Monday, January 31, 2011

The First Alaa Abdelnaby Award for the Least Team-Oriented Offensive Player

This week, we will attempt to identify the NBA’s least team-oriented player (or, at least, one of the league’s least team-oriented players).  To make such an analysis more accessible, I will start with a glossary of statistical terms, which can be referred to by the reader.
SPR = [2PFGM + 1.5(3PFGM) + (FTM/2) + AST]/[FGA + (FTA/2) + AST + TOV]
TOT = TOV/[TOV + FGA + (FTA/2) + TRB + STL + AST]
SAR = [FGA + (FTA/2)]/AST

I will admit from the outset that identifying the least team-oriented offensive player in the NBA, and subsequently bestowing him an “award” named in “honor” of Alaa Abdelnaby, is not entirely fair to Mr. Abdelnaby.  While he was a senior “forward-center” (a Finisher, by my calculated player quintile) at Duke University in 1989-90, Abdelnaby inherited the derogatory moniker “The Black Hole” – an acknowledgement of how infrequently the ball came out of his hands after he received a pass in the low post.  As a Duke senior, it appeared that Abdelnaby seldom found a ball that he did not find suitable for shooting, and said balls inevitably found their way into the vortex that becomes either a made basket, or an opponent’s rebound.
With a Shot-to-Assist Ratio (SAR) of 16.3 in his final college season, the nickname seemed appropriate on the surface.  But a deeper look reveals that Abdelnaby converted his field goals 62% of the time, and his free throws greater than 77% of the time – both rates that justify his inclination to shoot.  Perhaps detractors felt that in light of his talented teammates – he played that season with future NBA players Christian Laettner, Bobby Hurley and Brian Davis – Abdelnaby should have given the ball up more on the basis of the riches that surrounded him.  But Abdelnaby’s shot selection was excellent that year (his Shot Selection Index, or SSI, was .509), and he converted offensive possessions with remarkable efficiency:  His Successful Possession Rate (SPR) was .602, which would rank him among the best of playmakers, and his Turnover-Adjusted Points per Shot (TAPPS) was a sky-high 1.16.
And you couldn’t argue with Abdelnaby’s overall results, either as an individual or a team player.  Taken on his own, Abdelnaby averaged 15.1 points per game in the 1989-90 season, and added 6.6 rebounds.  As a team member, Abdelnaby started on a Blue Devil squad that went all the way to the NCAA Championship Game, where they lost to a virtual All-Star team from UNLV (one that included Larry Johnson, Stacy Augmon, and Greg Anthony).  So “The Black Hole” nickname was, at the time, entirely unfair.
Nevertheless, it was prescient:  After being selected in the first round of the NBA draft in June of 1990, Abdelnaby went on to have an NBA career that could qualify as selfish.  Compare below the statistics Abdelnaby compiled in his senior year at Duke with those he accumulated during his entire NBA career:
                        PPG      RPG     FG%     FT%      SAR      SSI        SPR      TAPPS  TOT
Duke, ’89-’90   15.1     6.6       .620     .775     16.3     .509     .602     1.16     .068
NBA Career     5.7       3.3       .502     .701     19.3     .260     .473     0.89     .093

So Abdelnaby got to the NBA and both his scoring and rebounding rates went down – not surprising given the improved level of competition, and the fact that Abdelnaby was a bench player as a pro.  What is remarkable, however, is that Abdelnaby’s shooting percentages – both field goals and free throws – also declined, and yet his SAR went up from 16.3 in college to 19.3 in the pros.  What this means is that, as Abdelnaby’s ability to score with accuracy went down, he nevertheless chose to shoot at an even higher rate.
What’s more, Abdelnaby’s shot selection as a pro deteriorated, suggesting that he was forcing the issue – his SSI went from an outstanding .509 to a slightly below average .260.  And, again, even as Abdelnaby’s ability to contribute to team success diminished – his SPR fell to a marginal .473 as a pro; his TAPPS was a pedestrian 0.89; and his TOT of .093 represented a turnover rate seen with the likes of swashbuckling passers, but not low-post players – he held on to the ball even more, and passed it out even less.
And so it is with that precedent that I have endeavored to award the First Alaa Abdelnaby Award for Least Team-Oriented Offensive Player.  The nominees for the 2010-11 NBA Season are:
1.      Drew Gooden
2.      Charlie Villanueva
3.      Yi Jianlian
4.      Al Harrington
5.      Carl Landry
6.      Emeka Okafor
7.      Morrese Speights
Before we get to our “finalists,” I would like to discuss the cases of three players who I suspected of selfish offensive play, but quickly removed them from the list of nominees after examining the record.  Those players are Tyson Chandler, Serge Ibaka and Andrew Bynum.  Chandler and Ibaka were originally chosen because of their astronomical SARs (18.9 and 19.8, respectively), while Bynum was chosen for a slightly high SAR (10.5), though one he accrued while playing with some of the most efficient offensive players in the league (Kobe Bryant, Pau Gasol, and Lamar Odom).  But a peek at their statistics shows that none of these players are truly selfish:
                        PPG      RPG     FG%     FT%      SAR      SSI        SPR      TAPPS  TOT
Chandler         9.9       9.0       .670     .790     18.9     .854     .626     1.22     .062
Ibaka               9.8       6.9       .562     .755     19.8     .322     .549     1.07     .050
Bynum             11.4     7.3       .575     .684     10.5     .436     .564     1.05     .061

Chandler can justify just about any shot he takes: his field goal shooting is phenomenal; his free throw shooting is excellent; his shot selection is beyond reproach; his SPR is in the Magic Johnson range; his TAPPS is at the top of the league; and his turnover rate speaks of his ability to take care of the ball.  Chandler’s SAR is essentially irrelevant here – every shot he takes can be justified, and you couldn’t ask for more of a team player.
Ibaka, it appears, is a younger and less mature version of Chandler, but nearly as good.  He is an excellent shooter from the field and the line; his shot selection is slightly above average; his SPR is very good for a low-post player; his TAPPS is excellent; and he takes remarkably good care of the ball.
And Bynum, as you can see, is somewhere in the middle of Ibaka and Chandler – and his shot selection is much better than that of Kobe Bryant, his nearly deified teammate (if only Bynum could improve from the line).  In summary, none of these players, though quick to shoot the ball, are at all selfish – their ends justify their means.
And so we move on to the seven “finalists” for the First Alaa Abdelnaby Award for Least Team-Oriented Offensive Player.  Here are their statistics:
                        PPG      RPG     FG%     FT%      SAR      SSI        SPR      TAPPS  TOT
Gooden            10.8     6.5       .442     .776     15.3     .277     .473     0.88     .058
Villanueva       13.0     5.8       .437     .761     15.0     .189     .526     0.99     .051
Jianlian            5.9       3.3       .436     .744     14.2     .289     .451     0.84     .087
Harrington      12.0     5.0       .418     .743     6.71     .171     .557     0.94     .083
Landry             12.4     4.9       .488     .719     12.8     .447     .501     0.93     .081
Okafor             11.1     10.2     .598     .549     18.2     .539     .526     1.01     .072
Speights           5.9       3.9       .500     .725     10.6     .274     .503     0.92     .072

Though I was pulling for Harrington to win the Abdelnaby Award, it is obvious that he does not deserve it – and it is not just because of his relatively low SAR of 6.71.  Despite having an absolutely horrid SSI of .171 (because Al, as those who have watched him, loves to stand behind the three-point line and either catch-and-shoot, or catch-and-drive), Harrington nevertheless makes a remarkably high percentage of those poorly chosen shots: Though his FG% is only .418, most of those are three-pointers (shooting 40% on three-pointers is the equivalent of shooting 60% on two's), and his free throw shooting is not too bad.  Given the relatively high rate at which he passes, Al turns the ball over more than he should, but not as much as I would have expected.  For making the most out of his relatively poor decision-making, Harrington must be excluded from final consideration for the Abdelnaby Award.
Ditto Charlie Villanueva, who is virtually the same player as Harrington – with the same type of arc-oriented game, and similar shooting percentages (though much less passing).  Villanueva, however, takes much better care of the ball than Harrington (his TOT is only .051, in part because he passes so infrequently), and he thus is eliminated from serious contention for the “Alaa.”
Like Villanueva and Harrington, Emeka Okafor is just too good to win the award.  His excellent shot selection and his accurate field goal shooting justify his extremely high SAR of 18.2.  If only Okafor could hit his free throws, he would not even merit a nomination on this list, and his fair SPR of .526 would be much higher.  Still and all, even adjusted for his average turnover rate, his TAPPS still exceeds 1.00.
I had nominated Carl Landry with the intention of throwing out his nomination, just as I ended up doing with those of Chandler, Ibaka and Bynum.  Surprisingly, Landry’s numbers demonstrate that he deserves to be on this short list.  Though Landry’s shot selection is very good, his field goal percentage and free throw shooting are only so-so; he turns the ball over an awful lot for a guy who threads an assist only once for every 13 of his shots; and his SPR barely escapes that of the marginal.  And Morrese Speights is, as you can see, virtually the exact same player as Landry, though one with poorer shot selection.
But neither Speights nor Landry can come close to the achievements of Drew Gooden and Yi Jianlian.  Gooden, in fact, has stats that are so eerily similar to those of Abdelnaby’s career that I wonder if the award should be renamed in Gooden’s honor:
                                    FG%     FT%      SAR      SSI        SPR      TAPPS  TOT
Gooden                        .442     .776     15.3     .277     .473     0.88     .058
Abdelnaby                   .502     .701     19.3     .260     .473     0.89     .093

But, no, Gooden will be spared, for if there is any renaming of the award for the least team-oriented basketball player, the eponym will belong to Yi Jianlian.  Jianlian (or is it Yi?) has an SAR of 14.2, which suggests that he does not like to share at the playground, while producing other figures in his stat line that indicate his selfishness is in no way deserved.  Jianlian’s shot selection is average.  His free throw shooting is average.  His field goal shooting is average.  His rate of turnovers is awful – and thus his TAPPS and SPR is in a range so marginal, it calls to mind Adam Morrison (and not the Adam Morrison who played at Gonzaga, but the one who sat courtside and watched the Lakers kindly gather him two rings). 

And so the first Alaa Abdelnaby Award will be the last – and heretofore will be named in honor of its more suitable inspiration, Yi Jianlian.
Final note: Two players with nearly median SARs – World B. Free and Allen Iverson – are often noted as two of the more selfish players to ever take the court.  I wanted to test the hypothesis, using the two players’ signature seasons (Iverson’s nearly successful run at the Championship in 2000-01, and Free’s “Prince of Midair” season in 1981-82, back when he was still called Lloyd).  The analysis is below:
                        PPG      RPG     FG%     FT%      SAR      SSI        SPR      TAPPS  TOT
Free                 22.9     3.2       .448     .740     5.91     .410     .547     0.91     .076
Iverson            31.1     3.8       .420     .814     6.68     .400     .522     0.92     .074

The tale of the tape shows that both Free and Iverson, during the signature years, would have qualified as Balanced Scorers – the third quintile among players, as defined by SAR – with Free producing assists at a slightly higher rate than Iverson.  Their field goal percentages were OK by the standard of each player’s era (Iverson’s 42% should be considered in the context of the weightier role the three-point shot played during his career, as opposed to Free’s).  Both players, as evident in their SSIs, had pretty good shot selection, and Iverson was an excellent free throw shooter, while Free was about average.  Each player’s SPR, TAPPS and TOT was good, but not great (Free gets the edge in SPR, once again, because of his higher assist tally).
In summary, neither Free nor Iverson were terribly selfish players – they passed the ball a moderate amount, they took good shots, and they made them with a degree of consistency.  The real issue with the perception of both of these players, I think, is that both were good, but neither was great – and since they each made themselves the focus of their respective teams, both on and off the court, they were perceived to be selfish.
Next week’s post: Kemba, Jimmer – or Jared?

Thursday, January 27, 2011

Sunday, January 23, 2011

Does Carmelo Anthony Make Sense for the New York Knicks? A Statistical Comparison

Carmelo Anthony has marked his territory, and its limits are bound by 31st and 33rd Streets, between Seventh and Eighth Avenues.  Were it not for the intricacies of contractual obligations and industry-specific labor agreements, Carmelo Anthony would be a New York Knick.
Or would he?
Lost in all the energy that surrounds rumors of Anthony going to the Knicks in a trade – for some combination, purportedly, of Eddy Curry’s expiring contract; a first round draft pick that would be manufactured out of a trade of Anthony Randolph; and the trio of Danilo Gallinari, Wilson Chandler, and Landry Fields – is consideration of whether or not the deal makes sense for New York.
It is widely reported that the Denver Nuggets are not impressed with any potential package the Knicks might offer, but I have a bigger concern:  Should the Knicks be so impressed by the one-man package of Carmelo Anthony that they would offer up any player that is in their current rotation?
Let’s take a look, and render a verdict.  To make such an analysis more accessible, I will start with a glossary of statistical terms, which can be referred to by the reader.
SPR = [2PFGM + 1.5(3PFGM) + (FTM/2) + AST]/[FGA = (FTA/2) + AST + TOV]
TOT = TOV/[TOV + FGA + (FTA/2) + TRB + STL + AST]
SAR = [FGA + (FTA/2)]/AST

Anthony, now 26 years old, has a Shot-to-Assist Ratio (SAR) this season of 7.79 – slightly above his career SAR of 7.49, but one that still renders him in the fourth position quintile, Primary Scorer, where he has played for the entirety of his career.   Anthony, however, is suffering through one of the worst seasons of his career in 2010-11 – though it  is worth mentioning that he has had to endure a very difficult road of late, including (self-imposed) trade speculation in the media, injury, and the death of his sibling.  Nevertheless, 2010-11 has represented a statistical slide for Carmelo.
This season, Anthony’s Successful Possession Rate , or SPR, is a paltry .513 – below his career SPR of .525, and well below the .550 standard that is often reached by the All-Star caliber players within the Primary Scorer quintile.
Anthony’s Turnover-Adjusted Points per Shot, or TAPPS, comes in this season at 0.89 – again, far below the All-Star standard of other Primary Scorers (approaching 1.00), and well below his career average TAPPS of 0.94.  This decline primarily reflects his poor field goal shooting this year, particularly from three-point range.
If there is good news for Anthony, it is that he is taking much better care of the ball as he gets older: his Turnovers per Touch, or TOT, is .075, down from his career TOT of .083.  As stated, his shot selection is also good, as his Shot Selection Index (SSI) this year is .431 (well above the approximate league average of .300).
So let’s compare Anthony to a couple of the players he is rumored to be traded for. 
Danilo Gallinari, with a season SAR of 7.47, would also qualify as a Primary Scorer, and thus could be compared fairly to Anthony, a player who plays within the same quintile.  Gallinari, however, has an SPR this year of .592 – certainly well above the .550 mark that represents excellence within this quintile, and very near the high SPRs registered by many Primary Distributors (“point guards”), who tally up large assist totals.  In addition, Gallinari also eclipses Anthony in TAPPS, with an eye-opening 1.08, built largely upon his excellent three-point shooting, excellent free-throw shooting, and low turnover rate.
Meanwhile, in the areas in which Anthony is excelling this year – turnovers and shot selection – Gallinari also eclipses his better-paid counterpart:  Gallinari has a TOT of only .050 this year (better than Anthony’s .075), and an SSI of .538 (Anthony, again, registers a .431).
And, yes, Gallinari accrues these statistics while commanding a 2011-12 salary of $4.2M – or nearly $18M less than Anthony is seeking for next year, and about $14M less than Anthony’s 2011-12 player option.
The comparison does not get any more favorable for Anthony if one turns his eyes toward Gallinari’s teammate, Wilson Chandler.  With an SAR of 9.13, Chandler, too, resides within the same player quintile as Anthony and Gallinari.  Like Gallinari, Chandler also eclipses Anthony in his season SPR (.560) and TAPPS (1.03).  Chandler, however, takes remarkably good care of the ball:  Though he is an absolute gunner from the floor (his SSI is only .188, well below the league average), Chandler, like Gallinari, does not give the ball away easily: his TOT this season is only .052.
Adjusted for salary, Chandler’s value, as compared to Anthony’s, gets even better: Chandler is due a qualifying offer next season for only $3.1M – or roughly $15M less than the player option due Anthony.  Even if Chandler negotiates himself a salary that is twice his qualifying offer, he will still be making $15M less than the maximum contract that Anthony is seeking.
Put together in a table, the comparison between Carmelo Anthony and the two players he might be traded for looks like this:
                        SPR                  TAPPS             TOT                 SSI       Proj. 2011-12 Salary
C. Anthony     .513                 0.89                 .075                 .431     $18.5M (player option)
D. Gallinari     .592                 1.08                 .050                 .538     $4.2M
W. Chandler   .560                 1.03                 .052                 .188     $3.1M (Qual. Offer)

A third player who has been rumored to be a possible piece in any deal for Anthony is rookie Landry Fields.  With an SAR of 4.43, Fields is more of a Combination Distributor (“combo guard”), in the second of the five player quintiles, and thus it is not entirely fair to compare Fields with Anthony.  Nevertheless, the comparison is compelling (particularly the salary line):
SPR                  TAPPS             TOT                 SSI       Proj. 2011-12 Salary
C. Anthony     .513                 0.89                 .075                 .431     $18.5M (player option)
L. Fields           .589                 1.02                 .073                 .247     $0.8M
Even corrected for his player quintile, Fields achieves an SPR, TAPPS and TOT that is closely aligned with those of the most qualified players at his position.  Clearly, Fields needs to work a little bit on his shot selection (as most members of the New York Knicks do), but at a salary that will be at least $18M less than what Anthony is likely to sign for, the Knicks should be absolutely giddy with their return on investment, and Fields’ room for future upside.
It is hard for many people to believe that Carmelo Anthony is not as good as what the Knicks already have, and one of the points that has been brought up in recent days (specifically by Nate Silver of the New York Times) is that Anthony’s presence on the court makes his teammates better.  As I acknowledged in the previous post (see the post on January 17, 2011), Anthony, indeed, appears to elevate the game of his teammates, whereas Gallinari and his Knick cohorts do not seem to do so: the SSI and TAPPS of Anthony’s teammates are much better than that of the Knicks (excluding Amare Stoudemire), suggesting that Anthony does create more favorable spacing for his teammates on the court.
But that does not change the fact that Anthony is asking for an awful lot of money – which, in the salary cap era, limits who your teammates can be, and thus whose game you might elevate – and so I think it only fair to compare him to another player within his quintile who also elevates the play of his teammates.  Below is a table that compares Anthony with his positional counterpart (SAR of 8.43), Kevin Durant:
SPR                  TAPPS             TOT                 SSI       Proj. 2011-12 Salary
C. Anthony     .513                 0.89                 .075                 .431     $18.5M (player option)
K. Durant        .557                 1.02                 .085                 .444     $13.6M
As demonstrated, Durant has a much better SPR and TAPPS than Anthony, and a slightly better SSI; Anthony is slightly better at taking care of the ball, as demonstrated by their TOTs.  But Durant is slated to make almost 25% less than Anthony is next year – and it is worth pointing out that Anthony’s player option for next season is greater than next year’s salaries of LeBron James ($16M), Chris Bosh ($16M), and Dwyane Wade ($15.5M).
So what does this all mean for the New York Knicks?
Well, for one thing, if Carmelo Anthony’s greatest value as a player is his ability to elevate the play of his teammates, then it does not make sense to trade the very players that stand to improve the most by Anthony’s presence (Gallinari, Chandler, Fields) when you can simply sign Anthony in the summer as a free agent, and surrender no one.  Wait for the summer to come, sign Anthony in July, and provide him the complementary cast he needs from day one.
But the other thing to note is that the market has spoken, and the Knicks should listen: If the very best players in the game are willing to play for at least 33% less than what Anthony is clamoring for, then New York should hold fast in its resolve and sign Anthony at a reasonable price only (neither his player option nor his maximum contract option are reasonable, according to the market as defined by Durant/James/Wade/Bosh), and then use the money for what they really need: a front-line banger and a back-up point guard.
Next week’s post: Who is the least team-oriented player in the NBA?

Monday, January 17, 2011

Core Statistics: Turnovers per Touch and the Shot Selection Index

In this post, we will define two more basketball analytics – Turnovers per Touch (TOT) and the Shot Selection Index (SSI) – which will complete a core glossary of statistics on the Basketball I.Q. website.  Though new analytic methods will be added in future posts, this post will provide Basketball I.Q. readers with an analytic foundation (along with Successful Possession Rate, Turnover-Adjusted Points-per-Shot, and Shot-to-Assist Ratio, see earlier posts) with which we can start the real fun – analyzing rumored trades, identifying league All-Stars, labeling our favorite goats, etc.
Turnovers per Touch (TOT)
In baseball, everybody knows that errors and fielding percentage are flawed statistics, and the Gold Glove is an award for defensive performance that seems to be based upon everything but defense.  The problem, of course, is range:  Derek Jeter, as he plays through his late 30’s, has little of it – and as a result, fields fewer balls and consequently makes fewer errors than many shortstops.  Because of this, and the fact that the balls he does not reach are the most difficult to field cleanly, his fielding percentage is always pretty good.  This may explain why he wins a Gold Glove over fellow shortstop Elvis Andrus, who appears to be able to play all nine positions by himself and, as a result, makes more errors.
Basketball has the same problem with turnovers (TOV).  The TOV is a statistic that measures a player’s error, and it is a pretty important error, as TOV absolutely ends a possession, with no chance for the player’s team to make up for it until they get the ball back.  The problem with measuring TOV as an absolute value is that the number is going to be higher for players who touch the ball a lot – and try to do a lot with the ball when they have it – than it will be for player’s who touch the ball infrequently and do not try to do a lot with it.  Consequently, the TOV statistic alone will unfairly punish players who take on a heavy scoring load for their teams, and those that try to create plays for teammates off the dribble – just like total errors will unfairly punish baseball players who are able to make a lot happen in the field.
Statisticians have tried to correct for this flaw in the TOV stat in a number of different ways.  One way is to look at TOV per minute – but this statistic still unfairly punishes those who touch the ball a lot, as opposed to players who spend their court time without the ball in their hands.  Another statistical correction has been the assist-to-turnover ratio, which seems reasonable since players who tend to create for their teammates (Primary Distributors, please see the January 8, 2011 post) make a lot of turnovers, too.  But the problem here is that players can do a lot of other things for their team with the ball, too – e.g., create a shot off the dribble – and an assist is just one of them.
The statistical measurement of turnovers that I propose is also a ratio, though a more comprehensive one – one that I refer to as the Turnovers per Touch (TOT).  This ratio attempts to measure an individual’s TOV in relation to how often he tries to do something with the ball.  As the statistic implies, the numerator of the TOT measurement is simple: TOV.  There is nothing more to measure.
But the denominator is an estimation of all touches a player may have on the floor, all of which have the opportunity of producing a turnover.  This estimate includes TOV (also present in the numerator, as stated), field goal attempts (FGA), free throw attempts (FTA), total rebounds (TRB), steals (STL) and assists (AST).  Because a FTA, in essence, represents half of an attempt to do something with the ball, it is weighted in the TOT statistic by half (FTA/2).  As a sum, the denominator of the TOT statistic is:
[TOV + FGA + (FTA/2) + TRB + STL + AST]
Taken together, the formula for TOT is:
TOT = TOV/[TOV + FGA + (FTA/2) + TRB + STL + AST]
As usual, my first step was to try it out on a bunch of different players, and just see what the numbers bore out.  Magic Johnson, Steve Nash and Isaiah Thomas, for example, have career TOTs of .095, .103, and .109, respectively (put another way, they commit a turnover on 9.5%, 10.3%, and 10.9% of their touches).  Shaquille O’Neal and Patrick Ewing (for their careers) and Dwight Howard (for 2009-10) have TOTs of .073, .085, and .097, respectively.  [Note: These statistics may have changed since last analyzed two weeks ago.] 
Again, just as the case was with analysis of Successful Possession Rate (SPR), it is unfair to compare players’ TOT if they do not assume similar roles on the floor.  As was previously discussed, the SPR (see the posting on December 26, 2010) gives disproportionate weight to players who accumulate a lot of assists.  In this instance, the TOT gives disproportionate weight to players who forgo an attempt at an assist – and run the risk of making a turnover – in favor of just shooting the ball, whether they make it or not.  As a result, “playmakers” will have high TOTs and “scorers” will have relatively low ones.  As with SPR, it became apparent to me that the comparison of player TOTs should only be made between players of the same quintile (i.e., players with a similar Shot-to-Assist Ratio, or SAR, see the posting on January 8, 2011), since that would be a more accurate comparison of players’ ability to protect the ball.
As examples, I would like to refer to players implicated in recent trade activity.  Let us take the comparative case of Carmelo Anthony of the Denver Nuggets and Danilo Gallinari of the New York Knicks – two players who are rumored to be part of a trade for one another, in a deal that seems unlikely to happen.  As of a couple weeks ago, Anthony has a career SAR of 7.49 (he shoots the ball about 7.5 times for every assist he registers), while Gallinari has a career SAR of 8.02 – rates that are very similar, and put each player in the quintile referred to as Primary Scorers.  In this manner, they are similar players. 
However, Gallinari’s TOT is a remarkably low .057 – he turns the ball over on less than 6% of his touches – while Anthony’s TOT is .083, which is a rate associated with players who accumulate many more assists than Anthony does.  By this measure Gallinari is far more protective of the ball than Anthony, his positional peer. 
If you would like to defend Anthony’s TOT, relative to Gallinari’s, because of his scoring prowess, it could be countered that Gallinari’s Turnover-Adjusted Points-per-Shot (TAPPS) is a remarkably high 1.05 (because of good three-point shooting and excellent free throw shooting, combined with low turnovers), while Anthony’s is a pretty good (but not quite as good) 0.94. 
If you would like to further defend Anthony, as Nate Silver did in the New York Times this weekend, by saying that he does more for his teammates, this might be countered with two further statistics:  Gallinari’s SPR (which combines scoring with assists to teammates) is .572, while Anthony’s is only .525 (please see the December 26, 2010 post for further explanation, but to put it roughly, if they were baseball players, Gallinari would have an on-base percentage that is almost 50 points higher).
The other statistic that might be invoked in the Anthony vs. Gallinari debate is the Shot Selection Index, which is described in the second half of this post.
Shot Selection Index (SSI)
How do you know if a player is taking good shots?  I suppose one of the ways in which you might estimate this is to look at total points scored – if you score a lot of points, you must be taking good shots – but the flaw in this measure is easy to detect: A player can score a lot of points simply by taking a lot of shots (Brandon Jennings), whereas another player can score only a modest amount of points by taking nothing but good shots (the 2011 version of Shaquille O’Neal).
Another way to look at this would be shooting percentage, or the vogue statistic, true shooting percentage, which weights three-point shots by 50%.  By these metrics, players with high shooting percentages – “raw” or “true” – are clearly taking good shots.  There are two problems with this measure, in my opinion:  First, this statistic eliminates the absolute best shot a player can take – an absolutely open one, with no defender allowed in front of you, directly in front of the basket with full use of the backboard, otherwise known as a free throw. 
The second problem is that shooting percentages do not necessarily take into account your opponents’ opinion of the shots you are taking.  By my reasoning, if your opponent would rather give you the opportunity to shoot two uncontested one-point shots (in other words, he fouls you), rather than let you take the shot you are about to attempt, then you must be taking pretty good shots. 
In other words, if you are a 75% free throw shooter and your defender fouls you in the act of shooting, he must think the shot you are taking has greater than a 75% chance of going in – probably even greater, since he is willing to push himself 16.7% closer to being disqualified from the game by doing so.  Even if you are a 50% free throw shooter (like Shaq), a foul in the act of shooting means that your opponent thinks your shot has a better than 50% chance of going in, which is still pretty good – especially when you consider, again, that your defender is willing to push himself toward disqualification (“fouling out”) in his attempt to send you to the line.
And so what I devised is the Shot Selection Index (SSI), which is a very simple statistic:
It is free throw attempts divided by field goal attempts, and it estimates your opponents’ opinion of the likelihood that your shots will go in, which I hypothesize is the best gauge of your shot quality (taken in conjunction with someone’s shooting percentage, “raw” or “true”).
As a reference, the team median for SSI in 2009-10 was .296, while the team mean was about .301.  Players, on average, shoot free throws a little less than a third as often as they attempt field goals.
As individual examples, Shaq has an SSI this year of .698 – the quality of his shot selection is more than twice as good as the league average (though no doubt this is impacted by his poor free throw shooting).  Lebron James, who is a good free throw shooter, has an excellent SSI of .482, while Kobe Bryant (also good from the foul line) is well above the league average at .388.  Meanwhile, Brandon Jennings has an absolutely average shot selection (.303) and Wilson Chandler of the Knicks, who makes 80% of his free throws, has a remarkably low SSI of .193 – which, to me, means that his coach might be asking him to shoot too many three’s, and is not designing enough “clear-outs” to get this very athletic player driving to the basket.
Let’s re-visit the Anthony vs. Gallinari debate, using SSI as a platform.  By a few measures, Gallinari appears to be getting more done when he has the ball.  As mentioned, however, Nate Silver of the New York Times suspects that Anthony’s court presence alone creates a lot of easier opportunities for his teammates.
Even by SSI, Gallinari puts up the better number: .534 (excellent) vs. Anthony’s .425 (still very good).  However, let’s argue Silver’s point that Anthony does a lot for his teammates.   Looking at Gallinari’s point guard (Raymond Felton), swingman (Wilson Chandler) and big man (Amar’e Stoudemire), they have respective SSIs of .253, .193 and .436 – with the exception of Stoudemire, all below average, and all below Gallinari’s SSI.  Meanwhile, the same position players who play with Anthony – Chauncey Billups, J.R. Smith, and Nene – have SSIs of .633, .305, and .655, which is absolutely fantastic, and two of these three SSIs are better than Anthony’s own SSI.  By this measure, Carmelo really might be creating more opportunity for his teammates, just by being there.
The next step in the analysis would be to look at what the players’ respective teammates actually do with these opportunities.  What you could look at is the TAPPS of the players’ teammates.  Felton, Chandler and Stoudemire come in at 0.89, 1.04, and 0.96 – all of which are pretty good, but none of which are as high as Gallinari’s career TAPPS.  Meanwhile, Billups, Smith and Nene come in at 0.99, 0.94 and 1.16 – which not only is significantly better than their Knick counterparts, but all of which are as high or higher than Anthony’s career TAPPS – suggesting that Anthony might be making his teammates better than himself.
I must concede at least one point to Nate Silver: Carmelo Anthony may very well make his teammates better, just by lacing up his sneakers.
Next post: The comparative trade value of Carmelo Anthony, done in greater detail.

Saturday, January 8, 2011

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.