Sunday, March 4, 2012

Jeremy Lin Advanced Statistics: Is Lin the next Nash or Stockton?

The answer to the question above, you will find, is a definite maybe.  To evaluate this query – can Jeremy Lin be the next Steve Nash or John Stockton? – the Editorial Board of Basketball I.Q. decided to compare the age-23 seasons of all three players (which happens to be the first season in which all three players averaged more than 20 minutes per game).  The age-23 season serves as a nice basis of comparison for each of these three players: they are each the same age, of course; it was the second professional season for each player; it marks a strikingly similar arc in their professional careers, as each player also completed four full years of college ball at a Division I mid-major; and they each averaged a very similar number of minutes per game in these respective seasons.  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
E = SPR + TAPPS + (1 – TOT)
wCE = (MPG/48) x [SPR + TAPPS + (1 – TOT)]
P/E = Salary/[SPR + TAPPS + (1 – TOT)]
wP/E = Salary/(MPG/48) x [SPR + TAPPS + (1 – TOT)]
EG = (Present Year’s E – Previous Year’s E)/(Previous Year’s E)
wEG = (Present Year’s wCE – Previous Year’s wCE)/(Previous Year’s wCE)

Despite all the surface similarities between the current, age-23 season for Jeremy Lin and the same respective seasons for John Stockton and Steve Nash, Lin has accumulated his playing time in stark contrast to the other two.  Stockton, for instance, was a back-up to able veteran Rickey Green of the Jazz, and achieved his playing time steadily, with very few starts.  Nash, similar to Stockton, was not at the top of the depth chart, but third behind two All-Star veterans in Phoenix – the young Jason Kidd, and the old Kevin Johnson – and also accumulated his minutes in a steady fashion, rarely starting a game for the Suns.
But Lin has been buried behind no one on the Knicks: he has simply waited his turn behind an ineffective Toney Douglas and a worn-out Mike Bibby, and barely played while doing so.  When he finally got his turn, his minutes surged, and he has averaged his 24.5 minutes per game (Stockton had 23.6, Nash had 21.9) by becoming an entrenched starter after having barely played at all.
The first question we will address, using the alternative metrics of Shot-to-Assist Ratio (SAR), Shot Selection Index (SSI), Three-point Rate (3PR), and Three-Point Skew (3PS), is whether or not Lin, Stockton and Nash are comparable players at all.
                        SAR     SSI       3PR      3PS
Stockton 23     0.93     .440     .032     .009
Nash 23           2.39     .147     .334     .302
Lin 23              2.27     .484     .176     .125

Indeed, based on the SAR of each player, Stockton, Nash and Lin all fall into the first quintile of player classification, the Primary Distributor (referred to in the vernacular as “point guard”), as each player has an SAR below 2.77.  As you can see, Lin and Nash have extremely similar SARs, and at age 23 made their own scoring a mildly prominent part of their game.  Stockton, however, accumulated more assists than shots taken in his age-23 season, which is a remarkable achievement, even for a Primary Distributor.  Clearly, passing was an even more important part of Stockton’s game than Lin’s or Nash’s – but they are still similar players, stylistically, with a knack for playmaking.
Based on the SSI, you can see that the two most similar players were Stockton and Lin, who each had almost half as many free throw attempts as field goal attempts.  This suggests that each player, when he chose to score, attempted to do so by driving to the hoop (and getting fouled a fair amount of the time).  This is further corroborated by their 3PR and 3PS: a small proportion of their field goals attempted (about 18% for Lin, and only 3% for Stockton), and even smaller fraction of their field goals made (about 12% for Lin, and only 1% for Stockton) were from the perimeter.  The difference between Lin and Stockton, in regards to three-point attempts, can probably be explained by their different eras: in 1985-86 (Stockton’s second year), the three-point shot was reserved mostly for the latter seconds of a possession, whereas the current game sees treys going up relatively early on in possessions.
Nash, on the other hand, played his individual offensive game out on the perimeter: a third of his shots were treys, and nearly a third of his makes (he was an astonishingly good three-point shooter).  Not surprisingly, given that he was so far away from the basket when he shot, Nash did not get to the line all that much (he took only 15% as many free throws as field goal attempts).
In sum, all three players were Primary Distributors, with slightly different flavors: Lin was a willing passer who drove to the basket; Nash was a willing passer who shot from the perimeter; and Stockton was an absolute pass-first player who, like Lin, drove toward the basket when it was time to score.
Having established that Lin, at age 23, is sufficiently similar in style to both Nash and Stockton, let’s turn our attention to their performance statistics.  The first statistics that we will evaluate are the standard ones:
                        PPG     RPG     APG     FG%     FT%     MPG
Stockton 23     7.7       2.2       5.1       .489     .839     23.6
Nash 23           9.1       2.1       3.4       .459     .860     21.9
Lin 23              14.4     2.8       5.8       .471     .766     24.5

The standard statistics suggest that, of the three, the age-23 Lin is clearly the best player: he scored many more points per game, collected more rebounds, and distributed the most assists.  Even if you reduce these numbers by 10% for Lin, acknowledging that he played about 10% more minutes per game, he still comes out with the better numbers.  If we try to explain away this apparent superiority by his higher field goal attempts, this argument is weakened by his field goal percentage – all three players shoot at virtually the same rate, with the slight differences in percentage explained by their varying rates of three-point attempts and makes.  It is only in free throw percentage that Lin demonstrates a weakness relative to the other two.
Can this be true?  Is the 23-year-old Jeremy Lin really better than John Stockton and Steve Nash at the same age?  Though the standard statistics suggest that this is the case, the alternative metrics suggest a slightly different conclusion.  Let’s take a look at those comparisons, using the Successful Possession Rate (SPR), Turnover-Adjusted Points per Shot (TAPPS), and Turnovers per Touch (TOT):
                        SPR      TAPPS TOT
Stockton 23     .687     .855     .100
Nash 23           .616     .954     .081
Lin 23              .588     .875     .129

The SPR reflects a player’s ability to create a successful scoring opportunity for his team as a whole, and the 23-year-old Stockton is clearly superior to Nash and Lin at the same age.  Some of this is due to statistical skew, since Stockton’s low SAR would emphasize the value of an assist, and thus inflate this statistic.  Still, even taking this statistical artifact into consideration, Stockton’s SPR is much better than that of the other two, and he accomplished this on a mediocre team.  Nash’s SPR is slightly better than Lin’s, and this is mostly accounted for by his superior turnover rate.
The TAPPS reflects a player’s ability to create a successful scoring opportunity for himself, and in this arena the 23-year-old Nash is clearly superior to Stockton and Lin at the same age (in reality, Stockton is 12 years older than Nash, and 27 years older than Lin).  Nash’s superiority in this stat is mostly explained by his extremely low turnover rate, but also by the contribution of his excellent three-point shooting (and playing in an era that, strategically, placed great value on the three-point shot).  Lin’s TAPPS is slightly better than Stockton’s, but this is mostly accounted for by the different eras in which they played, and the relative emphasis on the three-point shot in each era.
The TOT reflects the rate at which a player turns the ball over relative to his meaningful touches.  The watermark TOT for a Primary Distributor is 10%, which is exactly the number that the 23-year-old Stockton achieved.  Lin’s TOT of nearly 13% reflects the most glaring weakness in his game – and the reason why, no matter what the standard statistics say, Lin is a notch below Stockton, Nash and the like at the same points in their careers.  Nash’s turnover rate of about 8% is absolutely phenomenal for a player who takes so much responsibility for the ball, and getting it to his teammates.
Taken all together, the SPR, TAPPS and TOT suggest that, even at age 23, Stockton and Nash were showing glimpses of greatness, while Lin is a very good player who lags a degree or so behind them.  A couple different ways to appreciate the aggregate of these statistics are the statistics of Earnings (E) and weighted Cumulative Earnings (wCE).  The E combines the three stats analyzed above, whereas the wCE does so while taking into account playing time.  In this manner, the E tells you what a player does when he is on the court, whereas the wCE tells you his relative contribution for a full 48 minutes, including the time in which he sits on the bench.
When looking at E and wCE in a young player, it is helpful to evaluate their growth – what is their improvement (or decay) from one season to the next.  To evaluate Earnings Growth (EG) or weighted Earnings Growth (wEG), one can calculate the E and wCE from a preceding year and compare it to the year in question.  To that end, the E and wCE of Lin’s, Stockton’s and Nash’s age-22 and age-23 seasons have been calculated, and their growth from their rookie year to their sophomore campaign has been estimated:
                        E          wCE     EG        wEG
Stockton 22     2.31     0.88     --          --
Stockton 23     2.44     1.20     5.6%    36.3%

Nash 22           2.29     0.50     --          --
Nash 23           2.49     1.17     8.7%    134%

Lin 22              2.21     0.45     --          --
Lin 23              2.33     1.19     5.4%    164%

Taking first things first, the age-23 Earnings for Stockton and Nash are indeed excellent – and Lin is, in fact, a step behind them.  When playing time is taken into consideration (wCE), the age-23 Lin, Stockton and Nash all brought virtually identical value to their respective teams – but that is because Lin played more than the other two.
The interesting thing to consider here is growth: is there something about the change in performance from one year to the next that suggests that Lin is not a flash in the pan, but on a career arc that would justify comparison to some of the game’s better players?  From the rookie season to their second year, each player’s EG (what they did when they were on the court) improved significantly, with Nash’s jump almost off the charts.  But Stockton and Lin grew quite nicely, and at similar rates – which suggests that Lin is on a segment of the learning curve comparable to that of the game’s better players.  Lin may never be as good as the best, but early signals suggest that he will, in the least, continue to improve.
The stat of wEG, for these players at this stage of their careers, is, admittedly, meaningless.  The tremendous jumps in wEG for all three (especially Nash and Lin), merely reflect the fact that they were getting into the game for meaningful minutes in their second years, while in their first years they were used sporadically.
So back to the original question: Is Jeremy Lin the next John Stockton or Steve Nash?  The early returns suggest that he is not, although he might come pretty close.  But let’s close our eyes and dream a little.  Let’s say that, over the next year or two, Lin demonstrates a growth in on-court Earnings of 5%, and does so while averaging 36 minutes per game.  That would project, for Lin, an E of 2.44, and a wCE of 1.83.
Put in perspective, in 2010-11, league MVP Derrick Rose posted an E of 2.45 and a wCE of 1.91.  So the current Lin phenomenon may represent equal parts reality and wishful thinking, but there is enough substance there to suggest that happy dreams should not be extinguished.