lot still needs to be addressed regarding quite a few playoff teams. Let’s see how the last five weeks play out. The next two days should especially be entertaining thanks to a ton of good matchups.

For related posts, check out drastic movements in the lottery over the last two months of the season and what 20 wins before Christmas means in the West.

Shot locations and shooting efficiency in graphs

LeagueAvg

The percentage of a team’s points, sorted by location.

Sometimes I get bored and look for unusual topics to post about, which eventually leads to spending too much time on something like making graphs revolving around scoring and defense.

The graphs I made are pretty basic, I suppose. I might have fun with more over the weekend but I’ll just show what I fooled around with already. Basically, there are four different graphs for every team: team point distribution across six locations, team effective field goal percentage in five of those spots, and the same two for a team’s defense. All of the stats I used were from NBA.com.

The point distribution graphs show what percentage of a team’s points come from the restricted area, paint not in the restricted area, mid-range, the corner three, above the break three, and free throws. I experimented with field goal attempts per spot, but the graphs compared to point distribution looked about the same.

Below is a GIF of all 30 teams, sorted in alphabetical order. (The picture above the first paragraph was the league average for point distribution.)

Team points on Make A Gif

I can certainly post individual team graphs at another time, but I chose not to here for the sake of the amount of space it would take up.

That doesn’t mean we can’t compare some, though.

Portland and Houston are quite a contrast in styles, given one’s love for the mid-range jumper (and for a very legitimate reason) while the other neglects that part of the floor.

They both value the three equally, however:

Portland-Hou on Make A Gif

Philadelphia is somewhat similar to Houston except they rarely score from the corner three and their mid-range game is more prevalent. Also, they might have the right idea on offense but as we’ve seen recently they don’t score all that well and they struggle to defend. More on that in a bit. For now: POOR THADDEUS YOUNG.

Among other similarities are Atlanta, Brooklyn, Golden State, the Lakers, and Toronto all looking alike too.

Starting from the restricted area and going clockwise, the leader in points distributed to each category are: the Detroit Pistons (41.72%), Memphis (14.21%), Boston (22.62%), New York (21.41%), Miami (10.68%), and Houston (20.47%).

Below are graphs for where a team allows points:

Defense Distribute on Make A Gif

Among other teams, Indiana’s offense and defense are quite similar, for better or for worse.

The leaders in each category, starting at the restricted area and going clockwise are the Lakers (36.65%), Golden State (12.14%), Indiana (23.19%), Oklahoma City (18.98%), Miami (8.39%), and Phoenix (19.95%).

Effective field goal percentage from those areas of the floor — minus the free throw line — were another batch of charts I made for each team for the heck of it. You can really see where some offenses are great and others struggle from, though it won’t paint the clearest picture. The same goes for defense.

Below is offensive EFG%:

Team EFG% on Make A Gif

Miami’s efficiency is pretty freaky, especially when compared to Philadelphia’s. It helps when LeBron James, Dwyane Wade, and Chris Bosh can score at the rim far above the average accuracy all while having shooters playing alongside them.

For Philadelphia, it doesn’t help when they’re a strong candidate to “Bobcat” and very few of their players can stretch the floor consistently, and Michael Carter-Williams isn’t one of them. Like mentioned earlier, the 76ers have a good idea on where to score on offense while playing at a frantic pace, but they don’t score anywhere near enough and their defense has fallen off a cliff.

Below is their contrast in their own EFG% and their opponents’:

philly on Make A Gif

Possibly noticeable in the GIF of offensive EFG% is Chicago, who also struggles mightily on offense but their defense holds its own.

Miami’s another interesting case. They can light teams up from the corners but that’s also a place opponents have shot well from.

Below is a GIF of the 30 teams and their defensive EFG% at certain spots on the floor:

Def EFG on Make A Gif

I also made GIFs of teams sorted by their offensive and defensive ratings, but overall there wasn’t a clear difference in those highly efficient in one area of the floor and those who struggle. Portland, for example, scores a bunch from mid-range with the help of LaMarcus Aldridge, but they’re also a top-5 team in offensive efficiency. On defense, the percentage they allow at the rim is quite good but they allow a ton of attempts from that area of the floor. Defense is weird.

In the future, I might fool around a little further with these kind of graphs for both teams and players. The ones listed here are pretty basic and obviously won’t paint a clear picture on offense and especially defense, but hopefully they were fun to look at and compare team by team. As (sort of) mentioned earlier, a page with every team’s graphs wouldn’t take long at all, though I chose not to include them here because of the amount of space it would take up when combined with GIFs.

Any thoughts, even if the graphs weren’t all that cool to look at, or requests on these are certainly welcome. Feel free to chime in.

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