Wednesday, March 9, 2011

Quantifying Growth in an NBA Player

In the last post, we generated a Price/Earnings (P/E) ratio on player contracts – a relationship between the production a given player might provide his team, and the cost (viewed as a multiple of that production) involved in obtaining that performance.  In this construct, we were able to determine player value – whether or not a player is reasonably priced, over-priced, or a relative bargain – much in the manner that investors determine the value of a stock’s share in relation to its earnings.
In this week’s post, we are looking to borrow from another Wall Street paradigm – the PEG ratio, or Price/Earnings Growth ratio.   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)]

In a PEG ratio analysis, a stock’s P/E ratio is divided by the growth it demonstrated in the previous year:  PEG = (P/E)/(growth%).  In this manner, a company whose stock share costs $10 and earns $1 per share has a P/E of 10.  Additionally, if the same company demonstrated 5% growth in the preceding year, its PEG would be 2 (10/5).

For NBA players, we defined unweighted P/E and weighted P/E (wP/E) with the formulas listed above.  Similarly, Earnings (E) and weighted Cumulative Earnings (wCE) are defined with the formulas listed above.  Using a measure similar to that of corporate earnings growth, unweighted Earnings Growth (EG) is now defined as:

EG = (Present Year’s E – Previous Year’s E)/(Previous Year’s E)

And weighted Earnings Growth (wEG) is defined as:

wEG = (Present Year’s wCE – Previous Year’s wCE)/(Previous Year’s wCE)

In sum, the formulas for unweighted PEG and weighted PEG (wPEG) are thus:

PEG = (P/E)/EG
wPEG = (wP/E)/wEG

I initially decided to try out the new formulas (EG, wEG, PEG, wPEG) on players who are at relatively early stages in their careers (second or third year, for the most part), since older players are more likely to already have long-term, guaranteed contracts.  Also, older players are generally at a point in their careers where they are compensated for what they do (or, all too often, what they have done), rather than for what they will do.  The ten players I chose to evaluate were Derrick Rose, Marc Gasol, Danilo Gallinari, Stephen Curry, Darren Collison, Eric Gordon, Brandon Jennings, Brook Lopez, Russell Westbrook, and Tyreke Evans (all players who have yet to test free agency).

As a means of explanation, I will begin with a comparison of Eric Gordon of the Los Angeles Clippers and Tyreke Evans of the Sacramento Kings, as each player has similar styles that nevertheless demonstrate very different growth patterns.  First let’s look at their traditional statistics over their last two seasons:

                                    PPG      AST      REB      FG%     FT%

Gordon, ’09-’10           16.9     3.0       2.6       .449     .748
Gordon, ’10-’11           23.7     4.4       3.0       .465     .821

Evans, ’09-’10              20.1     5.8       5.3       .458     .748
Evans, ’10-’11              18.3     5.5       4.9       .411     .763

As the traditional statistics suggest, Gordon has shown tremendous improvement from last season to the current one, and Evans seems to have taken a step backwards.  Furthermore, the traditional stats suggest that in ’09-’10, Evans was the better player by a fairly wide margin, whereas this year Gordon appears to edge out Evans.  What the traditional statistics do not tell us, however, is how significant these changes really are.  For example, is Gordon really 40% better this year than last, since his scoring average this year has increased by 40%?  And was Gordon really half the player that Evans was in ’09-’10, since he was only able to produce half as many assists and rebounds?  Both claims seem equally implausible, and we will address this later in the post, when we analyze each player’s cumulative earnings. 

Let’s now take a comparison of the same two players in the same two years, but this time we will use the alternative, Basketball I.Q. statistics:

                                    SPR      TAPPS    TOT

Gordon, ’09-’10           .561     .970       .096
Gordon, ’10-’11           .588     1.021     .081

Evans, ’09-’10              .562     .899       .086
Evans, ’10-’11              .522     .811       .095

The alternative statistics suggest that Gordon truly is improving, and Evans’ sophomore campaign indeed represents a decline.  Gordon’s Successful Possession Rate (SPR) last season, which was pretty good for a backcourt player, has begun to approach All-Star levels.  Meanwhile, his Turnover-Adjusted Points per Shot (TAPPS) started off as extremely impressive, but now has him at a level seen by the very best of low-post players, who take nothing but high percentage shots (this is probably the result of Gordon’s significantly improved free throw shooting, as well as his generally improved shooting from the floor).  Gordon is even taking much better care of the ball, as his Turnovers per Touch (TOT) have declined tremendously.

Unfortunately, you can say just about everything has gone in the opposite direction for Evans: his SPR has declined to a rate that is quite low for a backcourt player; his TAPPS is dwelling in the region of many marginal players; and he is not taking as good care of the ball this year as he did last.

But what might be even more revealing about the two players’ alternative statistics is that they challenge one of the conclusions that the traditional statistics would have you believe, which is that Evans was the better player last year.  Yes, Evans scored more, tallied more assists, and collected more rebounds – but these statistics probably reflect the fact that Evans simply demanded the ball more than Gordon did.  In reality, Gordon was clearly the more efficient player last season:  Gordon’s SPR was virtually the same as Evans’; Gordon’s TAPPS was significantly higher than Evans’; and Evans did, indeed, take better care of the ball.  The sum of these differences – and the growth from year to year – can be best explained by a comparison of the two players’ Earnings (E), weighted Cumulative Earnings (wCE), Earnings Growth (EG), and weighted Earnings Growth (wEG):

                                    E          wCE     EG          wEG

Gordon, ’09-’10           2.44     1.83     --            --
Gordon, ’10-’11           2.53     1.99     3.69%    8.74%

Evans, ’09-’10              2.38     1.84     --            --
Evans, ’10-’11              2.24     1.76     (5.88%)  (6.52%)

These measures – all derived from the previous statistics we have discussed – shed quite a bit of light on the comparison between Gordon and Evans.  Last year, Evans, the ballyhooed Rookie of the Year in the NBA, had less unweighted earnings than Gordon did, though the wCE (which takes playing time into account) was virtually identical between the two players.  This year, however, Evans has had a 5.88% decrease in his unweighted earnings, while his weighted earnings fell even more, 6.52%, as the result of his slightly diminished playing time.  Meanwhile, Gordon has grown impressively – 3.69% in EG and 8.74% in wEG (which reflects his significant increase in playing time). 

And these numbers seem to make more intuitive sense, in terms of their scale – Gordon probably really is about 8% better than he was last year (as opposed to the 40% his scoring average would indicate), whereas Evans probably has declined at about a 5-6% rate.  Furthermore, Evans and Gordon were equally good players last year (as opposed to Evans being twice as good as Gordon), whereas this year Gordon is about 13% better than Evans is (a significant difference).  There may be logical explanations for these statistics – Gordon is now benefiting from the presence of Blake Griffin, opponents have caught on to the fact that if you can stop Evans you can stop all of Sacramento, etc. – but this seems to be what the numbers between the numbers say.

It was at this point in the post that I intended on discussing PEG and wPEG – in other words, taking the players’ salaries and dividing them by the growth in their earnings.  But as I was about to do this, something occurred to me:  Though players have value, and no one with an eye on the salary cap wants to overpay for that value, absolutely no team would take on a player just because he might grow from being marginal to mediocre.  That strategy might make sense for a stock trader, who benefits from appreciation, real or perceived, of just about any kind – but for a professional basketball general manager, growth is useless if it does not represent absolute excellence. 

Furthermore, since you cannot sell a player back to anybody for a higher price than you paid – alas, there are no transfer fees in American sports, as there are in European soccer (perhaps FIFA should come up with its own PEG), and NBA basketball players are not true commodities on an open exchange – you can’t simply move a player from, say, the Wizards to the Rockets, and then collect on the difference in that player’s value from when you obtained him to when you dealt him.  And so I discarded the PEG (and the wPEG) before I ever calculated its value on a single player.  Unlike P/E and wP/E, which might help you determine a fair salary for a given player, the PEG does not give you information that is in any way practical or actionable.

But the growth statistics, as illustrated by the example of Gordon and Evans, appear to be very useful – at least for young players who have not yet hit free agency.  It shows you who is getting better and by how much, and, in a world in which a multi-year contract might be structured to have annually increasing salaries, it can guide you in determining the slope of those pay escalations.  Furthermore, for older players, the growth statistics (EG and wEG) might tell you when the plateau of his career has begun, and when he has begun to descend the other side of the mountain.  Last, a comparison of composite earnings – here referred to as E and wCE – appears to be a far better measure of player performance than traditional statistics.

Below is a table of the alternative Basketball I.Q. statistics, including earnings and growth, on eight other young players who will be re-negotiating their contracts in the next couple years.  Traditional statistics are published in multiple other venues, and so have been excluded for the purpose of brevity.  The first line for each player represents the ’09-’10 season, and the second line represents the current ’10-’11 season.

                        SPR      TAPPS  TOT     E          wCE     EG%     wEG%

Rose                .574     .920     .092     2.40     1.84     --          --
Rose                .590     .929     .087     2.43     1.92     1.25     4.34

M. Gasol          .587     1.035   .073     2.55     1.90     --          --
M. Gasol          .564     .939     .088     2.42     1.67     (5.10)   (12.11)

Gallinari          .562     1.026   .061     2.53     1.79     --          --
Gallinari          .584     1.073   .055     2.60     1.89     2.77     5.59

S. Curry           .598     .941     .099     2.44     1.84     --          --
S. Curry           .618     .993     .100     2.51     1.75     2.87     (4.89)

Collison           .599     .878     .113     2.36     1.37     --          --
Collison           .574     .868     .098     2.34     1.48     (0.85)   8.03

Jennings          .546     .818     .083     2.28     1.55     --          --
Jennings          .537     .832     .078     2.29     1.58     0.44     1.94

B. Lopez           .539     .971     .080     2.43     1.87     --          --
B. Lopez           .503     .937     .083     2.36     1.69     (2.88)   (9.63)

Westbrook       .573     .807     .096     2.28     1.63     --          --
Westbrook       .585     .887     .095     2.38     1.76     4.39     7.98

A review of the above statistics allows for a few, brief conclusions:

Marc Gasol is not a growth prospect.  Besides being the oldest and most experienced player on this list, Gasol has demonstrated the greatest decline this season among this focus of players.  To be fair, Gasol had an excellent 2009-10 campaign, and this season might simply reflect a return to earth.  But when a player’s wEG is smaller (or, in this case, more negative) than unweighted EG, it means that the player is getting less playing time than he did the previous year – which is an important statement about what your coach thinks about you.  Gasol becomes a restricted free agent after this season, but I would be wary of offering him too much, lest he emerge as the second coming of Jon Koncak.

The Brandon Jennings hysteria of 2009-10 should be put on hold.  Jennings’ EG in the last year is essentially flat, and the slight increase in wEG is a reflection of increased playing time, rather than improved play when he is on the court.  A review of his last two seasons’ statistics demonstrates that he is essentially the same player both years.  There are many Knicks fans, of course, bemoaning the fact that Jennings was taken just after the Knicks took Jordan Hill in the 2009 draft.  Though Jennings is almost certainly better than Hill, it should be noted that Hill begat the expiring contract of Tracy McGrady; which begat the cap space that created Raymond Felton; who begat two years of a more-than-serviceable Chauncey Billups; whose retirement will beget either Deron Williams or Chris Paul.  And who would you rather have – Chris Paul/Deron Williams, or Brandon Jennings?

Derrick Rose is darn good, and getting better – but look out for Stephen Curry.  By the alternative statistics, Derrick Rose was a great player last year, and even better this year – a perception confirmed by his traditional statistics, and bolstered by the media speculation of his MVP candidacy.  He appears deserving of the praise.  But look at Curry:  With the exception of his TOT, all of his alternative statistical parameters were superior to those of Rose (wCE was even for both players last season, and Rose gets the edge this year, but that is only because Rose plays more minutes).  And not only are his statistics better than Rose’s, but he is demonstrating greater growth (the decrease in Curry’s wEG is entirely due to the fact that his minutes are down almost 7% this year; last year his minutes benefited from the absence of Monta Ellis, who missed 18 games – but when Ellis plays, he has led the league in minutes per game both last year and this).  It is equally impressive that Ellis’ return to full strength this year has not had an adverse effect on Curry’s game – despite the fact that Ellis and Curry are similar players, Curry has gotten better with a full season of Ellis, which I think tells you something about how unselfish Curry’s game is.  Golden State management should take notice: if they ever have to choose between Ellis and Curry, Ellis may be appropriately valued, but Curry (not yet eligible for free agency) is under-valued.          

The Knicks gave up a lot when they traded Danilo Gallinari.  Look at the numbers.  Absolutely everything he does got better from last season to this – and he was pretty good last season.  He has demonstrated growth in EG and wEG – which means that his performance improved even with increased minutes.  He is still on the steep end of the learning curve.  And Denver has fewer super-models than Manhattan, and so look for this trend to sustain itself. 

Darren Collison is a good example of how increased minutes can skew statistics.  I like Darren Collison – I think he is a pretty good player.  He filled in ably for Chris Paul last season, when Paul was injured, which is why he was a coveted player in the off-season and ended up at Indiana.  He scores more than last year, he rebounds more than last year – but he also plays more than last year.  If you look at his alternative statistics, he is slightly worse this year than last.  His EG is a little bit negative, but close enough to zero that we can call it “flat.”  But his wEG is way up – all due to a 7% increase in playing time.  Collison is who he is – which is pretty much the same player as last year, who just spends a little more time on the court this year.

Russell Westbrook is a good, yet over-rated, player – but he is getting better.  There is very little that Westbrook does that is as good as two of his peers, Rose and Curry.  He takes slightly better care of the ball than Curry, and his wCE is essentially equal to Curry’s (as a result, again, of increased playing time).  There is nothing that he does as well as Rose.  Still, Westbrook is very good, very young, and very adaptive – he has the most impressive EG on this list, and his wEG is right near the top.

Brook Lopez is not exactly Bill Walton.  Unless he breaks his foot and moves to San Diego.