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.

I’m a big believer in striking while the iron’s hot. With Zach Harper’s breakdown of Darren Collison’s assists lighting a fire under the Hardwood audience, I thought I would take a deeper look at the assist variety.

I’ll begin with the assertion that not all assists are created equal, no matter what the box score tries to tell you.  The traditional box score specifies the number of shots coming from beyond the three-point line for each player but the assists column offers no such detail.  This shields the basketball world from a more complete understanding of ball distribution for each contest.  Let’s pull the veil on that part of the game.

In Tuesday night’s Utah Jazz massacre over the Chicago Bulls, Deron Williams dropped 17 dimes which is a season-high for the former Illini.  But did you know that seven of those led to treyballs?  Probably not, unless you picked up your daily advanced box score at Hoopdata.  On the same night, Raymond Felton dished out 11 assists, with 8 of them setting up for gimmes (layups and dunks).   These two point guards aided their teammates to score from high efficiency areas on the floor but this valuable information hadn’t been unlocked in the public domain. Until now, of course.

Depending on a combination of skill set, fellow personnel, and X-and-O’s, every point guard varies on how they compile their assists.  Some earn their dimes through dribble penetration and dishing to a cutter to the basket after the defense collapses.  This type of distributor tends to yield a high percentage of at rim buckets for his team.  Others make a living instead by patiently waiting for the perfect moment to hit their sharpshooting teammates on the perimeter rather than exploiting the porous help defense on dribble drives.  These types tend to tally a slew of assists leading to long twos and three-pointers.

So, who are these guys?  Let’s compare two of the best assistants out there, LeBron James and Jason Kidd.  One is a 6-8 dominant scorer and the other is a 36-year old Hall of Fame distributor.  Both average over 8 assists per game.  The pie charts display the shot location share of their assists in terms of the five zones: at rim, short (<10 feet), mid (10-15 feet), long (16-23 feet), and threes.

As you can see, these two ball-handlers get their high assist totals in much different ways.  Over 75 percent of LeBron James’ assists yield a three pointer or a bucket at the rim, highlighting just how devastating LeBron James can be as a ball-hander.  If he’s not scoring himself, he commands the help defense and double-teams, opening up the high efficiency areas for his teammates.  Actually, 3.9 at rim assists per game understates how many buckets he yields at the rim.  In his last ten games, the Chosen One has dished out 5.7 assists per game at the basket, nevermind every other area on the floor.  Consider for a moment that Kevin Durant, Carmelo Anthony, Kobe Bryant, and Dirk Nowitzki each average fewer than 5.7 total assists per game. And LeBron leads the League in scoring.

Conversely, fellow All-Star Jason Kidd splits his assists between the mid-range and the high efficiency areas, which says as much about him as a distributor as who receives the delivery.   Dirk Nowitzki, the most frequent shooter on the Mavs, lives in the mid-range and chucks up a league leading 8.5 attempts per game from 16-23 feet.

Moving along, when we look at assist numbers, it might be worth it to break down each assist according to their expected point value.  The numbers tell us that at rim shots and 3-point shots have a higher expected value than mid-range jumpers which only go down 39.5 percent of the time and only have a 2-point payoff but each assist is treated as equal to one.   To account for this value distribution, I created a simple metric that assigns  a weight to each assist zone, giving point guards who distribute the ball to high efficiency areas a boost in the bottom line.

The weighting doesn’t arbitrarily assign point values that I plucked out of thin air.  Rather, I found it appropriate to weight the assists according to the expected pay off of the shot location.  The average non-fouled shot at the rim converts at a 60.8% percent rate so the expected payoff, fouls aside, is the product of probability and point value or  .608 * 2 = 1.216.   Shots taken from 10-15 feet have the lowest conversion rate (.396 field goal percentage) and thus, the expected value from this area amounts to just .792.  Threes have a higher expected value than the mid-range because of the added point bonus.

Taking LeBron James as an example, his weighted assists per game (wAPG) would be calculated as:

wAPGLeBron = (At rim APG * 1.216) + (Short APG * 0.880) +

           (Mid APG * 0.792) + (Long APG * 0.794) +

           (Threes APG * 1.062)

wAPGLeBron = (4.8*1.216) + (0.5*0.880) + (0.2*0.792) + (0.8*0.794) + 
            (2.8 *1.062)

wAPGLeBron = 9.1

Without accounting for the types of assists, LeBron has a 8.5 assists per game so the net difference is only 0.6 assists per game.  As is, at rim shots have about a 50% premium on the mid-range shots inside the three-point line.  Admittedly, the model would be improved if we accounted for shots that led to free throws but my powers are limited at this point in time.  If that were the case, distributors like LeBron would see even more of a boost since most fouls occur around the basket.

This adjustment derives its theoretical foundation from Dean Oliver’s “Basketball on Paper”, where he argues that assists to the perimeter should be discounted relative to shots at the basket because the outside shooter holds the most responsibility for nailing the shot.  The passer only changes that likelihood slightly.   However, since defenses rarely opt to allow big men to get open around the basket, the point guard receives more credit for creating that opportunity.  Put another way, do you think Chris Paul should receive the same credit for his patented alley-oop floater pass as he does for a routine pass to Peja Stojakovic who hits a fallaway mid-range jumper?  This model doesn’t think so either.

Who isn’t excited about this adjustment? As you might of guessed, Jason Kidd loses some of his point guard moxie with the tweak.  While most point guards see a higher wAPG, Jason Kidd, Derrick Rose, and Jerryd Bayless each have a lower wAPG than raw APG.   Here are the leaders and trailers as measured by percentage difference, among those who average 4 ast per 40 minutes.

If you’d like to see the full spreadsheet, I’ve uploaded here on Google Docs.

Cheers.

The objective of any defense is to prevent the team from scoring.  To this end, a defense can discourage high-percentage shots (shots at the basket), high-value shots (3-pointers and fouls), and create turnovers.  Quantifying defensive efforts, especially on an individual level, has long been an intriguing frontier of the basketball analytical world.

Preventing quality shots at the basket is important.  It’s why Hasheem Thabeet was drafted second overall.  It’s why teams use the 2-3 zone.  It’s why the 3-second rule exists.

So how do we grade this part of the game? Let’s start with blocks.  Blocks have traditionally stood as the measuring stick for paint defense but there are inherent problems with this using blocks as a proxy.  Not all blocks are recovered by the defensive team and thus, they offer opportunities for the offense to restart their offense and work a better shot.  The ego-fueled swat that sends the ball flying into the stands has in fact caused coaches to spew steam out of their ears.  And for good reason.  It’s probably best to just do this.

Another negative externality of the blocked shot is the fouling side effect.  The typical shooting foul will put about 1.5 points on the board.  This is the one of the many reasons why Thabeet was recently demoted to the D-League.  Among players who play 10 minutes a game, only two players fouled more than the UConn product.  After running a cost-benefit analysis, the Grizzlies decided he was better off playing for their JV team.  Sometimes, a block just isn’t worth it.

In the end, blocks do not correlate with good post defenses nearly as much as one would expect.  A superior way to measure basket defense is how well opponents shoot at the rim, or as we at Hoopdata.com have termed at rim field goal percentage.  This statistic captures not only a team’s shot-blocking ability but also their ability to alter shots by calculating how teams shoot on layups, dunks, and tip-ins.

The Boston Celtics, who rank fourth in at rim FG%, do not feature the shot-blocking prowess as some other teams but are much more effective at provoking missed shots around the basket.  Conversely, the Clippers have the second highest block rate in the NBA, thanks to the defected Marcus Camby, and yet find themselves 22nd in at rim field goal percentage.  The Celtics protect the basket far better than the Clips but you wouldn’t have guessed by only looking at their shot-blocking ability.

So let’s move away from blocked shots as a proxy for basket protection and focus more on at rim percentage.  I could offer a straight up leaderboard of opponent at rim percentage but I want to take this a step further.  Even at rim percentage can be misleading.  Why?  It still misses the foul component of basket defense as fouled shots are not included in field goal percentages.

Imagine if a coach told his players to foul every time the offense got an easy look at the basket.  It would probably work for a while but then the team’s best defenders would start fouling out by halftime and non-shooting fouls would earn a trip to the foul line sooner.   No coach would honestly advocate that strategy, but it appears that the Pacers have employed a version of it.  The Pacers have the third best at rim defense in the NBA as measured by at rim FG%.  However, they also foul their opponents a ton.  As a result, they have just an average defense when their at rim defense suggests they should be a defensive powerhouse.  Consider that the other leaders in opponent at rim FG% are Orlando, Chicago, Boston, and Cleveland– all excellent defenses.

To illustrate this dynamic, I plotted each team’s  opponent free throw rate (FTA/FGA) and their opponent at rim FG% below.  The text size and color gradient represents the portion of at rim attempts the team allows. The more you allow, the louder the data point.

Teams should strive to be in the lower left region, where opponents miss shots and don’t get to the line.  The Warriors, however, feature just about the worst combination of fouling and easy buckets, and likewise find themselves in the upper right region.

Orlando has an incredible post presence in Dwight Howard and at 4.1 fouls per 40 minutes, he fouls less often than the average center.  Perhaps the reason Dwight Howard isn’t getting the MVP recognition many believe he deserves is because he impacts the game in ways that the media can’t articulate.  Well here’s the evidence they’re missing.  The Magic protect the basket better than any other team in the NBA and they own the third best defense in the land.  He’s why.

It’s interesting that many analysts believe Brendan Haywood is the post presence that the Mavericks desperately needed when one considers that the Wizards allowed by far the highest at rim FG% in the NBA.   While they don’t give up a high percentage of shots from that area, they add to their post defense woes by fouling at a moderate rate.

The Bulls probably don’t garner the attention they deserve. They don’t foul, nor do they let opponents get any shots off at the rim.  They lost their best post defender in Tyrus Thomas but let’s not forget that he’s only played about a quarter of the teams minutes this season.  Joakim Noah has been superb on the defensive end this year but unfortunately for the Bulls, he’ll be out for the next three weeks with plantar fasciitis.   The Bulls hope they can hang onto a playoff spot without Thomas and Noah protecting the rim going forward.

As demonstrated here, teams like Indiana and Milwaukee have deflated opponent at rim percentages as a result of their fouling rates.  Others genuinely own the rim and create nightmares for their opponents without sending them to the charity stripe.  Keep this in mind as you watch the different defenses get prepped for their playoff run.