Quintiles: Classifying Players by Their Offensive Tendencies and Shot-to-Assist Ratios

In most circles, LeBron James is considered a small forward.  Never mind the fact that, at somewhere around 6-foot-8 and well over 240 pounds, James is by no means small, even by typical NBA standards.  But it should also be noted that, in most ways, he is not even a forward, let alone a small one:  For his career, the rate at which James passes up his own shot in order to assist his teammates exceeds that of his own sidekick, shooting guard Dwyane Wade – a trend which continues this year, even as they play together.

Or consider the case of Bill Laimbeer.  The heart of the championship Detroit Piston Bad Boys is considered by just about everyone as having played the center position – and at 6-foot-11, few are going to argue.  But at the height of his career, Laimbeer was hoisting over 150 three-pointers per season – and nailing them with a guard’s accuracy – as well as distributing the ball to teammates at a rate associated with front-court swingmen such as Michael Jordan and Kobe Bryant.

And then there is 1980’s defensive legend T.R. Dunn, who is generally listed as a shooting guard.  But there is one problem with that distinction – Dunn almost never took a shot.  At the height of his career, Dunn took less than five shots per game.  There were years, in fact, in which Dunn gathered more rebounds than points.

The point of all of this – James, Laimbeer and Dunn – is that basketball players don’t have positions as much as they have roles.  These roles, of course, are defined by the intersection of the player’s strengths, and what his team asks him to do.  Distinctions such as “point guard,” “shooting guard,” and “power forward” are false ones, and appear to have more to do with the body habitus of players, and what we as observers think they should be doing with that body.

But it became apparent to me while I was devising the formula for Successful Possession Rate (SPR; see the Dec 26, 2010 posting) that players attempt to achieve their success in very different ways on the offensive end, and it affects the way we might interpret their stats.  As I mentioned in the previous post that describes SPR, the inclusion of assists in the formula is going to make players with high assist totals look distortedly better than players who get fewer assists, but tend to score more points. 

This is due, in part, to statistical artifact: the formula’s numerator includes a stat associated with success (field goals made [FGM]), and the denominator includes both successes and failures (field goals attempted, or FGA).  But for assists, there is no real statistical counterpart to include in the denominator that reflects all attempts, including failures.  Sure, I put turnovers (TOV) into the denominator, and players who dish out a lot of assists tend to turn the ball over more frequently, too – but players who shoot first and pass later also make turnovers.

And so what I noticed with the SPR was that players we typically associate with passing the ball (Magic Johnson, Danny Ainge, Raymond Felton, e.g.) had significantly higher SPRs than teammates of theirs who were at least as good, and perhaps even better (Kareem Abdul-Jabbar, Larry Bird, Amar’e Stoudemire, e.g.) – all because of the differential passing and shooting tendencies the players demonstrated.  This much became clear:  Comparing the SPR, and other relative stats, of players at different positions was essentially comparing apples and oranges.  You must compare like with like – or, in this case, you must compare players who play the same position.

But what is a position?  As I suggested before, the way a player is listed in the game program is more a function of his height than what he truly does on the floor – King James is more “point guard,” if there is such a thing, than forward.  And Bill Laimbeer was more “shooting guard” – again, if there is such a thing – than center, at least on the offensive end of the court.

So I was looking to find an objective way to characterize players by position, or playing styles.  What I came up with was the Shot-to-Assist Ratio (SAR), an objective qualitative value – in other words, a way of assessing what a player is, rather than how good he is.   The formula is:

SAR = [FGA + (FTA/2)]/AST]

Basically, it is a ratio that compares a player’s tendency to shoot (all field goal attempts, plus half of free throw attempts) to his tendency to pass (assists).  There are some obvious flaws with the formula, of course: “and-one” free throw attempts and technical foul attempts slightly skew one’s shooting tendency, and attempts to assist a basket would be a more reflective measurement than assists that actually reached fruition – but it appears close enough.

And upon evaluation of all 30 NBA teams from the 2009-10 season, looking only at the eight players on each team who accumulated the most minutes played, you can see that the different SAR of each player sort of segregates itself into quintiles – or five different positions.  But unlike the positions touted in the game program, these quintiles are derived from a player’s actual actions on the court.

From here on in, this post will A) define the SAR of players within each quintile; B) assign a position title that more accurately reflects the role of players within each of these quintiles; and C) give examples of within which quintiles players from the 2009-10 season would fall.

Quintile I (SAR 0.01 – 2.88): Primary Distributors

This would be the quintile that most conventional basketball fans would associate with point guards, and it includes players who assist their teammates just about as much as they themselves attempt to score.  Though the SAR of Primary Distributors starts at 0.01, the player with the lowest SAR in the NBA last year was Jason Kidd, with an SAR of 1.00 (he assisted baskets exactly as much as he attempted to score them, according to the statistic, and this seems to reconcile with what the naked eye tells us about Kidd).  There is a range, of course, within this quintile of players, and some Primary Distributors shot more than twice as much as they assisted – which, for an NBA player, is still quite a low ratio.  Below are 10 representative examples of Primary Distributors, based on last season’s statistics:

1.      Jason Kidd (1.00)

2.      Rajon Rondo (1.32)

3.      Steve Nash (1.23)

4.      Chris Paul (1.53)

5.      Baron Davis (1.94)

6.      Stephen Curry (2.63)

7.      Russell Westbrook (2.10)

8.      Mike Miller (2.23)

9.      Deron Williams (1.58)

10.  Andre Miller (2.48)

I included both Millers, Mike and Andre, in this example to illustrate a point.  Andre would be described by just about everyone who watches the game as a point guard, and his SAR of 2.48 would support that distinction.  But Mike would almost certainly be defined as a shooting guard – perhaps even a three-point specialist – and yet his SAR (2.23) is even lower than Andre’s, suggesting that Mike Miller is actually a player who, relatively speaking, is looking to pass the ball.

Quintile II (SAR 2.89 – 4.70): Combination Distributors

This is the quintile that many observers might describe as “combo guards,” or perhaps shooting guards: willing passers who nevertheless get significant contributions from their shooting game.  Just as with Primary Distributors, the Combination Distributor quintile is a continuum, not a quantum, and thus you will find varying degrees of players within this class, just as in any class.  Below are 10 representative examples of Combination Distributors from the 2009-10 NBA season:

1.      Derrick Rose (3.29)

2.      Dwyane Wade (3.72)

3.      Lamar Odom (3.15)

4.      Brandon Roye (4.12)

5.      Manu Ginobli (2.92)

6.      LeBron James (2.94)

7.      Joe Johnson (4.12)

8.      Pau Gasol (4.70)

9.      Grant Hill (4.29)

10.  Gilbert Arenas (3.13)

Of the 240 leading accumulators of playing time in the NBA last year, just under 50 would qualify as Combination Distributors, only 10 of which are named here.  But I chose these 10 to illustrate an important point, which is that players accomplish distinctive roles no matter what we choose to call them.  Derrick Rose, Dwyane Wade, Brandon Roye and Manu Ginobli are all Combination Distributors, and I am sure that this surprises few who have watched these excellent players perform.  But LeBron James, who most would qualify as a “forward,” “swingman,” or even “power forward,” has an SAR (2.94) that not only qualifies him as a Combination Distributor, but as one with a lower SAR than even Rose (3.29), or his new teammate Wade (3.72).

Perhaps the most remarkable examples of Combination Distributors would be that of two teammates, Lamar Odom and Pau Gasol of the Lakers.  Even by conventional standards, Odom is difficult to classify – Is he a power forward? A small forward? A Center? – but the numbers bear out that he balances his front-court game with a lot of passing, sort of like Larry Bird, the archetypal “point-forward.”  And the 7-foot Gasol is viewed by just about everyone as a center – albeit one who is an excellent passer – and yet his SAR of 4.70 renders the center distinction meaningless: Gasol is a distributor who likes to shoot from the post, and is good at it.

Left off of this list would be another European front-court player, Andrei Kirilenko, who comes in with an SAR of 3.70, lower than that of Grant Hill and Joe Johnson.

Quintile III (SAR 4.71 – 6.75):  Balanced Scorers

This quintile, deemed the Balanced Scorers, would defy easy classification from even those who ascribe to conventional basketball wisdom.  Some might call these players "shooting guards," others might call them "swingmen," and still others might call them "small forwards."  By any name, these are players who are shooting just about five times as often as they pass.  Mind you, this is not a value judgment on these players, merely a qualitative judgment.  Players with lower SARs are not better than those with high ones, nor are they necessarily less selfish – they are just playing a role that emphasizes passing.  And players with high SARs are not necessarily self-serving stat mongers – for the most part, they are being asked to do a very difficult job by their teammates, which is to finish the play and put the ball in the hoop.  This brings me to the side point that SAR should not be done to quantify a player, only to qualify him – it tell us what more than it tells us how much.  Below are 11 examples of Balanced Scorers from 2009-10:

1.      Kobe Bryant (5.04)

2.      Monta Ellis (4.71)

3.      Ray Allen (5.24)

4.      Paul Pierce (4.97)

5.      Kevin Garnett (4.77)

6.      Carlos Boozer (5.22)

7.      J.R. Smith (6.19)

8.      Jamal Crawford (5.30)

9.      Vince Carter (4.95)

10.  Tim Duncan (5.16)

11.  Eric Gordon (5.02)

I chose 11 because this quintile is so interesting.  It includes a player, Eric Gordon (5.02), who is generally considered a combination guard, right alongside another player, Tim Duncan (5.16), who is going to make the Hall of Fame as either a power forward or center.  This list includes two future Hall of Fame playmakers from the same team (Ray Allen and Paul Pierce), both of which have slightly higher SARs than their “power forward” teammate, Kevin Garnett, who demonstrates a great deal of balance to his game. [Note: I found it elucidating that an excellent team, the 2009-10 Boston Celtics, had their three best players demonstrating Balanced Scorer tendencies, while a fourth player – Rajon Rondo (SAR 1.32) – was constantly giving up the ball to them, and thus may have been the indispensible cog in that wheel.]  The list also includes a bruiser, Carlos Boozer (5.22), who I randomly chose over his equally bruising ex-teammate, Paul Millsap (6.47), and I should state that “dirty work” guys (like Horace Grant, who for his whole career had an SAR of 4.75) often fall into the Balanced Scorer, or even Combination Distributor, category.  Lastly, I included a player often recognized as selfish (Vince Carter, 4.95), who proves to not only be a balanced offensive player, but to have slightly more balance to his game than a scorer who is recognized for his selflessness (Allen, 5.24).  But as I said: SAR should not be used to characterize a player as good or bad, selfish or unselfish – a player, like a person, is who he is.

Quintile IV (SAR 6.76 – 9.21): Primary Scorers

This quintile represents players who are absolutely looking to score when they have the ball in their hands, yet appear to have enough court vision and passing skill to kick the ball out when the opportunity is not there or, in the case of some big men, pass it out of the post.  This group of players has perhaps the fewest number of surprises in it, at least to me: almost every player in this group, to my eye’s perception, appeared to be shoot-first players who nevertheless had at least a minimum ball distribution responsibility.  Ten representative players from 2009-10 who would qualify as Primary Scorers include:

1.      Shaquille O’Neal (7.20)

2.      Carmelo Anthony (8.14)

3.      Danny Granger (7.91)

4.      Andrew Bogut (8.10)

5.      Kevin Durant (9.03)

6.      Dwight Howard (8.63)

7.      Brook Lopez (7.40)

8.      Rashard Lewis (8.36)

9.      Chris Bosh (8.75)

10.   Danilo Gallinari (8.00)

These 10 players, I thought, gave some nice examples of the many different faces worn by a Primary Scorer.  Shaq, for example, is a classic low-post player, who appears to be a willing passer out of the post – particularly if he has an excellent shooter (like LeBron James last year, and Dwyane Wade before him, and Kobe Bryant before that, and Penny Hardaway going way, way back) to pass to out of the double-team.  Dwight Howard, also on this list, would be a similar example (with excellent shooters such as Rashard Lewis and Vince Carter, to whom he could pass out of the low post when he played with them last season).  Andrew Bogut qualifies similarly, though those who have watched his game know that his passes are often of the interior variety.  Kevin Durant and Carmelo Anthony are classic go-to guys, for whom you might clear the court and run some isolation plays – and yet they seem to pass at least a little, with a similar frequency to a center who passes out of the post.  Rashard Lewis and Danilo Gallinari, meanwhile, have very similar games to one another, though different from the aforementioned players: They both spot up near the three-point line and are clearly looking for a teammate to pass to them, either after dribble-penetration or out of a double-team.  Nevertheless, there is a little bit more to their game than shooting alone.

Quintile V (SAR 9.22+): Finishers

To reiterate an earlier point, these quintile SAR values are continuums, not quanta – these are not all or none distinctions, as much as they are differing colors with various shades within them.  Nevertheless, this group of players is doing exactly what their classification suggests: finishing.  Some, whose SAR hovers in the range of 9.50, are still relatively willing passers, but clearly looking to take the ball to the basket first and foremost.  Others, whose SARs are well above this number, may truly have one-dimensional offensive games.  But another point about SAR should be reiterated – these are not necessarily value judgments.  A player may have a one-dimensional game because his team needs him to have a one-dimensional game – there might not be anybody else available to do the heavy lifting, and the single dimension the player shows may, in an unusual way, reflect a sort of inside-out, team-first philosophy.  It might also reflect the way that player’s coach runs plays for him and the rest of the team – by design, perhaps, the player’s coach is asking him to score, or at least try, and passing is just not a scripted option.  With those caveats, here are representative players from 2009-10 who would qualify as Finishers:

1.      Amar’e Stoudemire (19.27)

2.      Zach Randolph (10.53)

3.      Al Harrington (10.80)

4.      Andreas Bargnani (13.55)

5.      Serge Ibaka (41.60)

6.      Mickeal Pietrus (12.10)

7.      Elton Brand (10.01)

8.      Yi Jianlian (14.03)

9.      Charlie Villanueva (16.83)

10.  Michael Beasley (11.60)

11.  Udonis Haslem (14.01)

12.  Emeka Okafor (14.42)

I chose 12 players here because, again, the Finishers category was such an interesting cast of characters.  Starting at the top, Amar’e Stoudemire had an extremely high SAR (19.27), though did so on a very successful team (conference finalists last year).  His SAR may very well represent a combination of the team asking him to do the heavy-lifting, plus his coach (Alvin Gentry) and point guard (Steve Nash) designing plays to end with him having the ball near the basket.  This year, Stoudemire has an SAR of only 9.22 – the lowest value possible for a Finisher, and almost a Primary Scorer – no doubt because his current coach (Mike D'Antoni) emphasizes tremendous ball movement, and he has a healthy complement of dead-eye shooters (Danilo Gallinari, Wilson Chandler, Shawne Williams) surrounding him.  Mickeal Pietrus is a slasher, but unlike many from this mold, he apparently is looking at the basket only, and not looking to pass off penetration, as he makes his way to the hoop.  Yi Jianlian comes from a mold not all that different from Rashard Lewis or Danilo Gallinari, but he clearly is not looking to pass the ball at all, and Michael Beasley appears, on first glance, to be a poor man’s Carmelo Anthony or Kevin Durant – and yet he seems to pass the ball off even less than these All-World players.  Haslem and Okafor, who don’t shoot all that much, nevertheless appear to shoot just about whenever they touch the ball.  Serge Ibaka, at an SAR of 41.60, is an absolute vortex with the ball – which, on the surface, seems like a curious style to have when flanked by Kevin Durant, Russell Westbrook, Jeff Green and James Harden (but, as I will explain below, there is a method to the madness).

If I seem like I may, in fact, be going against my own word and making value judgments against certain Finishers with very high SARs – well, I must admit that I am feeling a tinge of that, but certainly not for all of these players.  Stoudemire, Bargnani and Randolph, for instance, score with tremendous efficiency, both from the floor and the free throw line, and the teams of Stoudemire and Randolph had greater success last year than anybody expected – I don’t hold their high SARs against them at all.  And Ibaka shoots so infrequently, and with such high accuracy from the floor (and improving this year from the free throw line), that it appears that his vortex-like SAR is really a reflection of the fact that he only gets the ball when wide open near the basket, and his shots are clearly beckoned by his teammates and his coach's design.  But players like Beasley and Pietrus – I look at their SARs, and I think about how their unwillingness to pass might have been denying opportunities to former teammates Dwyane Wade and Dwight Howard, respectively -- and perhaps that is why they are former teammates (both Beasley and Pietrus are now playing elsewhere).

And so this rather lengthy post concludes, with the establishment of player quintiles – classifications that will allow us to interpret a player’s statistics within an appropriate context.  A player’s SAR has the greatest effect on a player’s SPR (Successful Possession Ratio), because of any statistical skew caused by assists, but it is nevertheless worthwhile to classify players by what they are actually trying to do on the court.

Future posts that evaluate players, possible trades, and player comparisons will do so within the context of the SAR.