NBA HD: Adjusting How We Measure and View Assists

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.


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