Spreading the wealth

Posted on 01/04/2011 by


“Figures often beguile me, particularly when I have the arranging of them myself; in which case the remark attributed to Disraeli would often apply with justice and force: “There are three kinds of lies: lies, damned lies and statistics.””
– Mark Twain’s Own Autobiography: The Chapters from the North American Review

In honor of the upcoming 100 thousandth view of this blog, I had decided to do something special for all my dozens of loyal readers. I was torn as to what exactly that was going to be. It had to be cool, it had to be topical. Most of all it had to give me an excuse to post a Batman image.

2 out of 3 ain't bad, right?

After much thought and debate, an obvious answer came to me. This blog is about made up stats and amusing series where I give a different take on the NBA. It’s about me making it up as I go along and finding out something new. Sometimes, it’s about me going back and revisiting unfinished business.

I really,really should have finished this series way back when

With that in mind, get ready for a trip back in time. Get ready for something different (or eerily similar depending on how meta you get) . Get ready folks for Gimme the Rock Rankings take 2.

Gimme the Rock The Series V.2

The background comes first of course.This could rightly be considered part 5 of the Gimme the Rock Series (or Part 2.1). The previous parts are:

The Intro and the Paradox of Melo

Point Guards and the Nash Equilibrium

Shooting Guards and the Shooters Dilemma

Small Forwards: Jacks of all Trades

The genesis of this series came from an article on Carmelo Anthony by Jeremy Wagner of Roundball Mining Company:

The motivation of that article is that the author, cannot believe the premise that Carmelo Anthony is inefficient. While he admits that he in most cases believes in statistics, in this case the statistics do not match his conclusions drawn from direct observation. Faced with this quandary, he decided that he was going to take a look at the numbers himself and while I admire his efforts I disagreed with his results. He argued that while Melo was not an efficient scorer he could be if he chose to be. In essence, he played with the numbers until they matched his perception.

As you might imagine, I have issues with this idea. I think young players can be molded to appropriate behavior by the right system but veterans are who they are for the most part.

Yeah, I know, it's a re-reun but it's appropriate

My take is that there is an ineffable calculus that makes a person an efficient generator of offense. The end goal is simple, the player needs to find the best possible look or find the man that has it and get him the ball without turning it over. The details, is he open, is it a three, will he get an and 1, etc., are not so simple. If the player is successful his team scores. The needs of the many do indeed outweigh the needs of the few or the one. Measuring this is a challenge and by now you know how I feel about challenges.

The Metric & The Recap

The goal remains to develop a simple measure for the return (points) on investment (possessions) for players on offense (i.e. Player offensive efficiency). The concept is based on the idea that were I an NBA gm paying a player I would care about getting value (points) from my assets (possessions). I want to do this simply in a way that anyone can understand and using publicly available information.

There were a few things wrong with the last iteration but I’m making some fixes.

My method will be as follows (fixes are in red):

  • Look at all the data for the Current Season for every player and get:
  • Player Position
  • Minutes Played (and eliminate all players with less than 180 Minutes Played this year which leaves 332 players)
  • Pts48 (points per 48 minutes)
  • FGA48 (field goal attempts per 48 minutes)
  • Pts per Attempt (pts per attempt = pts48/fga48)
  • AST48 (assists per 48 minutes)
  • TO48 (turnovers per 48 minutes)
  • FTA48. This was added because of two of my fabulous readers (some dude and Man of Steele take a bow) who pointed out that some free throws while free do end possession. They’re right of course. So we are going to add the SD-MOS hack-a-shaq correction.
  • Offensive possessions used per 48 (FGA48+AST48+TO48 +.44 *FTA48 term (an approximation for possessions used thru Free Throws from Prof. Berri) this is the possesions spent by the player)
  • The BIG FIX: Offense Generated (Pts*(% of Points not credited to Assists)  +Assists *(Avg Points per FGA/2) per 48.

Let me explain. One of the big complaints with the metric was that I was double-counting assist. As a correction, I decided to give the passer a half credit for the points generated from each assist and give the rest to the shooter(a 50%/50% split). So for the 2010-2011 the numbers are:

Assists 20574
Total Points 96102
Pts per FGM 2.69
Pts per Assist 1.35
Pts from Assists 55418.0
Total Value of Assists 27709.0
% of Points from Assists 28.8%
Multiplier for Points 71.2%
  • So Assists are valued at half the average value of a made field goal. This leaves us with a multiplier of 71.2% for Pts to make sure everything adds up properly.
  • Offense generated per possession used. This is the key measure as it reflects how many points the team generates when the player in question gets the rock.
  • Offense Generated at 30 possessions used. Here I’m just projecting every player at an even number of possessions.

And this gives us the Gimme the Rock Metric take 2.

Now I could look at every player together but I noticed a funny thing:

Role & position play a huge role in how you affect the offense so for this series we’ll be looking at players by position and then ranking them.

Then while looking at the Shooting Guards. I noticed something else. Usage.

Take a look:


Now the implication isn’t that efficiency and usage are linked. Diminishing returns doesn’t actually happen when players increase their usage. Go to the article below for detail


My take is that the populations in the data are different depending on position and usage. My personal belief is that there is a unique optimum point for returns for every player (So for example Jordan high, Rodman low) . However, we can only observe the player’s efficiency at the level of usage they exhibit during the seasons. Take a look at this graph for economies of scale:
Economies of Scale

For some players an increase would be good and for some players a decrease would be good. Studies such as the one referred to above show that players who took more shots on average increased their efficiency. They took/were given more shots because on average their taking more shots would yield increasing returns so the data has a built in bias. My population sample shows the same skew. The fact that on average increased usage is proportional to increased efficiency just means to me that as a whole the coaching fraternity of the NBA can recognize and assign more possessions to successful earners of points (at least on average 🙂 ).

So if I’m going to use my gimme the rock metric to evaluate efficiency, I need to do it by position and by usage. I’ll do this by using the possession use stats I have lying around for everybody and standardizing and dividing every group into quarters:

  • Group 1 :Very High Possession Usage for Position
  • Group 2 : High possession Usage for Position
  • Group 3: Low possession Usage for Position
  • Group 4: Very Low possession Usage for Position

Ok, long explanations out of the way, let’s get to the fancy tables!

Gimme the Rock The Series V.2

We’ll be doing 5 tables in this post.

Yeah you heard me 5.


Well do each position and group all players by usage type.Be prepared to be surprised, keep in mind I’m trying to measure offensive return and decision making. Rebounds, steals and blocks are nowhere to be found.

Point Guards First:

And if we look at the above average performers (>1 std deviation from the mean):

Player Team Position Usage Group by position Offense Generated at 30 possesions used Standard Deviations from Mean
Chris Paul NOH 1 1VeryHigh 29.2 2.5
Steve Nash PHO 1 1VeryHigh 28.7 2.2
Rajon Rondo BOS 1 1VeryHigh 28.0 1.8
Deron Williams UTA 1 1VeryHigh 27.3 1.4
Jose Calderon TOR 1 2High 27.5 1.6
D.J. Augustin CHA 1 3Low 27.2 1.4
Luke Ridnour MIN 1 3Low 27.1 1.3
Jason Kidd DAL 1 3Low 27.1 1.3
Mike Bibby ATL 1 4VeryLow 27.2 1.4

Only nine point guards of sixty point guards qualify as above average. Not surprisingly, CP3,Nash, Rondo and D-Will are the best of the very high group. Calderon and Kidd are not a surprise. Augustin, Ridnour and Bibby are. It’s interesting to note that as group the very high usage players have the best average (even allowing for Baron and Brandon :-))

Next we do Shooting Guards:

If we again  look at the above average performers (>1 std deviation from the mean):

Player Team Position Usage Group by position Offense Generated at 30 possesions used Standard Deviations from Mean
Manu Ginobili SAS 2 1VeryHigh 26.2 1.4
Kevin Martin HOU 2 1VeryHigh 25.3 1.0
Ray Allen BOS 2 2High 26.1 1.4
DeShawn Stevenson DAL 2 3Low 27.9 2.3
J.J. Redick ORL 2 3Low 26.8 1.7
Kirk Hinrich WAS 2 3Low 25.9 1.3
Arron Afflalo DEN 2 4VeryLow 26.2 1.4

A smaller group here as only seven shooting guards of sixty-two qualify as above average. Only Manu and Kevin Martin are above average for the very high quartile SG’s.  Jesus Shuttlesworth still has game apparently. Stevenson, Redick, Hinrich and Affalo don’t kill you.  The real interesting point for the Shooters is that there not a lot of spread here. In fact the real value apparently is to be found in Shooting Guards who do things other than shoot (paging Landry Fields, Landry Fields to the window).

Let’s do Small Forwards:

If we again  look at the above average performers (>1 std deviation from the mean):

Player Team Position Usage Group by position Offense Generated at 30 possesions used Standard Deviations from Mean
Paul Pierce BOS 3 1VeryHigh 26.3 2.0
LeBron James MIA 3 1VeryHigh 25.4 1.5
Grant Hill PHO 3 2High 25.3 1.4
Reggie Williams GSW 3 2High 25.1 1.3
Andre Iguodala PHI 3 2High 24.9 1.2
Danilo Gallinari NYK 3 3Low 25.7 1.6
Richard Jefferson SAS 3 3Low 25.6 1.6
Francisco Garcia SAC 3 3Low 24.7 1.1
James Jones MIA 3 4VeryLow 27.6 2.7
Brian Cardinal DAL 3 4VeryLow 26.1 1.9
Shane Battier HOU 3 4VeryLow 25.2 1.4

A larger group here as 11 of sixty-seven Small Forwards qualify as above average. Only the Captain and the King are above average for the very high quartile SF’s (Lot’s of Celtics so far).  Grant Hill and Iggy pair with a surprising Reggie Williams for group 2. As for the rest we have Gallinari (yay aging), Jefferson(yay coaching),  Garcia (hey,I know you play on Sacramento but at least you know the Maloofs), Jones/Cardinal (proving the power of good teams) and Battier.  For SF, the difference between the haves (Lebron,Pierce) and have nots (hello again Melo) is significant.

Now we get to the first group of bigs, the Power Forwards:

If we again  look at the above average performers (>1 std deviation from the mean):

Player Team Position Usage Group by position Offense Generated at 30 possesions used Standard Deviations from Mean
Dirk Nowitzki DAL 4 1VeryHigh 25.8 1.5
Lamar Odom LAL 4 2High 25.8 1.5
Hedo Turkoglu TOT 4 2High 25.5 1.4
Paul Millsap UTA 4 2High 25.3 1.3
Craig Smith LAC 4 2High 25.0 1.2
Anthony Tolliver MIN 4 3Low 24.9 1.2
Shawne Williams NYK 4 4VeryLow 28.5 2.7
Chuck Hayes HOU 4 4VeryLow 25.3 1.3

Here we have 8 of 56 Power Forwards qualify as above average. Dirk stands alone as the best high usage Power Forward. Odom is not a surprise, Turk lends some credence to the point forward rhetoric, Milsap shows why Utah has not missed a step and Craig Smith made me go huh for the high usage group.  For the lows, we have Tolliver (making Rambis and the KLove early benching look a microscopic bit less crazy), Shawne Williams (justifying his continued spot on nba rosters) and Chuck Hayes . Similar to SG’s this is a very bunched distribution.

Finally we get to the surprising Centers:

If we again  look at the above average performers (>1 std deviation from the mean):

Player Team Position Usage Group by position Offense Generated at 30 possesions used Standard Deviations from Mean
Brad Miller HOU 5 1VeryHigh 27.1 2.0
Al Horford ATL 5 1VeryHigh 26.3 1.8
Pau Gasol LAL 5 1VeryHigh 25.2 1.3
Nene Hilario DEN 5 2High 27.9 2.3
Marc Gasol MEM 5 2High 24.5 1.1
Shaquille O’Neal BOS 5 2High 24.3 1.0
Matt Bonner SAS 5 4VeryLow 27.3 2.1
Ronny Turiaf NYK 5 4VeryLow 27.2 2.0
Tyson Chandler DAL 5 4VeryLow 27.2 2.0

For our largest group (87 Centers ) we have the smallest group by percentage (nine) qualify as above average. Horford and Gasol we expected for the high usage centers but Brad Miller? He can apparently pass the ball very effectively for a big (surprised me too). Nene (your probable starting center for NBA All-Stars for the West)  and Fredo Gasol join the Diesel in his dotage as the members of the high usage group.  The three very low usage centers that round out the group are Bonner,Turiaf and Chandler. The spread here is very large and all the members of our above average center group play for what would now be playoff teams (except for Miller and that might change).

So at 2200 words I’ll stop and leave it to you my dear readers to mull over.  Keep it fun but keep it civil. Cause remember kids, at the end of the day, it’s just silly little stats.

Image courtesy of xkcd.com

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