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NBA HD: Counting the And 1

April 16, 2010 in by with 3 Comments

In last week’s post, using regression analysis I looked some of the players who get blocked more than they should given how they often they get to the rim for their shots.  I also flipped it around and looked at who avoids the block while also taking into account how often they get to the rim.

We can look at another part of the game that often gets overlooked: the And-1.  Most NBA websites don’t track how often a player gets an And-1 but Hoopdata tracks every single And-1 that has occurred since 2006-07.   To clarify, the And-1 that Hoopdata presents does not require the bonus free throw to be made for it to be classified as an And-1.  Dwight Howard and Shaquille O’Neal should be very thankful.

So why should we care about And-1s? With And-1 numbers, we can find the strongest finishers in the game.  It takes a guy who can withstand hard contact and use his strength to convert the basket.  Additionally, it takes not only strength but a strong vertical to buy time to redirect an altered shot.  With this in mind, let’s take a look at the And-1 leaders as measured by And-1 percentage (And1%) which is simply percentage of total FGA that end in an And-1 (20 minutes per game, 20 games required).

I’ll note that the Hoopdata dataset has kept each stat line for traded players so Brendan Haywood’s And1% above covers only his time in Washington.  Given Dwight Howard’s superhuman athleticism and strength, it should come as no surprise that he gets And-1s more often than any other player.  This list features mostly large centers (Haywood, Oden, and Shaquille O’Neal) as well as some more athletic bigs (Smith, Stoudemire, and Varejao).  I’m surprised by Varejao’s ranking on this list but he has a way with selling contact to the referees.

How about the players who get the least And-1s?

Yup, Jarvis Hayes has yet to get an And-1 this season in over a thousand minutes of playing time.  Steve Blake has accumulated just two this entire season.  This ranking answers the question “Which regular gets And-1s the least often?”  but I’m not satisfied with this Q&A.  Why?  These guys don’t take the ball to the rack.  Ever.  This might provide some good fodder for bar conversations (you’re welcome) but I’m more interested in taking this further.

Perhaps this is a more revealing question: Given how often a player gets to the rim, how often should he be getting And-1s?

It’s nearly impossible to consistently get And-1s on the perimeter so a player who strictly plays at the basket will automatically tally a few And-1s just by habitat.  For example, does Brendan Haywood have a And-1 skill or does he simply shoot nothing but gimmes around the basket?  In order to get closer to our quest, I drew up a scatter plot that charts And 1% and At Rim percentage (the percentage of a player’s shots taken at the basket).

Just like last week, we’re looking for players who separate themselves from the norm (as illustrated by the trendlines.)  Steve Blake and Jarvis Hayes’ lack of And-1s can be directly attributed to the fact that they never shoot near the rim where they can draw contact.  Likewise, they find themselves near the trendline.

The trendlines offer us the ability to derive an expected And-1 percentage (eAnd1%) through regression analysis.   Given the position and appetite for at rim shots, how often should they get And-1s? Using this expected And-1 percentage, we can really find the strongest finishers and not just the ones who play near the hoop.

So I have gone ahead and sorted each player by their eAnd1% differential. First, the ones who beat the model’s predictions the most.

Well, it seems as though Dwight Howard doesn’t care for my adjustment; he still tops the list.  As a center with 58.2 percent of his shots coming at the rim, we would expect that his And-1 percentage would be 4.3 percent but he’s nearly double the expectation.  Actually a couple players double their expectations, one of which is unsurprisingly LeBron James. Perhaps the most surprising member of this ultra-exclusive club is Kevin Martin who in Sacramento posted an And-1% that one might expect for a big man.  His And-1 rate is superb for a player who only took one fifth of his shots at the rim.  In fact, 16 of Martin’s 37 makes at the rim in Sacramento earned him a shot from the charity stripe.  Now in Houston, Martin is an extremely underrated finisher at the rim especially after considering his thin frame.  Rockets fans must love having two of the toughest finishing guards in the game with Martin and Kyle Lowry in the backcourt.  It’s also worth noting that Lowry was also acquired in a midseason trade executed by GM Daryl Morey last year.

Now that we have identified the strongest finishers, what about the softest ones?  These guys get fewer And-1s than we would expect given their position and shot taste.

With the regression, the basket allergic guards who dominated the previous list have all disappeared.  Instead, we have bigs who get fewer And-1s than we would expect.  Is Shawn Marion the softest big in the game? Well, not exactly.  Maybe it’s more appropriate to say he’s the softest big who still shoots at the rim.  Plenty of bigs would rather sit on the perimeter than take it to the rim (I’m looking at you Channing Frye!).  Nonetheless, Marion has the fifth highest blocked percentage among regular small forwards (7.8) and only takes 1.8 free throws per game.  Not exactly a thunderous presence down low.

Elsewhere, it’s amazing to me that 6-6 Chuck Hayes has more And-1s this year than Samuel Dalembert despite getting guarded by the same personnel.  If I were Hayes, I would remind Dalembert every time they play eachother, which unfortunately isn’t often.

As I mentioned in the last post, it might be a worth a look to add predictor variables to At Rim Pct.  I could see height, free throw percentage, and assist percentage all being significant factors in predicting And-1 percentage.  I’ll save that for a later time.  For now, feel free to brag to your friends at the bar that not only do you know who draws the most And-1s, you  also know the hardest and softest finishers in the game.

NBA HD: Blocks Not Just A Defensive Stat Anymore

April 8, 2010 in by with 15 Comments

Today’s post explores  a fairly new basketball statistic that hasn’t been analyzed in the public forum: percent blocked (%Blkd).

Well, maybe that isn’t totally accurate.  Matt Moore flirted with the shot blocked stat earlier this year in this very space but his love affair phased out as the season went on.  It’s a shame really because %Blkd awareness has plummeted ever since.  What is %Blkd? It’s the percentage of a player’s shots that get blocked.  Simple enough.  Although, it’s not to be confused by Basketball-Reference’s handy BLK% which calculates the flipside for the defender.

%Blkd is so simple that it feels like we should have had this information all along.   We make a big deal out of blocks for defenders but we ignore the other side of the ball.  Luckily, Hoopdata began publishing this data this season for the swat hungry masses.

Looking at the leaderboard of those who get denied a lot and those who leave the court unscathed, you find some interesting results.  No one’s safe from the swat.  Some of the tallest players to grace the court get blocked and the some of the shortest ones never do.  Seven-footer Brendan Haywood gets blocked more often than his 5-11 Carolina counterpart Ty Lawson.  Sure, Brendan Haywood lives in block territory and Ty Lawson only takes about half as of his shots at the basket (which is astoundingly high for a point guard) but evidently it takes more than height to be the last one to touch the ball as it approaches the rim.  In the former Knickerbocker department, Nate Robinson, who stands 5-9,  gets blocked less often than Darko Milicic who stands 84 inches tall.  Guess who takes more shots at the basket? That’s right: Nate. #wordaapp.

So anyway, who finds himself on the Most Blocked List? Let’s take a look at the ranking if we trim those who don’t play 20 minutes per game.

No surprise there with Chuck Hayes at the top. He’s undersized for a shooting guard but he’s employed at the 5.  But what about athletes like Tyson Chandler, J.J. Hickson and Gerald Wallace? Did you think their other-wordly hops would protect them? Not so actually.

And what about the Least Blocked List?

Notice some trends here? Bigs who lack an outside shot lead the blocked shot list and the guards who are allergic to the paint have gotten blocked fewer times than a highway patrol squad car.  Most blocks occur around the basket so if a player made it a priority to not get blocked, he could just live on the perimeter.

With that in mind, if the object is to learn something about the skill set of the players, these rankings probably aren’t all that informative.   We might as well look at their shot locations since there’s a very strong correlation between  the percentage of a player’s shots taken at the basket and how often they get blocked (r = .708, in fact).

What we want to find are the players who attack the rim cleanly without getting their shot swatted into the first row.  To do this, it’s worth looking at the relationship between percent blocked and how often they take shots at the basket. We measure the latter through at rim percentage.

In the chart below, we can glean more information about the player’s block evading skills if they display a separation from the pack.

At Rim Pct
At Rim Pct

There’s a lot to take in here, I know. Names, colors, lines. Oh my! Don’t worry, I’ll walk you through it.  (Click here for the standalone graph).  First, I elected to display the data points as player names instead of regular dots.  I mean, there are real people behind those dots so I just went ahead and identified them.   Secondly, the colors of those names correspond with their position. Consult the legend at the top left.  You’ll notice the orange centers cluster to the right. Lastly, the lines you see are trendlines for the positional distribution.  I wouldn’t put too much weight in the G and F trendlines since they only represent a few observations in the dataset but they’re there anyway.

Looking at the graph, we see that the Portland (and also injured) version of Marcus Camby has a much lower blocked percentage than we would expect given how much he works the basket.  Maybe he’s learned a thing or two from all the shot-blocking he does himself.  Or maybe it’s just a small sample of games (it is).  On the other end of the spectrum, Carl Landry strays from the pack, getting blocked on about 14% of his shots in Houston which is much higher than what we’d expect for someone with his taste for layups.  And the full season Landry (Carl Landry TOT), isn’t much better. You can see Steve Blake tucked in the bottom left hand corner.  He’s right on top of the trendline which tells us his tiny %Blkd isn’t really special.  Move along.

Speaking of which, why do we have the trendlines? For one, they provide a nice baseline so if the player finds himself above it, that tells us he gets blocked more than we would expect.  And vice versa below the line.  Secondly and most importantly, the regression equation associated with the trendline for each position enables us to derive an expected %Blkd with what we know about their propensity to take layups, dunks, and tip-ins.  For example, a 10 percent increase in At Rim Pct for centers increases %Blkd by 1.2 percent.  Furthermore, point guards suffer more compared to centers the more layups they take which seems logical given their stature.

So we want to find those who deviate from the expected line the most.  In other words, who gets blocked way more than they should given their appetite for layups?

Chuck Hayes no longer tops the list, all though he’s still a card-carrying member of this shameful group.  The new leader, 6 foot 7 Chris Douglas-Roberts gets blocked three times more than he should for a small forward taking 44 percent of his shots at the rim.  Gerald Wallace, for all his explosiveness, dunking chops, and athleticism, features an alarmingly high blocked percentage, moreso when he consider his position.  If all of Crash’s 101 blocked shots came at the basket, that would mean that one out of every five shots he takes at the rim get blocked.  If there’s a dent in his game, this is it.  And he’s not the only stuffed athlete on this list; Corey Maggette, Rudy Gay, and Caron Butler find themselves here as well.

Butler’s stint in Dallas has not been a slam dunk and maybe it’s because he hasn’t had enough of them.  He’s had his shot blocked a whopping 23 times in his time in Dallas, a high total considering he only takes a few shots at the basket per game.  He’s traditionally been blocked more than average but this is definitely something Mavericks fans should note as they march into the playoffs.

With the weak finishers taken care of, what about the undeniable attackers?

As remarkable as it is that Marcus Camby has only been blocked twice in Portland, the real leader on this list is Ben Wallace who should have given up about twice as many swatted shots as he has.  This is particularly interesting because Ben Wallace at 6-9 is woefully undersized for a center.  He’s not Kevin McHale underneath the basket but he certainly picks the right spots to get a clean look at the basket.

Notice that many of these players double as shot blockers on the defensive end.  Iguodala and especially Wade rank among the top shot-blocking guards.  On a per minute basis, Chris Andersen blocks more shots than any regular.  Dalembert and Camby are right up there.   Perhaps these players possess a shot blocking intuition and instantaneous jumping ability that helps not just on defense but on both ends of the floor.  Of course, not all shot-blockers avoid getting their own shots swatted (ahem, Brendan Haywood) but this is certainly an intriguing finding that I’m not sure I’ve seen before.

In the future, I’ll call up player height and And-1 percentages in effort to get closer to the heart of finishing ability. The findings here certainly warrant a deeper look to investigate further if shot-blocking ability translates to offense as well.

Evaluating The Playoff Race At All-Star Break Through Four Factors: Eastern Conference

February 16, 2010 in by with 8 Comments

We’re at the halfwaypoint, and some things we know, and some things we think we know. We think we know how good the Cavs, Lakers, and Nuggets are. We know how bad the Nets are. We know that the Western playoff race will likely come down to the end. We know the Hawks have the Celtics number, and the Magic have the Hawks number, and everyone has Golden State’s number. What we don’t know is just how good the playoff teams are, and if their record is befitting their performance. So I decided to take a look.

Continue Reading…

NBA HD: Analyzing Shot Location Matchups by Team

February 15, 2010 in by with 6 Comments

Last week, for my debut article here at Hardwood Paroxysm, I used shot location data from my mother site Hoopdata.com to see whether good shooting teams from a particular area from the floor enjoy an advantage against weaker foes in that shot location.  I found some compelling results; teams who dominate around the rim have generally shot better against weak post defenses, and vice versa.  I also discovered that a good three-point shooting team has not exhibited much of an improvement between facing a poor 3-point defense and an average defense, which was the only area to show that type of diminishing return.  So a team like the Suns, who terrorize opponents from downtown, may not see their deadly shooting talents magnify against a poor three-point defense.

My findings provided enough juice to take this a step further.  This time, I’d like to amp up the focus and look at specific teams this year.  I replicated the method I used last time and grouped the teams in tens depending on their opponent field goal percentage in each shot location.  I tossed the top ten teams into the “Good” pile, the bottom ten in the “Poor” pile and the rest in between were classified as “Average”.  You can find all this good info in the team shot location pages over at Hoopdata.  If you’ve read my work before, you know I really, really love adding colors to charts and graphs.  Each color has been formatted like a heat map to correspond with their relation to the group norm.  Looking at the FG% column, green fill illustrates a team’s excellent standing in that particular area and the opposite holds for red fill.  As it follows, yellow fill indicates a number close to the norm.  For the FGA column, the gradient ranges from yellow to burnt orange.   The colors should help you identify the extremes and digest the numbers faster.  The following chart shows how each team performs at the rim (layups, dunks, and tip-ins) when facing a good, average, and poor defense in the same area.

We’ll start with the Cavs.  They don’t miss at the rim, no matter who they face.  Led by LeBron James’ 73.8 at rim FG%, the Cavs shoot better at the rim against good defenses than 21 teams fare against poor ones. They shot 19-24 vs. the Lakers on Christmas Day.  In their two games against the 5th-ranked Pacers at rim defense, the Cavs nailed 30 of the 39 attempts at the basket.   LeBron’s finishing abilities are contagious in the sense that he pulls help defenders toward him as he drives, opening up easy buckets for his teammates cutting to the rack.

Looking elsewhere, the Raptors and Spurs are the only other two teams who finish above-average against all three groups while the Bobcats, Nets, and Bucks struggle against all defenses.  The Celtics wilt before top at rim squads but otherwise, they finish with gusto.  A lot of their problems at the rim would be solved if they never have to face the Magic.  In three of their four games against the Magic this season, the Celtics have missed 42 of their 73 chip-ins.  Granted, the Magic have the best post defense in the league but we’re talking layups here.

Do teams take more shots against poor defenses?  Not many, if at all.  On average, teams shoot 25.7 shots at the basket against good post defenses which is only one fewer than the rate against lesser defenses.   So the difference is marginal on the whole.  Interestingly enough, the Lakers don’t seem to be taking advantage against the weaker teams and actually take fewer shots at the rim in those scenarios.  Their .610 field goal percentage against poor defenses ranks 6th-worst in the NBA.  Kobe Bryant, who shoots 57.5 percent at the rim,  shares some of the blame for the Lakers woes.  He is actually a below-average finisher at the basket compared to his shooting guard positional comrades who average 59.8 percent.

Moving away from the basket, let’s take a look at how teams shoot on long twos.

Despite experiencing a sizable 22 point advantage in field goal percentage, teams don’t really look to take more long twos against poor perimeter shooting teams; teams average 0.4 fewer long twos against poor defenses than their portion against good ones.   It’s harder to distinguish between a good defense and a poor one in this range because the spread is so small.  The 10th best long two defense allows 40.2 percent whereas the 10th worst allows 38.6 percent.   Not a huge difference.

Nonetheless, some teams have really struggled against good perimeter teams.  Houston plummets from a healthy 42.2 FG% down to a league-worst 34.6 FG% as the going gets tougher.   Although, their distaste for long twos keeps that damage to a minimum; they take the second-fewest long twos in the game

It’s hard to fathom how difficult it is to shoot nearly 50 percent from this range but the Mavericks somehow manage to do it against bad perimeter defenses.  Led by long two resident Dirk Nowitzki, the Mavs have shot 50 percent or better 17 times this season from that area.  The Bulls?  Three times.  And they take average eight more heaves per game.

Let’s move along to our final destination: behind the three-point line.

Just as we saw with long twos, teams don’t tend to take more threes against poor 3-point defenses.  In fact, teams on average attempt more shots beyond the arc against good defending foes (18.3) than the average (17.3) and poor (18.2) opponents, despite knocking them down at a higher rate.

The Cavs are on top of their game in the most efficient areas on the floor.  Just as they were unfazed at the rim, Cleveland shoots well from downtown no matter who they face.  Not all 3-point shooting teams weather the storm like the Cavs however.  Contrast the Cavs with the Suns, another sharpshooting team, whose three point shooting numbers fall from .428 to .379 as their opponent improves.   Count Denver in that group, too.

With a .454 field goal percentage beyond the arc against poor 3-point defenders, the Spurs effectively shoot .681 with the added one point bonus.   That’s an amazing figure considering it’s more than 100 percentage points above the rest of the league, in terms of effective field goal percentage.  If the perimeter exploitation continues, the Spurs hope to draw either the Suns or Mavericks  come playoff time as they both rank among in the bottom ten in 3-point defense.  Otherwise, the Spurs are a below-average shooting team from beyond the arc.

While teams enjoy an advantage against the different quality defenses, they don’t launch more from the perimeter depending on their opponent.  Since the likelihood of nailing a shot from downtown is much smaller than at the basket, the perimeter ranks may be more random variation than true representation of strength.

Curious about the short and mid-range numbers?  Take a look at them here and here.  I saved them for the sake of  space but they’re definitely worth a look.

This Usage Talk Is All The Rage

February 5, 2010 in by with 0 Comments

It is kind of a big but – it thinks the Bobcats would be worse with LeBron James than Gerald Wallace this season. And as big of a Crash fan as I am, that is preposterous. Now, it is not the tool’s fault: It just does not know any better. It was designed to say that if a new player comes in, the rest of the team will continue to perform at the same efficiency they have previously. But when you add a player like LeBron James, things are a little different – for one, he uses about 15 more possessions per 100 team possessions than Gerald. All of a sudden the rest of the Bobcats are responsible for splitting just 65 possessions, instead of 80 – hmm, wonder if that may make their jobs a little bit easier?

No surprises: It does. A great example is Raymond Felton’s performance from last year to this year. Last season, his usage ([fga+0.4*fta+turnovers]/100 team possessions) was 24.7 and his efficiency on those possessions (points per 100 possessions used) was just 82.0. This year, with the addition of Stephen Jackson, Ray’s usage is down to 20.7 and his efficiency up to 95.0. Looking across the league, this relationship holds true – as usage goes up, efficiency goes down. This is not to say that high usage players are the lowest efficiency players – that is not the case. No, what I mean is that as an individual player is called on to shoulder an increased burden, his efficiency drops. The chart below shows the usage versus efficiency on a per game basis for every player who played at least 8 minutes in a given game.

via Queen City Hoops – You mean Gerald isn’t better than LeBron?.

Brett’s updated the Player Swap Tool and I suggest you go take a gander.

Click on that for a look at Jamison for Z and the impact on the Cavs. Now, the win differential is null, but take a look at the possessions used. If you’re looking at the Cavs, you want someone who can absorb more possessions to take the burden off James and prevent the dreaded “everyone stand around and watch James dribble” offense. From Brett’s tool, it certainly looks like it.

Brett’s tool is also groundbreaking in that it’s the first tool to start moving to a conceptual analysis of the impact of players on teams, not just from a “let’s subtract this guy’s stats and add that guy’s” but from a look at the impact on elements that are dynamic, that is, they interact with the other team. You’re never going to be able to get everything covered in terms of chemistry, and defense will take a while to get a more accurate look at, but we’re headed in that direction. Take a look at what Brett’s doing. Pretty awesome stuff.

NBA HD: A Closer Look At Shot Locations

February 3, 2010 in by with 8 Comments

Hi, my name is Tom Haberstroh.  I write over at Hoopdata.com about the NBA and occasionally perform statistical magic over at ESPN Insider.  I have two middle names and enjoy watching Serge Ibaka play basketball.  Chris Paul, Randolph Childress and Muggsy Bogues went to my alma mater and my favorite Crayola color is jungle green.

The topic of interest in my first piece here at Hardwood Paroxysm centers around team shot location.   At Hoopdata, we track how teams shoot from five different areas of the floor: at the rim (layups, dunks, and tip-ins), less than ten feet, 10-15 feet, 16-23 feet, and beyond the three-point line.  There you will discover, among other things, that the Chicago Bulls take an outrageous number of long twos and the Washington Wizards’ defensive unit practically ushers the ball through the basket on shots at the rim.  Today, the statistic I am particularly interested in is shot location field goal percentage.  More specifically, if a team is horrible at shooting around the basket, how much worse does it get when they face a team that protects the rim?

Take, for example, Monday night’s matchup between the Milwaukee Bucks and Orlando Magic. The Bucks are just about the worst team in the NBA when it comes to converting shots at the rim as their 56.0 FG% from there ranks 29th in the league.  Dwight Howard and the Magic have the very best opponent at rim percentage (55.1 FG%).  So, what happened? The Bucks missed 11 of their 20 shots at the rim while getting swatted eight times on the evening.  And for the just the third time all year, Brandon Jennings didn’t take a layup all game.  I wondered if this was a typical performance for a poor-rim offensive squad taking on a stellar rim-defense and whether this opposite holds true when the tables are turned.

To shed more light on my curiosity, I ranked each team of 2009-10 by their field goal percentage from each area and separated the league into thirds depending on rank in the category.  Teams ranked 1-10 get tossed in the Good bin, 11-20 into Average, and 21-30 into Poor.  You may have seen this filing method before over at 82games.com.  So for example, the Chicago Bulls offense ranks 30th at the rim (Poor), 7th from less than 10 feet (Good), 5th  from 10-15 feet (Good), 28th from 16-23 feet (Poor) and 14th from 3-point (Average).  I then gathered every game (over 1,400 matchups in the sample) and calculated the field goal percentage in each shot location area.  So, on average, what happens to a poor at rim defense when it faces a good at rim offense? Let’s take a look.

I’ll walk you through this.  Defenses are separated by columns and the offenses are separated by rows.  At the end of each column and row, you’ll find the average for that group.  Ignoring the intersections for the moment, you see that the collective Good defensive group allows a .578 field goal percentage on shots at the rim and good offensive teams average .635.  Now when they meet (say, when the Cavaliers, a Good at rim offense, faces the Celtics, a Good at rim defense), the Good offense shoots 61.3 percent from the area, on average.  With me? I’ll take that as a yes.

As expected, teams perform better if their opponent defends worse in that area.  The empirical evidence confirms our intuition.  The Bucks-Magic matchup represents an extreme case on both ends,  so the Bucks’ 45.0 FG% makes sense.  On the other end of the spectrum, a good offense will dominates the poor defense, converting almost 2-out-of-every-3 shots at the basket.  Interestingly, a poor defense will make a poor offense look average by comparison and a good offense will make an average defense look poor.   Let’s take a look at shots inside 10 feet (not at the rim).

We see much of the same trends here in this one.  It really hurts to be a poor in this area offensively going up against a good defense.  Despite the near proximity to the basket, poor teams shoot  36.6 percent against good squads or roughly the same as the typical squad shoots from downtown.   This zone gets about a third less shot traffic compared to the at rim zone, so the results will be more varied in one-game snap shots.   How about the 10-15 feet area?

It doesn’t really pay all that much to be a good offensive team going against a good defensive team from the mid-range; the good and average offenses are nearly identical on average (.379 vs. .380).  That’s the first time we’ve seen such a case.  The typical team only gets about 7 shots per game from this area, so the numbers here will tend to exhibit more statistical noise.  Nonetheless, if you’re facing a good defense in the mid-range, don’t expect your shots to drop no matter how well you normally shoot from there.  Let’s take a look at what we see from the least efficient area of the five: the long two.

Long twos are much more stable than the rest of the fields we’ve looked at.  The spread between PoorO-GoodD and GoodO-PoorD is only 68 percentage points whereas in the  previous ranges the spreads were 111 at the rim, 139 from short, and132 from mid.  But this follows the bigger picture.   A good long two shooting team isn’t a whole lot better than a bad one.   However, if you can’t normally knock down long jumpers inside the three point line (attn: Bulls), don’t get too  excited when you face a bad defensive team on the perimeter.  You’re still probably going to miss more than 60% of your shots from there.

Interestingly enough, a good defensive squad in this area has the opposite effect compared to the mid-range.  Compare the good defense columns.  Field goal percentage against good defenses actually increases from .366 to .380 as you migrate further away from the mid-range to long-range twos.  Either a good mid-range D is especially suffocating or a good long-range D doesn’t amount to much in the end.   A third explanation could be that the low sample size of mid-range shots on a game-by-game level produces some whacky results.   And finally, moving onto the three point line.

For the purpose of staying consistent, I’ve presented the three-point numbers in field goal percentage as opposed to effective field goal percentage.  Just keep in mind that even though the most advantageous situation yields only a 37.9 FG%, the added bonus of 1 point makes a world of difference.  And much like shots from 16-23 feet,  the spread between the best and worst intersection is only 73 points.  Take a look at what happens when a good three-point shooting team goes from an average opposing defense to a poor one.  The percentage actually decreases on average from .386 to .379.  Good shooters from a particular area tend to improve across the board, however, from beyond the arc there doesn’t seem to be a discernible advantage.   I’d only be speculating as to why this might be the case, if there is in fact a real effect here, but it could be that the difficulty of three-point shooting caps the shooter’s ceiling.  The best shooting teams from long distance can only shoot so well since the threeball rarely goes in to begin with.

Like most studies, there’s plenty of room for more digging and statistical analysis.  The logical next step would be to gather the variability, or standard deviations, of the  presented figures.  That way, we can see the overlap and strengthen our expectations.  In this piece, I analyzed the league on a macro level but I could take this in other directions as well.  How does each team perform against the various defenses?  Moreover, do good shooting teams take more shots in areas where they have the upper hand?  I’ll have to save those questions for another time.  But for now, it does appear that teams experience greater success if the defense is weak in a particular zone.  So keep these numbers in mind as you prepare for your team’s next game.

Stay tuned for more shot location analysis in the future editions of NBA HD.

If you can’t knock down long jumpers inside the three point line (attn: Bulls), don’t get too  excited when you face a bad defensive team on the perimeter.

Nichols and Dime: NBA Player Pair Data

January 25, 2010 in by with 1 Comment

Last Thursday, I published player pair data for every NCAA Division I team at my own site, Basketball-Statistics.com. This was inspired by the NBA player pair data that has been available at 82games.com for the last few years. As I mentioned in my last article:

82games has compiled statistics showing how teams have performed with two specific players on the floor together. These “player pairs” are a complementary data view to our 5-man unit stats that measure unit performance. By focusing on two players at a time we can better understand which guys bring out the best in each other.

Unfortunately, that data is not currently available at 82games for NBA players. If it becomes available, I’ll be happy to point you in that direction. Until then, I have calculated the player pair data for the current NBA season, and it can be viewed here:

http://basketball-statistics.com/nbaplayerpairs.php

Enjoy!

Graphic Offense: A Look At Usage and PER Mid-Season

January 25, 2010 in by with 32 Comments

What does an offense looks like? I can give you some ideas from watching the teams. Houston moves really fast and really consistently and never underperforms or overperforms. Cleveland can slow to a crawl or detonate underneath a powder keg. The Lakers are largely impacted by Kobe, it feels like Gasol doesn’t get enough touches and Odom has been negatively impacted by Artest’s arrival, though overall they’re the biggest juggernaut in the league. Chicago’s a damn trainwreck.

But how do they look through numbers? Last year in the playoffs I broke down how San Antonio looked in the regular season and post-season with a Parker-heavy attack. I decided to take a similar look at all the teams and where they are as of right now, just past the halfway mark of the season, using data from HoopData.com.

Continue Reading…

Hoopdata Gives NBA Fans An Early Christmas Present

December 21, 2009 in by with 0 Comments

We’ve populated our database with all the box scores from the 2009-2010 season to date, and nightly box scores should be added to the database around 2am EST every night, which will also be the new time we update our stat database hopefully –- still might have some kinks to work out with that latter par. At this time, we have no plans to add box scores from prior to this season, but that could change if I get bored.

In addition to our advanced stats, we’ve tried to incorporate all the integral things fans are used to from the box scores offered at NBA.com and ESPN.com, while keeping the standard stuff in a format everyone is familiar with. We think we’ve worked out all the kinks over the past few days, but as always let us know if you spot any problems, and also if you think there’s something we could add or something we could display in a more user-friendly way.

Among the new things included in each box score are Four Factors, Offensive and Defensive Efficiencies, Possessions estimated, Shot Locations, Assist Locations, the usual Advanced Metrics, And1s, Plus-Minus, and pretty much everything else from our advanced database.

via Hoopdata – NBA Statistics and Analysis.

Thanks, Santa! It’s just what I wanted!

Here’s a few examples of what you can use this data to look at.

  • “Wade took 11 of his 31 shots from 16-23 feet at 45.5%, second best from any range. But at the same time, it illustrates that he wasn’t attacking as much as the Heat probably need him to, an effect of the back injury that’s limiting him. “
  • “Anthony Carter had a terrific game in the middle of Denver’s vomitous night, with 5 of his 7 assists going to the rim, and contributing 10.7 points on 9.3 possessions used, second best on the team behind Nene.”
  • “Ramon Sessions clocked in a 39.0 Usage rate with only a 49.6% TS% and 33%AS rate. In short, he sucked loudly.”
  • “The Hornets essentially split one of the four factors and won two of the others, losing only eFG%. Sometimes you don’t have to hit your shots to win. Today the Hornets needed to.”

The Diminishing Returns of Rebounds and Other Stats

December 7, 2009 in by with 9 Comments

Introduction

One thing many people have wondered is whether or not there are diminishing returns for rebounds. Basically, what that would mean is that not all of a player’s rebounds would otherwise have been taken by the opponent; some would have been collected by teammates. Therefore, starting five lead leaguers in rebounds would probably be overkill because eventually they’d just steal them from each other. At some point, there are only so many rebounds a team can grab, and some are just bound to end up in the hands of the opponent.

This principle is very important to statisticians who wish to develop player ratings systems. These ratings often assign weights to different statistics (including offensive and defensive rebounds), so knowing that a defensive rebound collected by one player would most likely otherwise have been collected by a teammate makes that stat less “valuable” in terms of producing wins.

Methodology

To test the effect of diminishing returns of rebounds, I decided to go through the play-by-play data (available at Basketball Geek) and compare each lineup’s projected rebounding rates (the sum of each player’s individual rebound rates for the season) to their actual rebounding rates (what percentage of rebounds that lineup grabbed while it was on the floor). After doing some research, I found out a very similar study was done by Eli Witus (formerly of CountTheBasket.com, currently of the Houston Rockets). Before you proceed with the rest of my article, you should read his. Although my method is slightly different, he provides a great explanation of why it’s useful to do the research this way and he also lists some advantages and disadvantages of this method.

Before I show you the results, I should explain the intricacies of my research and also some of the differences between Eli’s study and mine. The individual rebound rates I used were taken from the rebound rates I calculated myself using the play-by-play data. Because both the individual rates and the lineup rates were calculated from the same data, there’s less risk of error due to silly things such as differences in calculations or incomplete data. Also, to reduce the effects of small sample sizes due to lineups that didn’t receive a lot of minutes together, Eli chose to group lineups into bins based on their projected rebound rates. He then regressed each bin ‘s (a collection of different lineups with similar projected rebound rates) projected rebound rate to its actual rebound rate.

When I was coming up with my idea, I chose to do things a little differently, although the purpose is the same. Instead of grouping the lineups into bins, I simply only selected the lineups that met a minimum qualification for plays. Only lineups that appeared in at least 400 plays were included in my study. This left me with a sample size of 475 lineups. Like Eli, I then regressed the projected rebounding rates versus the actual rebounding rates. One final difference between us two is that his article was written in February of 2008, so I’m presuming he used data from the 2007-08 season. I’m using data from the 2008-09 season.

Offensive Rebound Rate

The graph for Offensive Rebound Rate is below:

ordiminishingreturns

The key to understanding this graph is looking at the slope of the line. Here, it is 0.7462 (close to the 0.77 number he got). If there were no diminishing returns for offensive rebounds, the slope would be 1. This would mean that for each additional rebound a player could offer to his lineup, he would actually add one rebound to the lineup’s total. If the slope is less than one (such as in this case), it means that each additional offensive rebound by the player adds about 0.75 to the lineup’s total, because some of those would have been taken by his teammates anyways. The slope I have here is pretty high, though, indicating that the diminishing returns effect for offensive rebounds isn’t too strong.

Defensive Rebound Rate

In his study, Eli found that the diminishing returns effect was much stronger for defensive rebounds. Can I replicate his results? Below is the graph for defensive rebounds:

drdiminishingreturns

Eli found a slope of 0.29. Mine was close, but slightly higher at 0.3331. Regardless of the minor difference, we both can come to the same conclusion: there is a much stronger diminishing returns effect at play with defensive rebounds than there is with offensive rebounds. While each offensive rebound adds 0.75 to the lineup’s total, each defensive rebound only adds 0.33, indicating that many defensive rebounds are taken away from teammates. Of course, individual cases can vary.

These results help explain why a lot of player rating systems make defensive rebounds “worth” less than offensive rebounds. Eli has a good explanation of it at the end of the article here. For example, in his PER system, John Hollinger assigns offensive rebounds a value more than double the value of defensive rebounds. This is partly due to the diminishing returns effect we found here today and originally in Eli’s work. As it turns out, my numbers indicate that offensive rebounds are in fact worth a little more than double the value of defensive boards. So hats off to Hollinger and his many contemporaries who have managed to weight rebounds appropriately.

Further Exploration

I could stop here, but I’d like to take this research a little further and see what other insights we can come up with. First, I’d like to break down the data by location (home and away).

Home Data

One thing to note is that the projected rebounding rates for the lineups are based on overall individual ratings, not just for home games. If rebounding was usually in favor of the home teams, this would lead the projected lineup rebounding rates to usually underestimate the actual rates in this case. However, since it would presumably do this for all lineups, we can still take a look at the effect of diminishing returns.

homeordiminishingreturns

homedrdiminishingreturns

With that being said, how does the home data compare to the overall data? For offensive rebounds, the slope is flatter, indicating a stronger effect of diminishing returns. However, for defensive rebounds, the slope is slightly higher, indicating a lesser effect. The differences are minor, though.

Away Data

We can also take a look at the away data:

awayordiminishingreturns

awaydrdiminishingreturns

As you would expect given what we now know about the home data, the effect of diminishing returns appears to be much weaker on the road for offensive rebounds. In fact, as we can see, the slope is getting close to 1. This indicates that there isn’t much in terms of diminishing returns for this type of rebound. Intuitively, this makes sense. If teams rebound the ball better at home, there are less offensive rebound opportunities for the visiting team. Therefore, it is more likely that an offensive rebound by a visiting player would otherwise have been grabbed by the opponent as opposed to one of his teammates, which in turn makes good offensive rebounders more valuable on the road. The same pattern doesn’t follow for defensive rebounds, though. In both cases, the difference isn’t gigantic, so we should be hesitant to draw any serious conclusions.

The one difference that is large and consistent is the difference in slopes between offensive and defensive rebounds, no matter the location. Confirming what Eli found in his original studies, this data says that the effect of diminishing returns is much stronger on defensive rebounds than it is on offensive ones. Therefore, offensive rebounding is a more “valuable” skill in terms of how you rate players, and some of the best player rating systems do take this into consideration.

Other Statistics

So far, this whole article has been about the diminishing returns of rebounds. However, we can also use the same lineup-based approach to look at other statistics. Today I’ll also explore the diminishing returns of blocks, steals, and assists. Eli already used his method to take a crack at the usage vs. efficiency debate, and I recommend you read that article for some fascinating insight.

Block Rate

Block Rate, for a lineup, is defined as the percentage of shots by the opposing team that is blocked by one of the players in the lineup.

Blocks are an interesting statistic to examine. After all, there are only so many block opportunities around the basket and occasionally on the perimeter. When you also take into consideration the fact that teams often funnel players into the waiting arms of a dominant shot-blocker, it seems as though the diminishing return for blocks should be relatively strong. That is, if you add a shot blocker that normally blocks 4% of the opposing team’s shots to your lineup, you shouldn’t expect to block nearly that many more as a team because of diminishing returns. To see if this is true, I used the same methodology that I did for rebounding and came up with this graph:

blockdiminishingreturns

As it turns out, the slope is at 0.6015. This puts Block Rate somewhere in the middle between Offensive Rebounds and Defensive Rebounds. A lineup full of good shot blockers will almost certainly block more shots than a weaker lineup, but the difference may not be as much as you might think due to effects of diminishing returns.

Steal Rate

Up next we have Steal Rate. For an individual, it is defined as the number of opponent possessions that end with the given player stealing the ball. Therefore, for a lineup, it would be defined as the number of opponent possessions that end with a steal by anyone from that lineup. The graph for Steal Rate is below:

stealdiminishingreturns

Here, we see the slope is nearly 1. This indicates that there is practically no diminishing returns effect on steals. If you add a player 2% better than average in terms of steals to your average lineup, you should expect to steal the ball almost 2% more than you currently do. Another way to put it is that usually, if a given player steals the ball, it’s not likely that someone else would have stolen the ball if he failed. Of course, like with every graph so far, the R^2 is still very low. This means that we can’t really predict how many steals a lineup will get simply by adding the Steal Rates of all of its players.

Assist Rate

Finally, we have Assist Rate. For an individual, it would mean the number of field goals made by a player’s teammates that he assisted on. For a lineup, it means the percentage of made field goals that were set up by an assist. The graph is below:

assistdiminishingreturns

Of any graph presented on this page so far, this one has by far the lowest slope. Normally this would indicate that there is a huge diminishing returns effect for assists. However, I’m not sold on this explanation just yet for various reasons, so for now I will just present the data as is.

Conclusion

I discussed a number of different issues today, so I think it’s good to recap what I’ve presented. First, using a method similar to the one Eli Witus used at CountTheBasket.com, I found that there is a large diminishing returns effect for defensive rebounds that is significantly larger than the effect for offensive rebounds. This confirms the common belief that offensive rebounds are “worth” more than defensive ones. When we split the data into home and away, it appears that individual offensive rebounding skill is particularly important on the road, indicated by a very high slope on the graph. Finally, I took a look at the diminishing returns of a few other advanced statistics and found the strongest effect on assists and a weaker but still significant effect on blocks.

If you have suggestions or comments about my work, please e-mail me at jonnichols@basketball-statistics.com. And again, much credit must go to Eli Witus, who originally thought of these ideas well before I did.

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