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[Red94]

New post: Should he shoot? Looking at the data of selfishness - Part 1
By: Richard Li

In the 2012 All-Star Game, Lebron James had the ball in his hands with the game on the line. Guarding him was Kobe Bryant, long lauded for his crunch time successes. Bryant told James to “Shoot the ******* ball.” James did not. He passed. Twice. James’s team lost.

The usual talking heads adopted their usual sides. In one corner, heroball pundits thought that James, as the anointed one, should have taken the shot. In the other corner, basketball purists thought that James made the correct basketball play, passing out of a double team to create a better shot for his teammate.

It is a debate that always surfaces. How selfish should NBA players be, especially the good ones? Is it more important to move the ball or for the best players to take the most shots? Until recently, clichés overwhelmed data. But the NBA, like all other professional sports, is quickly becoming more data driven, and we now have data to inform the debate. Who is selfish? Who is selfish and should be? Who is selfish and should not be? This is my contribution to the conversation.

Data

I am using three specific pieces of information from NBA.com’s new player tracking data:

1. Passes per game
2. Touches per game
3. Effective field goal %

The first two measures are self-explanatory. Effective field goal % takes into consideration that three-point field goals are more valuable than two-point field goals. Therefore, a player who hits 5/10 three-point FGs has a higher eFG% than a player who hits 5/10 two-point FGs.

All data were collected December 3, 2013.

Sample

I limited my analysis to players who average at least 22 minutes per game. I wanted to concentrate on starters, sixth men, and key role players. There were 192 such players as of December 3, 2013.

Analysis

I created a selfishness measure according to the following formula­:

• Touches per pass (TPP) – Touches per game / passes per game

TPP measures how many times a player touches the ball before passing. The higher the figure, the more a player does something else with the ball besides pass (assumedly shoots), and presumably the more selfish he is.

I also created a selfishness efficiency measure according to the following formula:

• Selfishness efficiency (SE) = TPP * standard deviation of eFG%

SE is a function of a player’s predilection to shoot and his efficiency when shooting. In other words, if a player likes to shoot the ball, what is the likelihood of his shots going in? A high figure indicates great efficiency relative to how frequently the player shoots. A low figure indicates poor efficiency relative to how frequently the player shoots. Players are “rewarded” for being selfish and making shots, but “punished” for being selfish and not making shots.

Standard deviation refers to how far above or below the mean eFG% a player’s eFG% is. I used it instead of just the eFG% to produce positive (above the mean) and negative (below the mean) SE values and because it makes for a prettier graph.

Limitations

Before presenting the results, there are several limitations that need to be considered.

TPP is an imperfect measures of selfishness. For one, it makes point guards look less selfish because they have a “free pass” every possession (the first one after bringing the ball up the court), provided they do not go coast-to-coast. The measure also does not consider that a player who is not passing is not necessarily shooting. A player could be fouled, for example, or turn the ball over.

SE has purposefully exaggerated extremes and a compressed middle of its distribution. Players who have very high/low TPPs or eFG%s will find themselves on the same end of the SE distribution, even if their other measure if comparatively less extreme. Thus, a player who has an average TPP (i.e., passes the ball regularly) but a very low eFG% will still be considered selfish and inefficient as measured by SE. Also, any player with average eFG% will have an eFG% standard deviation close to zero, and therefore also have an SE close to zero. Such a player will have an average SE, regardless of how selfish or unselfish he is.

Results

To show what players have what tendencies, I developed the following infograph (click for full-sized interactive version).

On the x-axis is eFG% and on the y-axis is TPP, labeled “Selfishness.” The top right quadrant (I) contains players who are selfish and have high eFG%. The top left quadrant (II) contains players who are selfish and have low eFG%. The bottom left quadrant contains players who are unselfish and have low eFG% (III). The bottom right quadrant contains players who are unselfish and have high eFG% (IV).

The axes’ units are in standard deviations in order to equalize physical spacing. This also means players’ tendencies are graphed in relation to each other.

In the next parts, I'll present ranked results of TPP and SE (because lists are great) and discuss what the results could mean for the Houston Rockets.

[redfaithful]

Great idea! The players far from the middle are most interesting - Klay Thompson, Nash, Battier, Korver and of course LBJ.

 

Could be interesting to look at it at the team level - calculate a team weighted average (weights being minutes), and create a similar graph for the teams. It will show team tendency to pass the ball against eFG%, should be insightful...

[redfaithful]

Oh, forgot Rudy Gay and Carmelo...

[NorEastern]

Nice! It is going to take me a while to go through this in depth, but how did you imbed the tableau graph like that?

[shirtless]

It's not embedded. I tried embedding it and the size just wasn't big enough. Right now it's a static image in the post that links to tableau's site.

[Red94]

New post: Should he shoot? Looking at the data of selfishness – Part 2
By: Richard Li

In part 1, we plotted players' selfishness against their eFG%. Now we're going to turn the four-quadrant chart into a ranked list. The two measures we are focusing on are touches per pass (TPP, our measure of selfishness) and selfishness efficiency (SE, a combination of how selfish a player is and how well he shoots).

Because SE essentially forces the chart, which has data in all directions, into a straight line, some sacrifices have to be made. As mentioned in part 1, because SE uses the standard deviation of eFG%, it is great for analyzing the extremes (players who shoot really well and really poorly). However, players who are average shooters will have an eFG% stand deviation close to zero, and thus their SE will also be close to zero, or basically average.

With that being said, the results of TPP and SE are displayed in the following tables (click for a full-size interactive version).

All columns are sortable (except team, which you can filter). The first table shows players' touches per game, passes per game, TPP, and their TPP rank. The second table shows players'  TPP, eFG%, SE, and SE rank.

Thought 1 - Visual Team Chemistry

Using the visual representation, we can also analyze players’ tendencies from individual teams and begin to understand how those teams operate offensively. Houston, for example, has one selfish player (Harden), who fortunately also shoots a high eFG%, with everyone else in the unselfish/high eFG% quadrant (Howard is on the cusp). The Spurs take unselfishness to another level, with almost everyone in the unselfish half of the chart (only Kawhi Leonard is barely selfish).

Of course, the quadrant that teams do not want players in is II, selfish and low eFG%. That signifies ball-stopping, iso-inclined players whose shots don’t fall. The Knicks and Raptors both have two players in this quadrant (Anthony/Smith and Gay/Derozan, respectively). Probably not fun to be on those teams. Though no team is as selfish and horrible as the Sacramento Kings, who have a whopping four players in the quadrant.

NOTE: This data was collected before Rudy Gay was traded to the Kings. The Kings have now added arguably the most selfish and poor shooting player to inarguably the most selfish and poor shooting team (they didn't trade away any of their selfish/poor shooting players). This could become very disastrous and/or hilarious.

Thought 2 - Roles Matter

Expectedly, a player’s role is strongly related to how selfish he is. The most selfish players (i.e., the ones who pass the least per touch), as measured by TPP, tend to be ball-hogging, isolation-happy, prone-to-chucking wings. Players like Eric Gordon, Nick Young, Rudy Gay, Demar DeRozan (eek, Raptors), and Carmelo Anthony are all in the top 10. The least selfish players (i.e., the ones who pass the most per touch), as measured by TPP, are pure point guards who are poor scorers, like Ricky Rubio and Shaun Livingston, and hustle/defense guys, like Joakim Noah and Anderson Varejao.

For selfish efficiency, spot up shooters top the list. This makes sense, considering their job is to seek out extremely open (usually three point) shots and not pass them up. Thus, we see the likes of Kyle Korver and Klay Thompson in the top 10. Range-limited big men also congregate near the top, likely due to their high percentage shot selection (Drummond, Dalembert, DeAndre Jordan). At the bottom are aforementioned volume-scoring wings (Rudy Gay again, and JR Smith makes an unsurprising appearance), and also players who are having terrible shooting seasons, like the entire Brooklyn Nets roster.

Thought 3 - Defying Expectations

Since players’ roles greatly influence their selfishness and selfish efficiency measures, players who buck those trends, one way or another, should be acknowledged. Considering how central he is to pretty much everything, Lebron James’s SE is unbelievable. He is ranked fifth, sandwiched between three-point specialists and dunkers. There isn’t even another star wing player in the top 30. In comparison, Carmelo Anthony’s SE ranks him at 166. For the same reasons, Chandler Parsons (11^th) and Trevor Ariza (13^th) also have impressive SEs.

While paint-clogging big men tend to have high SEs, their stretch counterparts can become very inefficient. Pau Gasol, Kelly Olynyk, and Kevin Garnett are all in the bottom 30 for SE.

In part 3, we'll talk Houston Rockets using these data.

[thenit]

Good job, very interesting

[bluemars]

I like your chart with selfishness and eFG% in the previous post. I find this chart to be more interpretable than the SE measure, which seems to be not much more than an attempt to project the selfishness vs. eFG% chart into one dimension. I think it would also be interesting to see a chart with selfishness on one axis and assists per pass on the other, allowing us to compare their selfishness with passing efficiency.

[shirtless]

I, too, like the chart better than the tables. As you mentioned, and as I also mentioned in part 2, compressing a multi-directional chart into a one-dimensional list results in compressing information. Basically, some integrity is lost. But it does allow us to compare two players like Kyle Korver (low selfishness, super high eFG%) and Klay Thompson (super high selfishness, above average eFG%). In the end, it's just another way to look at the same information, one that has advantages and disadvantages. Some might prefer it, while others might not.

 

Part 3 will actually combine both the chart and the table into one chart, and to some extent the chart from part 1 and tables from part 2 were lead-ins to this final chart. Hopefully that will be an efficient way to fulfill more people's data visualization preferences. 

[ale11]

Very nice job, very interesting stuff and easily understandable. Keep it up!

[Red94]

New post: Should he shoot? Looking at the data of selfishness - Part 3
By: Richard Li

In part 1 and part 2, we looked at selfishness from two different perspectives, one a graphical chart and one a more traditional table. I've combined these two visualizations into this single chart. It looks much like the first chart, but an added slider allows you to filter by players' SE rank. Thus, you can quickly identify, say, the top 10 players in terms of SE without having the leave the visual view. I plan to update this data every once in a while and, when I do, will only present the results in this view.

I'm now going to use these data to make some suggestions about how offenses, specifically the Houston Rockets offense, should operate. My comments are based on a few assumptions.

1. Players selfishness and eFG% are negatively correlated. In other words, the higher a player's selfishness, the lower his eFG%. This is due to players' shot selection becoming poorer by taking more shots. Here's a graphical presentation of what I mean:

[caption id="" align="aligncenter" width="360"] The more selfish this player is, the lower his eFG% is[/caption]

2. The strength of the relationship between selfishness and eFG% is different for each player. Some can take more shots without a huge change in eFG%, while some will see a huge change in eFG% by taking more shots. In math, we would call this the slope of each player's line. In economics, we would call this the elasticity of each player's eFG%. Here's a graphical representation of what I mean:

[caption id="" align="alignleft" width="225"] Can take lots of shots without a large decrease in eFG%[/caption]

[caption id="" align="alignleft" width="225"] Big drop in eFG% by taking a few more shots[/caption]

3. Some players are just better shooters than others (or at least shooting better presently). Everything else being equal (i.e., they take the exact same shots under the exact same circumstances), player A will have a higher eFG% than player B. In math, we would call this each player's constant. Here's a graphical representation of what I mean:

[caption id="" align="alignleft" width="225"] Good shooter, notice he starts out higher on eFG%[/caption]

[caption id="" align="alignleft" width="225"] Poor shooter, notice he starts out lower on eFG%[/caption]

 

 

 

 

 

Here's my premise. An inefficient offense is one in which the players are far apart on their eFG%. This means that, in the team's current offense, some players have a much better likelihood of making their shots than others at the players' respective rates of selfishness. In this case, players who are shooting better than others should be more selfish, and players who are shooting worse than others should be less selfish. Thus, a perfectly efficient offense is one in which the players have very similar eFG%s; basically the players would be situated in a near vertical line on the chart. Every team has this theoretical line. Let's call it the line of awesome. Here's what it would look like:

[caption id="" align="aligncenter" width="449"] Notice how all players are very close to the line of awesome[/caption]

Where on the x-axis (eFG%) a team's line of awesome would cross depends on the shooting abilities (constant) of each player. How high or low each player would be on his team's line of awesome depends on each player's capacity to absorb more shots without decreasing his eFG% (slope, or elasticity). If players' are close to their team's line of awesome, this means that every player is being as aggressive as he should within his own capacity relative to everyone else on the team.

OK, enough jabber. Onto the Houston Rockets. Here's the Houston Rockets offense from the chart:

The good news is that everyone is actually above-average in eFG% and is kind of close together vertically. In fact, if you compare the Rockets to other teams, the Rockets are doing quite a bit better than most others. Some teams just look completely hopeless. However, the Rockets can still make some improvements.

The two players that appear to be farthest away from the Rockets' theoretical line of awesome are Harden and Beverley. As it stands, every additional shot that these two take has a less likely chance of going in than an additional shot taken by five of their teammates. So even though James Harden is shooting the ball at a reasonably good rate, it just so happens that his teammates, at their current rates of selfishness, are shooting the ball at an even better rate.

The simply stated solution is for Harden and Beverley to pass the ball more when they touch it. But that doesn't mean Harden should start passing up fast break dunks. And it doesn't mean Chandler Parsons should just chuck the ball every time he has it and expect his shots to magically fall. It means that Harden should not take the most difficult shots he currently does, and that Parsons et al should take the least difficult shots that they currently pass up given their capacities and styles of play. So Harden should keep taking fast break dunks, but pass up the double teamed step-back 18 footers that he takes. And Parsons should take the somewhat-contested three-pointer he's on the fence about.

[Rahat Huq]

Very interesting and confirms the eye test. Harden could be MVP caliber if he bent his back on defense and stopped settling for bad shots. It took Lebron James until I believe age 26 to figure out the latter. Let's hope Harden gets it as he ages. Right now, I suspect he's still basking in being a team's #1 option, something he didn't enjoy from the start like other superstars did. Once the playoff losses pile up, he'll change. As far as the defense though..

[redfaithful]

While the obvious focus is on Harden, this graph also confirms that Beverley's shots aren't falling like others on the team. Being the most unselfish by this analysis is great, but I sure hope he regains his scoring touch, hopefully soon.

[Chichos]

Amazing explination of the basics before moving onto the meat of the analysis. 

 

One thought though, all shots are currently weighted evenly but we know that shots late in the shot clock have to be shot or we lose the ball to a 24 second violation.  I think shots taken in the last 4 seconds or so shouldn't be weighted as heavily as the rest since.  It would be the same idea as not counting half court heaves at the end of the half but obviously they still have to have some weight as they are part of standard offense.

 

If there is a way to see if Harden and Beverly are shooting a disproportionate amount of shots late in the shot clock that might explain some of their movement away from the line of awesome.  I am especially expecting it from Harden since he purposely dribbles until there is no time left and then takes a step back or kicks it to his release valve, often Beverly, who has to immediately throw it up.

 

I'm not sure if time left on shot clock when shot was taken is a stat anywhere, but in an age where NBA offenses go through three stages of offense in 24 seconds it definitely needs to be taken into account.

[goRockets]

You should show this to Morey, he'd like it.

[bluemars]

I am a PhD student in data analysis and I approve of this post. Maybe you could rank teams by standard deviation of their eFG% giving us a sense of which teams are closer to their line of awesome?

 

I would also love to see elasticity by player, looking at the data on a per game basis. In this case, it would be tempting to say that low elasticity implies a player can maintain eFG% at higher shot volumes.  However, there is the confounding factor that the player is choosing to shoot based on what is happening during the game. Suppose a player has very high "true elasticity", meaning if we told him to take more shots per game his eFG% would drop significantly. However, this player only shoots in situations where he has a good chance of making the basket. The player would appear to have low elasticity because the eFG% would be roughly constant even as the number of shots changes per game (due to the player having more good looks in some games rather than others).

 

More than anything, I think this metric would measure a player's intelligence with respect to shot selection. If we see a high elasticity of eFG% then when the player increases the number of shots in a game, he is taking worse shots. If we see a low elasticity then the player is taking more shots because he is getting more good looks.

 

If we could somehow get a measure of the number of good looks per game, we could control for this confounder and get a sense of the "true elasticity" (e.g. How good is a player at making difficult shots.  Will this player be able to maintain eFG% if we told him to increase his shot volume?).  Sadly, this measure would be very difficult to assess and certainly not widely available.

 

Also any thoughts on my suggestion about a chart with unselfishness on one axis and assists per pass on another? This way we get a sense of how much someone passes and whether those passes turn into points just like your first post showed how much someone shoot and whether those shots turn into points.

Edited by bluemars, 12 December 2013 - 06:20 PM.

[thejohnnygold]

In response to the request for two different types of data I have some tidbits.

 

First, 82games.com offers some data on when shots are taken (early, middle, late shot clock); however, I have found their data sometimes questionable--so take it with a grain of salt.  They also use what they call "crunch" stats which I believe measure end of game when the score is close shooting stats.  I just took a quick glance at Parsons (as he is on my fantasy team and I lament every 30 ft. heave he takes at the end of the shot clock because our ball movement was terrible) and they say about 11% of his total shots are taken with less than 4 seconds on the clock.  That does not mean they are all bad shots so, again, grains of salt.

 

Second, basketball-reference.com, has added a new feature that has lots of nifty little stats.  One of these is basically points created.  It tries to account for the points generated from assists (I doubt they count hockey assists).  The data is only available for previous seasons right now.  Here is Jeremy Lin's.

 

James Harden was credited with 1098 points off assists and he registered 455 assists last season which translates to 2.4 points per assist credited.  I haven't done any comps for scale, but that seems very, very good.  It certainly alludes to our penchant for kick-out threes and the success of those shooters.  (On a side note, why don't passes that lead to made foul shots get credited for the assist?  I don't understand that rule.  Is it because technically there was no fg attempt?)

 

Shot selection seems to be something that can only be graded with the eyes.  That would require watching games and subjectively keeping tallies for each player.  Who wants to volunteer for that one?

 

An example: I was watching a Bulls game the other day.  It was nearing the end of the first half and the Bulls were trying to get one more shot in before the buzzer.  Mike Dunleavy was camped in the right corner and got an outlet pass with about 3 seconds on the clock.  He was about to put up the three, paused and realized there was no one between him and the basket as the other team was doubling up top.  He brought the ball down, took two quick dribbles and dropped in a lay up at the buzzer.  His awareness of everything going on was very impressive to me.  None of that finds its way to the stat sheet.

[Sir Thursday]

I really like these articles - the data they present is very interesting! However, I have a slight quibble with the conclusion of the study. I don't think it's necessarily the case that the 'line of awesome' is the optimal offence for a team. In fact, I think the way the Rockets' offence is on that graph could well be the best way to set things up.

 

The reason I think that assumption needs challenging is that I don't think it's a given that you would see a constant slope on the graph for an individual player. There are a lot of role players in this league who would not be able to operate as the focal point of an offence. For these players, there would be a maximum USG% beyond which their efficiency would sharply tail off. If you are trying to rearrange shot allocations to make the team more efficient, you have to make sure the marginal gain in efficiency from decreasing the usage of a high-volume player exceeds the marginal loss from increasing the usage of these role players. This is not necessarily going to be the same as getting everyone to shoot the same eFG%, especially if increasing the usage of a player takes them over that efficiency cliff.

 

I propose an alternative way of looking at things. If you were able to draw a graph of elasticity for each player like BlueMars suggests, then you could identify where these efficiency cliffs are. In an ideal lineup, you could take each player on the court's optimum USG% and it would add up to 100%. Then you'd split up possessions accordingly. If it added up to more than 100%, you would have to decrease the touches of some of the players from their optimum. However, if the optimums summed to less than 100%, then you would have to select one or more players to handle some extra possessions. And you would choose the player whose efficiency doesn't fall off a cliff when he is given more load.

 

The above is an interesting situation because it is the one you find many 'Star' players who advanced metrics are disdainful of in. In a vacuum, yes you would want Carmelo to shoot a little less and distribute some of those possessions elsewhere. But if the rest of the Knicks are at their optimums then someone has to use some extra possessions and take the efficiency hit, and Carmelo is almost certainly the best player to do it on the team.

 

I hypothesize that the Rockets are a team in such a situation. Players like Casspi, Garcia and Jones are being asked to do exactly as much as they should be while they are on the court - any more and they would not be able to put up the efficiency they are doing at the moment. Harden is the guy picking up the slack, and as a result his efficiency suffers a bit.

 

Does that make any sense? It does in my head, but I'm not certain I've articulated it very well.

 

ST

[thejohnnygold]

I agree with you, Sir Thursday.  For a while now I have referred to this (in my head) as the "Russell Westbrook Effect".  He has long been panned for his poor efficiency, shot selection, and reckless play.  Yet, he is the catalyst that makes OKC's offense go.  His Tasmanian Devil attack wreaks havoc on defenses which opens up the floor for guys like Durant, Ibaka, Sefolosha, etc.  His injury proved as much as OKC was unable to maintain their overall effectiveness once he went down last year.

 

Another thing I noticed was the San Antonio Spurs.  Their "line" is nearly perpendicular to the proposed "line of awesome" (I presume that original line was conjured just to give a general notion and that individual teams' styles and players may necessitate a different orientation.)  Further, only one of them ventured into the selfish zone which supports the notion that their offense skews the line of awesome because they play a more team-oriented version of the game.  Only Kawhi Leonard crossed that selfish threshold.  Meanwhile, Tim Duncan's eFG% was lowest alluding to him bearing the burden of carrying the offense at times.  That last assumption may just be a result of a slow start to the season for him...I look forward to re-visiting this later and seeing how it has evolved.

 

Harden does bear this burden for the Rockets--and does so very well.  I would need to take some time to research it, but in my head it seems that the players best suited to this purpose/role are also able and willing passers.  Otherwise, the result ends up looking very stagnant.  Carmelo and Kobe tend to fall into this trap.  Both are capable passers, but the willingness doesn't always seem to be there.  On the flip side, Lebron, Harden, Paul, Lin and (bear with me) Brandon Jennings fulfill this role very well.  (I have watched most of Detroit's games this year and, aside from a terrible turnover problem, Jennings is playing great basketball on both ends of the floor.)

 

All of this definitely bears more investigation...

[bluemars]

Sir Thursday, I think I understand what you are saying but I actually really like the notion of "line of awesome". The theoretical line of awesome that Richard Li is talking about is not necessarily a perpendicular line through the mean of eFG% for each player. In fact, this theoretical line may be lower than the mean eFG% precisely because of the argument that you make. Taking shots from say, James Harden, and giving them to Chandler Parsons may decrease Parson's eFG% more than it increases James Harden's. (Not knocking Chandler or James just using them because of their positions on the chart.) Let's say that taking one shot from James and giving it Chandler increases James's eFG% from 50 to 51% but decreases Chandler's from 60% to 58%. This is still a better situation because that shot has a 58% chance of going in versus a 50% chance of going in! This argument continues to hold until Chandler and James's eFG% are the same. In the end, James will be taking a lot more shots than Chandler, but we are at "optimal efficiency".  Hence, the line of awesome!

 

Also, I appreciate the shoutout to my idea for measuring elasticity by player but as I mentioned in my post I'm not sure this would necessarily be a good way to measure whether a player should be shooting more.  As I said previously,

 

"In this case, it would be tempting to say that low elasticity implies a player can maintain eFG% at higher shot volumes.  However, there is the confounding factor that the player is choosing to shoot based on what is happening during the game. Suppose a player has very high "true elasticity", meaning if we told him to take more shots per game his eFG% would drop significantly. However, this player only shoots in situations where he has a good chance of making the basket. The player would appear to have low elasticity because the eFG% would be roughly constant even as the number of shots changes per game (due to the player having more good looks in some games rather than others).

 

"More than anything, I think this metric would measure a player's intelligence with respect to shot selection. If we see a high elasticity of eFG% then when the player increases the number of shots in a game, he is taking worse shots. If we see a low elasticity then the player is taking more shots because he is getting more good looks.

 

"If we could somehow get a measure of the number of good looks per game, we could control for this confounder and get a sense of the "true elasticity" (e.g. How good is a player at making difficult shots.  Will this player be able to maintain eFG% if we told him to increase his shot volume?).  Sadly, this measure would be very difficult to assess and certainly not widely available."

 

I am very much enjoying this data-oriented conversation :)

Edited by bluemars, 12 December 2013 - 11:47 PM.