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NBA HD: Market Update II

July 30, 2010 in by with 2 Comments

Richard Jefferson signed a few days ago which mean’s it’s time for another market update on the free agency price.  To recap, I’m comparing every newly-signed player’s salary to their WARP2 from last season. It’s a quick and handy measure of how much teams are willing to pay for talent this summer.  Last year, the going rate for free agents was $1.49M for each win.  This year? It’s risen to $2.2M.

Here’s the full run down:

To reiterate from last week, the last row on this table subtracts players who likely signed for lower than the free market rate (LeBron James, Dwyane Wade, Chris Bosh, and Dirk Nowitzki).  This takes a more accurate view of what teams pay free of cap spending restrictions.

$2.2 million per win is an increase since the last count because the newest additions have been sold at the rate of $3.3 million.  WARP2 didn’t think much of last year’s production of Ronnie Brewer, Joel Anthony, Richard Jefferson, and Marquis Daniels but teams were willing to pay more than the minimum and in some cases, much more than the minimum for these near replacement-level efforts.

Newly minted Matt Barnes looks like one of the best deals of the summer and should help bolster the Lakers’ chances of bringing home another championship.  It’s hard to imagine Ridnour posting another 5.3-win season but this objective method makes David Kahn look like a genius.

Next week, look for a team by team and position by position break down.  We’ll see if the summer’s $700,000 premium sticks.

Much thanks to Kevin Pelton of Basketball Prospectus.

NBA HD: Market Rate Update

July 15, 2010 in by with 8 Comments

In last week’s post, I calculated the going rate for free agents this summer by applying the dollars-per-win method that others have used in the past.  If wins were a known commodity (which they aren’t), then this would represent the price.  To be sure, not all teams value wins at the same rate.  Some teams have an easier time swallowing risk or ignoring risks altogether.  But aggregating the talent and dollars gives us a good window into the pricing climate.

I found that teams were paying about $2.23 million per win according to Kevin Pelton’s WARP system.  Since then, Kevin has kindly pointed out that he made an updated version of WARP (referred to as WARP2) and they haven’t been published yet on the Basketball Prospectus player cards just yet.  Being the helpful gent that he is, I was sent the WARP2 numbers for last season (denoted 10WARP2) and those numbers are reflected below.

You’ll notice I have cited two prices here.  The $1.69 million pricetag reflects the entire free agency lot with the max guys included.  However, several high-end players had their salaries artificially capped due to the CBA rules that restrict the max salary to about $20million annually if resigned by their former club.  Moreover, we witnessed a rare circumstance where players took paycuts below their max cap (LeBron James, Dwyane Wade, and Chris Bosh) so that the team could have more money to fill out the roster. Consider that Joe Johnson will get paid more than James despite only being half the player James is.

There isn’t a perfect way to handle this designed deflation but I chose to ignore the players fulfilled the following qualifiers a) received the max allowable contract AND b) produced at least 10 WARP2.  This takes out Dirk Nowitzki, Bosh, James, and Wade —  all of which would almost undoubtedly receive bigger contracts if the CBA gave them that right.  It’s arguable whether someone would have paid higher than the max for Johnson, Stoudemire, and Rudy Gay, but their included in the Total w/o “max” price.

So, with that in mind, it seems as though the market rate has slid from $2.23 million per win to $2.01 million per win (or just $2 million) over the past week.  As I mentioned in my previous post, the 2009 summer going rate was approximately $1.49 million which means NBA teams a whole are paying about half a million dollars more for each win.

You could interpret this finding in a number of ways.  An argument can be made that agents are simply getting better at selling the product but that’s probably not something that happens collectively overnight.  It could also be a sign that front offices are desperate to pacify their anxious fans and thus, will use their enormous cap space to land someone of name-value.  Remember, fans have been promised the moon in the Summer of 2010 TM and that demand has pushed up the price.  But it’s also very possible that the impending lockout has caused more players to enter the free agency market to secure a long term contract.  In turn, the supply has been raised as well, but maybe not as much.

It’s also worth noting that the $1.49m price from 2009 was derived with the original version of WARP and thus, the price could change slightly.  However, I don’t have any reason to believe it would change the price significantly as the system adjustment was merely a minor tweak to allocate more credit to 3-point shooters for floor-spacing.

So the $750,000 premium we saw last week has been reduced down to a not-too-shabby $500,000.  The players will take it — while they can.

NBA HD: Winging it with Length

June 17, 2010 in by with 3 Comments

The NBA draft is approaching.  Prepare for the cliches and buzzwords.

Freakish.

Tremendous.  Upside.  Potential.

Ceiling.

Length.

You’ll hear that last one probably the most. Length. Why do we care about length?  Well, extra length gives players advantages within a variety of basketball actions; deflections, live rebounds, and getting shots off requires extension above the opponent, to name a few.

Today’s post looks into the length of this year’s crop and who has notably long or short arms for their height.  It would be amusing to think of it the other way around but we don’t. This guy has the arms of a 6’2″ guy but he’s 6’8″!  He’s a giant!

Before we dig in, let me first say that Jonathan Givony’s Draft Express is our best friend and our valuable resource around draft time.  You can get all sorts of historical player measurements there.  I should also mention that they just started publishing advanced stats for college basketball.  Amazing stuff happening at Draft Express.

Anyway, the first thing I did was calculate the proportional wingspan of a player relative to his height using the prospect measurements dating back to 2000.  I used a regression to predict wingspan from player height (WITHOUT shoes on) with a sample of 916 NBA prospects.

Here we see a pretty strong linear relationship between player height and wingspan.  Want to know what your NBA prospect wingspan should be? Take 98.5% of your height in inches and add about 5.5.  My wingspan should be about 76 inches long.

Who has the longest go-go gadget arms of players that actually got drafted? Let’s take a look.

Oh my, the stars!  Not a very inspiring list, eh? Jason Maxiell had the most “freakish” arms as he’s one of those guys who can touch his knees without bending over.  Fingertip to fingertip, he is 10 inches longer than head to toe.  All told, his wingspan is about six inches longer than we’d expect and proportional for a 6-9 guy.  His extra wingspan is partly responsible for his rebounding rate we’d typically see from a center.

The rest of the list has some big time busts who may or may not have been overrated by their length.  Saer Sene got drafted 10th overall, Fred Jones 14th overall, and Shelden Williams 5th.  As we saw in Game 6, freakishly long arms cannot guarantee a successfully converted dunk in the biggest game of your life (right, Shelden?).  Marvin Williams, the second overall pick in 2005, sits just outside this list as his wingspan was 4 inches longer than we’d expect.

Some other notable extra wingspans: LeBron +0.5″. Thabeet +0.6″.  Durant +3.3″.  Beaubois +4.0″.

Let’s head over to the short arm prospects or as I like to call them, the capital T’s (just look at a capital T).  These guys have shorter arms than we’d expect given their height.

Martynas Andriuskevicius played only 9 minutes in his NBA career, way back in 2005 but he deserves a shot out here.  His arms were over six inches shorter than we’d expect given his 7’1.25″ height.  In reality, he has the wingspan of a 6’6″ guy.  Yes, observant reader, Fred Jones has a longer wingspan than Marty Andy.  For your information, he grabbed four rebounds in 9 minutes which translates to a crisp 17.8 rebounds per 40 mins.  Sample size be damned.

We have some pure shooters (Redick, Kapono) as well as some truly undersized point guards (Maynor, Jordan).  Redick relies on his hops more than most shooters since he wasn’t gifted with long arms. He got away with it in college but he’s taking threes at a much slower rate in the NBA, granted, for several different reasons.  Perhaps one of them is that he has the arms of a 6-footer.

Some notable curbed wingspans: Jon Brockman -3.7″, Chris Kaman -4.1″, Stephen Curry -3.0″, Jared Dudley -3.2″

While we’re at it, let’s go ahead and pull up the go-go gadgets arms and T’s of this crop of 2010 prospects.  First, the long arms:

And the T’s:

Looks like I’ve snooped out the market inefficiency that Coach K has been exploiting for years.  Short armed scorers.

In the future, expect some application of these measurements to NBA production to test their significance in predicting professional success.

NBA HD: Blocks, Steals, and the Scoreboard

June 11, 2010 in by with 1 Comment

One of the great mysteries in basketball is how to grade individual defense.  For years, the basketball fan glanced at a player’s steals and blocks to derive their opinions on whether a player was a good defender or not.  Blocks and steals were the extent of objective  information at our fingertips and conceptually, it made sense to use blocks and steals as a proxy for quality of defense.   While blocks and steals are both good contributions as a defender, they alone offer just a small window into the challenge of stopping the opposition from scoring– the ultimate goal of the defense.

Thankfully, we have more data these days.  The great resource that is Basketballvalue.com publishes the on court/off court lineup data for every player in the league.  What do on/off court defensive numbers tell us? They answer the following question:  How many points does the opposing team score when the player is on the court relative to when he’s on the bench?

In many basketball analytics circles, this is the most useful measurement available.  It ignores box score statistics all together and strictly looks at how a defender affects the bottom line: the scoreboard.

What happens when we compare the on/off court defensive stat to the box score stats?  Maybe you are interested in who tallies loads of blocks and steals, but fails to impact the team’s efforts on the scoreboard.   Perhaps you can’t sleep because J.J. Redick totaled just 32 steals and blocks in 1,808 minutes and you believe those numbers do a poor job of measuring his defensive ability.  Well, I’m gonna touch on all that in today’s post.

First, I gathered every player’s steal percentage (estimate of steals per possession on the floor) and block percentage (estimate of blocks per possession on the floor) from Basketball-Reference.com.  They are estimated because B-R’s calculation doesn’t have actual possession data but the estimate is very accurate. I used these instead of other stats measures because they remove the pace and playing time bias from overall stats numbers on the back of your old Fleer Ultras.  Then, I only looked at player’s who logged more than 500 minutes this season to remove the wild variances due to little playing time.

Next, steal percentage:

The negative trendline tells us that the players who steal the ball a lot tend to have a better (more negative) defensive on/off court differential and steal percentage is statistically significant in predicting defensive on/off differential (p=.0493).   While stealing is significant, you’ll notice that only a small relationship exists.  If they were perfectly correlated, you’d see a straight line of points but the distribution is much more scattered.

There are several reasons steals have a low correlation (-0.108) with on/off differential. For one, a player can steal the ball without playing good defense.  Most steals come from the stripping variety but players also can “steal” the ball by being in the right place at the right time and picking up a loose ball that falls to their feet.  Just like you can’t assume a double play in baseball, you can’t assume the possession would change until a player physically picks up the ball.  Additionally, players who go for steals all the time are playing risky basketball.  What we’d really like to look at is net steals, or the ratio of successful steal attempts to failed steal attempts.  Many players get tons of steals without actually improving their teams defense. Who are they? One way to find these sly cats is to compare their percentile ranks in steal percentage and defensive on/off court differential.  Don’t look at Andrei Kirilenko. He racks up a ton of steals (2.5 stl%, 95 percentile) and also helps the teams bottom line on defense (-5.1 points, 94 percentile).  Direct your eyes to these folk.

This should be a good time to mention that defensive on/off court stats have their faults as well.  It is a fact statistic but it isn’t adjusted to take into account the quality of their substitute players and the lineup they tend to play in.  Additionally, it’s still subject to random variation since there’s a lot of different lineups to tease out one player’s contribution.

Nonetheless, this is still an eye-opening exercise.  All these players saw their teams play better defense (fewer points allowed) when they were off the court.  Monta Ellis has one of the highest steals rates in the league but opposing teams scored more 4.1 points when he was playing defense than when he was on the bench.  Many of these guys are speedy guards but you also have Rasheed Wallace and Jeff Green in there too.  Jeff Green was this year’s worst defensive player if you use the on/off court number as the measuring stick.

I wouldn’t say all of these players are categorically overrated as defenders but we also shouldn’t let their steal numbers color our evaluations.  Steals are good but these players probably exhibit more risky and opportunistic defensive strategies rather than staying home and forcing bad shots.

Let’s move on to blocks.  Here’s what it looks like when we plot block percentage vs. defensive on/off court differential:

There’s  a stronger relationship between blocks and defensive on/off court differential than there was for steals.  Shot blockers clog the paint and prevent high percentage shots whereas guys who accumulate steals only get a couple per game and have less of an impact on preventing scoring.

Still, only 2.7 percent of the variation in a player’s defensive on/off court differential can be explained by their block percentage.  That might seem miniscule but also consider that there’s a fairly large percentage of variation that is simply random/luck.  But there are players who are empty shot blockers.  Typically, you see these guys swat every ball in sight, thereby leaving themselves vulnerable to pump fakes and weak side cuts.  Additionally, they tend to foul a lot and fouling a player going up for a shot is just about the worst thing a defender can do aside from laying down on the floor.

Let’s take a look at the shot blockers who actually don’t improve their team defense (as measured by defensive on/off court).

Theo Ratliff saw a huge boost in minutes after arriving to Charlotte from San Antonio this season.  Always a big-time shot blocker, he’s no longer the defensive asset of old.  He doesn’t take advantage of his height on the boards and he’s certainly slowed down at age 36.  The Bobcats were about 4 points better defensively with him on the bench, despite his shot blocking talents.

With Kurt Thomas, Nazr Mohammed, and Ratliff, we have a nice group of older veterans who may not have the quickness to stay in front of their younger opponents.  But we also have some youngsters (DeAndre Jordan, Brook Lopez, and JaVale McGee) who may have some more work to do.

As a reminder, the on/off court data aren’t adjusted for substitute effects and they are still vulnerable to random variance.  For non-rookies a good follow-up would be to do a 3-year average on/off court to get more accurate data but that would ignore yearly improvement and development.

In the end, it’s best to look at several measures to get an objective defensive evaluation. Clearly, there’s more to defense than just steals and blocks but you wouldn’t know that by looking strictly at the box score.  Steals percentage has little effect on the aggregate scoreboard and it’s best to not let them paint your overall evaluation of the player.

View the data here and you can see that J.J. Redick’s defensive on/off court differential sits in the 9th percentile.  Not so good.

Big thanks to Aaron Barzilai of basketballvalue.com for publishing on his site.

NBA HD: Inching For A Rebound

May 21, 2010 in by with 4 Comments

In last week’s post, I looked at the relationship between team height and rebounding.  It’s a good jumping off point to investigate the value of height in today’s game.  Building from that, I’d like to tighten my focus and hone in on the play-by-play data.  Aaron Barzilai graciously publishes play-by-play lineup data on his website basketballvalue.com and I’ll be playing around in that sandbox today.

Looking at the lineups, how much did a height advantage affect rebounding?

This approach improves upon last week’s analysis in a couple ways.  To start, we’re looking at play-by-play lineup data as opposed to overall rebounding numbers on a season-level.  This allows us to look into detailed matchups and focus on units rather than full rosters.  Secondly, I’m solely looking at the 3, 4, and 5 positions to better reflect those who affect rebounding the most.  In last week’s study, a few people pointed out that Derek Fisher’s smallness skewed the Lakers height numbers even though he doesn’t really matter on the boards.  (Perhaps the best solution is to weight the effective height by position).

The way the data is presented in the basketballvalue format is as follows:

Which ten players were on the floor? How many possessions were they on the court for?  How many offensive and defensive rebounds did each unit have?

Before I dove headfirst, I made some qualifications.  The units would have to have at least 30 possessions on the floor together.  Thirty possessions isn’t a whole lot (a little more than a quarter’s worth of a basketball game) but with the players held constant, it seemed like a fair line in the sand.  This qualifier eliminates about 63,000 lineup units and leaves a remaining sample of 326.

From there, I calculated the average height of the 3,4, and 5 players on each team and compared them to their opponent.  The widest margin of average height between two lineups was 10 inches or 3.3 inches per player (Grizzlies vs. Rockets). We’ll take a closer look at that matchup later.

For each lineup, I gathered their offensive, defensive, and total rebounding percentages during that time period. So, for example, a dataset may read as follows:

Westbrook, Sefolosha, Durant, Green, Krstic
Frontcourt avg height (Durant, Green, Krstic): 82.0 inches
ORR,DRR,TRR: 30.4%, 87.5%, 53.8%
vs.
D.Williams, Miles, Matthews, Millsap, Boozer
Frontcourt avg height: 79.3 inches
Margin: 2.7 inches
Possessions: 48

So, here we see that this particular Thunder unit made the most of their height against this specific lineup of the Jazz, grabbing 53.8 percent of all rebounds and locking up the defensive boards in partifular (87.5 pct).    Boozer and Millsap are known as talented board cleaners but against the Thunder height,they couldn’t make up the difference.  But not all matchups work in the taller team’s favor.  Digest:

Conley, Mayo, Gay, Randolph, Thabeet
Frontcourt avg height (Gay, Randolph, Thabeet): 83.0 inches
ORR, DRR, TRR: 10.5%, 72.2%, 40.5%
vs.
Brooks, Martin, Ariza, Scola, Hayes
Frontcourt avg height: 79.7 inches
Margin: 3.3 inches
Possessions: 36

Here, we see that the far superior team (in terms of height) got worked on the boards by their smaller foes.  In this matchup, the Grizzlies missed 19 shots but only recovered 2 of those missed shots.  That’s quite an accomplishment for a team giving up 10 inches underneath.  Once again, we bow down to Chuck Hayes’ rebounding prowess.

But these are just two of the 326 matchup pairings that lasted 30 possessions.  What does it look like when we look at all observations in the sample?

Here, we have all 362 lineups and their total rebounding percentages.  As you can see by the positive trendline, the taller the frontcourt, the more rebounds collected (p<.0001).  Earth-shattering stff, I know.  But how much does an inch help? We can use that handy regression equation:

Total Rebounding Percentage = 0.0165*(Height Advantage) + 0.4983

So, for every inch gained in Height Advantage, meaning each frontcourt player has an inch on average on their opponent, we would predict the total rebounding percentage to increase by 1.65 percent.  What’s 1.65 percent? For reference, the Thunder are the sixth best rebounding team in the NBA according to TRR and they are 1.69 percent better than average.   All else equal, having an inch on your opponent matters, but it won’t guarantee a rebound.  In case you were wondering, the lone blue dot on the bottom right represents the Memphis Grizzlies lineup mentioned above.

How about strictly looking at offensive rebounding? Does height more critical on the offensive boards?

It doesn’t appear that height margin matters more on the offensive boards than overall, given that they have nearly identical coefficients (0.01645222 vs. 0.01645211 to be exact).  Like overall rebounding, an inch in average height advantage tends to lead to 1.65 percent more offensive boards.  Any interesting matchups? As you can see on the graph, some units failed to get a single offensive rebound (0.0% ORR).  Who were they? For fun, let’s take a gander:

Curry, Ellis, Maggette, Hunter, Tolliver (-1.7")
vs.
Nash, Richardson, Hill, Stoudemire, Lopez
11 rebounds
31 possessions
-
Rondo, Allen, Pierce, Garnett, Perkins (-1.3")
vs.
B.Davis, Butler, Thornton, Camby, Kaman
13 rebounds
35 possessions
-
Udrih, Greene, Casspi, Thompson, Hawes (+0.3")
vs.
Fisher, Bryant, Odom, Gasol, Bynum
12 rebounds
31 possessions
-
Fisher, Bryant, Artest, Gasol, Bynum (+1.0")
vs.
Foye, Miller, Butler, Jamison, Haywood
9 rebounds
32 possessions

You got the obvious Warriors Nellieball lineup but you also have the Lakers on both ends of the deal.   I’m not surprised that the Odom, Gasol, Bynum lineup grabbed all 12 available rebounds even with Donte Green at the 2.  That’s a ridiculously tall lineup.  However, I didn’t expect the Lakers to be on the losing end of the deal against the pre-trade Wizards.  Interesting stuff, I say.

On the offensive end, it still holds that the taller your frontcourt, the more offensive boards you will tend to collect.  Let’s finish up with the defensive side of the boards.

Again we see a positive relationship with height advantage and rebounding rates but the coefficient here is greater (0.0175).  This means that an inch advantage on the defensive end tends to increase defensive rebounding percentage by 1.75 percent.  This contradicts my finding in last week’s exercised that showed that team minutes-adjusted height had almost a completely random correlation with defensive rebounding rate.

In the end, conventional theory holds true that it helps to be taller in order to grab rebounds. However, it’s not as strong of a correlation as I expected.  Of course, height doesn’t explain all the variation in rebounding rates because there are other factors that contribute to rebounding: wingspan, vertical jump, horizontal jump, reaction time, positioning, etc.  I like that this study holds the lineup personnel constant but I would always like to get a larger sample size. But that has it’s drawbacks too.  When we increase the requirement threshold, we lose reliability.

How do we reconcile this study with last week’s that said height mattered more to offensive rebounding?  Last week’s looked at the forest rather than the trees.  I only had 30 teams in the sample size and the height effects could have been clouded in the aggregate numbers.  Additionally,  in this post, I tried to improve the validity of the measure by only looking at the frontcourt height rather than the whole five.  Perhaps a weighted height would be the best option, giving more weight to the bigger position and less weight to the point guard position.  For another time.

Again, have to thank Aaron for providing such a helpful resource.  Assist point to you, sir.

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.

NBA HD: Evidence of Growth? Or Growing Pains?

April 1, 2010 in by with 0 Comments

After last week’s column about the sustainability of shooting, I want to build on that foundation and steer my thought into new directions.

In that piece, I mentioned Derrick Rose’s league-leading field goal percentage on short shots (58.2 percent) and wondered whether that was something he could repeat in years to come.  While we’re not quite ready to make projections from the raw data, I was curious about a related question:

Do rookies tend to improve their shooting percentage in their sophomore year?

I touched on this topic before in this space but not across all the shot locations.  So, Rose has experienced an enormous jump on shots within ten feet and I wondered if that was an outlier compared to the rest of the rookies/sophomores in the sample.  So I gathered all the rookie/sophomore seasons of the past four years (the span of the Hoopdata set) and set some qualifiers.  To reduce variability in the analysis, I set the sample frame to 50 shot attempts in the shot location in both their rookie and sophomore season.  That way, Steve Novak can’t bring the noise.

I have some reservations about setting the bar at that level because quite honestly, 50 shot attempts isn’t a whole lot but I also recognize that, by and large, rookies rarely get the opportunity to get that many shots in the first place.  Set the bar too high and the chart looks at the development of Kevin Durant and Joakim Noah.  As a result, two biases exist here.  A selection bias arises because we’re only looking at the players who got enough run to get their shots and secondly, a survivor bias exists because players who shot poorly in their rookie year might not shoot enough to qualify in the second.  But nonetheless, this situation is more desirable than analyzing a couple of data points.

Just as I did in the last article, I charted each player’s year 1 and year 2 field goal percentages from the following Hoopdata shot locations: at rim (layups, dunks, and tip-ins), short (<10 feet), mid (10-15 feet), long (16-23 feet), and three-pointers.  In this study however, the year 1 will always be the rookie season and year 2 will be the sophomore season.

Let’s take a look at how rookies performed on at rim shots in their first two years in the league.  Did rookies get better with a year of NBA play under their belt?

Of the 65 rookies in the sample, 32 improved their at rim field goal percentages the following year as you can see by the data points below the gray diagonal.  Surprised?  Well, before you conclude that all rookies will get worse at finishing layups in the following year, remember that 33 vs. 32 is not a convincing defeat by any means.  The average change in field goal percentage was actually a positive 0.006 or 0.6% but insignificantly so.

Still, for those expecting an general increase in ability to finish at the rim, this is a bit of a surprise.  When we break this down into positions, we find that 9 of the 13 point guards improved from rookie to sophomore year which is the best improvement of the five positions of the floor.  Interestingly enough, only 12 of the 27 big men in the sample (power forwards and centers) experienced an uptick in their success rate at the basket.

How about short shots? Where does Derrick Rose’s mark fit in?

In this sample, Derrick Rose and Rajon Rondo improved the most. Where can you find them? Rondo’s the southernmost point on the chart whereas Rose finds himself furthest east.  There were only 21 rookies in this sample so the conclusions are quite limited.  For what it’s worth, two-thirds of this sample improved into sophomore year but with such a small sample size, that’s easily due to random chance. In my study last week, I found that year-to-year correlations were the most random in this zone.  Brandon Roy and O.J. Mayo, both shooting guards (or hybrids in many situations) both declined in sophomore year from this range.  This area generally has the least focus among basketball players so a decline usually is nothing more than a tiny dent in production.

Moving on to the 10-15 feet shot which we can the mid-range.

With only 16 players who fit the criteria in this shot zone, the relationship looks to be completely random.  Some improved and some regressed.  LaMarcus Aldridge went from a 29.0 FG% shooter from the 10-15 foot range in his rookie year to one of the most successful mid-range shooters in the game in his second year.   His struggles in his rookie year didn’t discourage him as only six players took more shots from this area per game the following year and his field goal percentage soared to 45.3 percent.  Teammate Brandon Roy didn’t enjoy the same success, however. He shot a blistering 45.4 percent his rookie season and fell to 31.3 percent in his sophomore campaign.  Unfortunately, the tiny sample size doesn’t allow us to extrapolate much from this area.

What about long twos? Have sophomores shoot better just inside the three point line?

Like the mid-range shot, sophomores in this sample don’t seem to exhibit improvement on long twos.  Of course, this area of the floor probably is most sensitive to the biases since not every player possesses enough of this shooting skill to qualify.  Especially with bigs, the mid-range jumper is work in progress for the first couple years in the league.

Among the 11 shooting guards in the sample, only Randy Foye and Ronnie Brewer experienced more success on their long two jumper in their sophomore year. Aaron Afflalo, O.J. Mayo, Brandon Rush, Daequan Cook, and Eric Gordon all regressed following their rookie campaign.  In the case of Mayo, it was a regression to the mean after a sparkling rookie campaign where he shot 45.2 percent from 16-23 feet.  He’s about league average this season.  He’s not an exact comparable for Ty Lawson who’s shooting 48 percent this year but he should take note as most of the rookies who shot better than league average (40%) on long twos in their rookie year, ended up below the norm in year two.

How about the three-point line?  This is just the past four years but I’m sure longer studies have been done before.

Again, lots of randomness here but that’s to be expected with only 30 observations.  Half of the group declined and half improved their downtown shot.  The most stark correction came from Michael Beasley who shot 61.1 eFG% in his rookie year but just 40.2 eFG% this season.  This must be evidence of the curse of the No. 2 pick, right?  Actually, no.  2007 No. 2 pick Kevin Durant improved his three-point shot from 43.1 eFG% to 63.3 eFG% from year-1 to year-2.  That was a quick disposal.

So what did we learn? As much as we want to believe that “one year under the belt” theory, it hasn’t shone through in this crop of rookies.  If anything, we observe a regression to the mean as opposed to uniform improvement. There’s plenty more work to be done in this area and this certainly doesn’t wrap up the rookie to sophomore growth analysis.   As it is with a lot of basketball studies, we need more data to draw stronger conclusions.  The limited scope of shot location data keeps our extrapolation to a minimum.   But nonetheless, if you wonder if Ty Lawson’s 48 percent shooting from long two or Brandon Jenning’s putrid finishing ability are here to stay, you can refer back to these charts to see if past extraordinary rates continued the following year.

NBA HD: Dismantling the Assist

March 18, 2010 in by with 21 Comments

Sometimes we need to take a step back from it all and ask ourselves fundamental questions to find truth in our lives.

Today, we will have one of those moments.  Ask yourself this question:

Why do we care about assists?

I’m not saying we shouldn’t care about assists.  We should.  They tell us something, which is valuable.  But what exactly do they tell us?

An assist tells us when a player passed to someone and that pass lead directly to a made basket, but only it should only be recorded if the basket is made.  It is recorded in attempt to reward good passing.  Say Steve Nash passes to Jason Richardson who immediately nails an 18-footer from the wing.  Nash receives a token for his efforts in the form of a recorded assist.  The thought process being that we should award Nash some credit for Richardson’s made basket because he had something to do with that ball going in.

The assist represents an example of post hoc reasoning, or post ergo propter hoc. Translated into English, it means ”after this, therefore because (on account) for this.”  When this reasoning is incorrectly applied, it is referred to as the post hoc fallacy, which you’ve probably heard before.  The post hoc reasoning (or fallacy) states that if one event followed another, then it must have been caused by the original event.  A pass led to a bucket and therefore, it was a good pass.

Here’s where that reasoning becomes problematic.  How many times have you seen a player make a magnificent pass to a teammate, only for the teammate to subsequently blow it on the shot?  Countless times, I bet.  And how many times have you seen a great pass on a highlight reel where the player misses the shot? Almost never, right? We allow the shot result to influence our perception of the quality of the pass.  An outstanding pass transforms into highlight reel material or an assist only after the ball goes through the net.

Consider the following clip of Pau Gasol and Kobe Bryant:

Pau Gasol gets credit for only one assist because Kobe Bryant blew the dunk in the first play.  In reality, both passes were equally worthy of record.  When we speak of good passes or passes worthy of record, we’re subconsciously referring to passes that increase the chances of scoring from Moment A to Moment B.  In the first play of the clip, the chances of scoring when Pau Gasol has the ball 25 feet away from the rim (Moment A) pales in comparison to the chances of scoring after he rifles the pass to Kobe (Moment B).  Rather than changing it’s mind ex post facto, the ideal assist should try to capture that expected difference regardless whether Kobe Sprites it or not.

What we’re really after is the potential assist; a pass that directly leads to, not a made shot, but an attempted shot.  For some shots, a good pass is vital.  For others, the effect of a pass is negligible; the shooter would have made it anyway.  Unfortunately, passes that don’t lead to a made basket get lost in the black hole of basketball scorekeeping ignorance.  We don’t have any idea if threes are made more frequently if the shooter receives a pass as opposed to shooting off a pull-up J.  It’s a shame, really, because such information would be incredibly valuable for basketball research and analysis.

Well, thanks to 82games.com and their ultra-diligent charters, we no longer have to sit in the dark anymore.  A few years ago, they published a breakthrough study on their website that pulled the veil on good passing.  Rather than only focusing on made baskets, the team charted all shots and noted whether they were set up by a pass or not.  It’s a must read so go there and come back.  One of the several discoveries the 82 games team found in their charting was that non-assisted shots from close range are converted nearly 13 percent less than those that were set up by a pass.  Thirteen percent might not seem earth shattering but it is in the context of shooting.  Would you rather have Dwight Howard’s shooting percentage or Toney Douglas? That’s 13 percent.

Here’s the whole table from the outstanding study:

Interestingly, although most three-pointers are assisted (81 percent) according to 82games.com, the effect of a pass is smallest (+3.7 percent) compared to the others.  An assist on a close shot has over three times the impact.  In all, unassisted shots go went in .421 percent of the time whereas a pass propelled that figure up to .502 percent.   If you were wondering if passes really amount to anything, here’s your evidence.  All assists are not created equal.

These numbers take the macro view on the passing game and it would be foolish to assume that all players and shot types reflect the same percentage effects.  Certainly, there are personnel biases at play here and some particular point guards have no choice but to work within the confines of the offense sets.   Still, I wanted to apply these findings to the game’s best ball distributors and experiment how their assist total would change if we credited the assists according to each’s areas impact on FG%.  Last week, I asked how ball distributors get their assists with regard to high efficiency areas. This week, I’m asking a slightly different question: which players get their assists in shooting areas most impacted by the pass?

To get the quick and dirty measure, I set the average difference of 8.1% equal 1.  So an assist to a close shot receives a credit of 1.56 assists and likewise, a 3-point shot assist is credited 0.69 or ((3.7*1.5)/8.1) with the 1.5 adjusting for the bonus point.  Of course, there are several limitations to this exercise and should not be treated as an assist surrogate.  But it does shed more light about the assist variety.  Here’s the crop of the best in assists per game sorted by the difference in adjustment.

We find an interesting mix at the top.  Somewhat unexpectedly, Baron Davis paces the field and Mike Conley brushes shoulders with Deron Williams and Jason Kidd.  Why do they rank highly? By getting their assists in the areas most influenced by a set up pass.  Baron Davis feeds about 40 percent of his assists to chip shots around the rim which is far above than the average share.  On the other end, Jameer Nelson gives nearly 60 percent of his assists result to 3-pointers and dunks where the pass impact is generally low.

Note that New Orleans Hornets point guards Chris Paul and Darren Collison experience different effects after this adjustment.  Compared to his counterpart, Paul’s assists lead to a higher proportion of dunks to layups, which has pivotal implications on his differential.  I’m not sure how to coalesce the perceived immense value in Paul’s patented alley-oop floater with 82games.com’s dunk findings but I’d be willing to guess that a hybrid adjustment would be necessary.

Interestingly enough, the “impure” point guards gather at the bottom at the list.  Tyreke Evans, LeBron James, Kobe Bryant, and Dwyane Wade don’t receive a substantial upgrade by this measure because their dribble penetration play styles generate a high proportion of 3-point assists.  In fact, LeBron dishes out a 3-point assist nearly twice as often as his point guard Mo Williams.

Unfortunately, we’re limited to looking at these players using league average field goal percentage effects.  Admittedly, this a shortcoming that must be resolved before we get a complete picture of passers.  Some players cannot create their own shot off the dribble and have no choice but to get all three pointers from the catch-and-shoot (think Antawn Jamison).  They will undoubtedly experience varying passing effects than the norm.  Moreover, the component of foul shooting must be considered.  Read more about that in the 82games.com article.

In the end, if we get complacent and treat all assists the same, we’re missing out on the big picture of ball distributors.  We would benefit from rethinking the way assists are recorded and how we interpret those numbers in the box score.  With evidence to suggest close shots have are highly influenced by a pass, we can sharpen our approach in evaluating the impact of point guards and passing in general.  Hopefully after reading the last two articles, you’ll have a more complete understanding of the passing game and the drawbacks of the assist statistic design.  If anything, we must ask more questions and dig for more data to get at those elusive basketball truths that we seek.   I think I need an assistant.

And For Their Next Trick, HoopData Will Blow Your Mind

February 8, 2010 in by with 0 Comments

What you just experienced was a moving montage of each season since 1999-00, in terms of offensive efficiency and usage among active players. That was just for kicks. Now let me attempt to fully explain the power of this chart and describe its nearly limitless array of functions. Try not to jump ahead as I walk you through this. Come along for the ride.The color of the data points are not random. They actually represent each player’s minutes per game MPG for that season. You can see the colorful scale in the top right, beneath the MPG field. In this case, blue indicates a bench player and red indicates a player who rarely got any time on the pine. I weeded out all the seasons with less than 10 minutes of action per game to eliminate outliers.

So how is this useful? Take a look at Monta Ellis while in the year 2010 which you should be if you haven’t rushed ahead. You can find him all red-faced at the intersection of 30 USG% and 100 ORtg. He is the new Allen Iverson– the star Jack Russell terrier who racks up tons of points but does so inefficiently. Want another possession-waster? Look for a sunburnt circle west of 25 USG and south of 100 ORtg. That’s Trevor Ariza. Can’t see him? Click and on the intersection of 80 ORtg, 25 USG% and drag to create a box up to ORtg 100, 15 USG%. Bam! There he is in his orange glory. He’s still a valuable asset for the future even if he’s struggling in his new role.

via Hoopdata – NBA: Where Motion Happens.

I cannot tell you how amazing I consider this tool to be. Not just in terms of how pretty it is, but to be able to track, consider, and analyze players’ comparative performance across time in a visual format? It immediately brings a different perspective. Being able to see where precisely players’ growth spurt and decline begin is fascinating, and could allow us to keep those things in mind when looking at similar players. It puts things in context (try Bosh vs. Melo, PER vs. Time), and brings us to another level of understanding. It’s nothing that changes the way we look at the game, but it’s a phenomenally useful tool.

In short, GO CLICK NOW. KTHXBAI.

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.
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