What to Expect From LeBron James, Quarter by Quarter
Aug 31st, 2009 by Jon Nichols

Now that I’ve explored shot types at the team level, it’s time to move on to a single player.  What better player to look at than the league’s MVP, LeBron James?  Using the play-by-play data at BasketballValue, I will explore how James changes his style of attack as the game progresses, and whether or not he optimizes his shot selection.

The graph below shows LeBron’s shot selection for each quarter during the 2008-09 season:


Midrange shots (in terms of the way I define them) are the most common shot attempt in the game, so it’s no surprise that most of James’ shots come from this area.  His preference for this type of shot stays consistent throughout the game.  However, he’s no dummy, and he uses his size and athleticism to attack the rim early and often.  Of course, when we compare these shots to three-point attempts, we notice a strange pattern.  Despite being much more efficient on close attempts (more on this later), LeBron shies away from this type of shot as the game progresses and instead takes more threes.  In the third quarter he actually takes slightly more three-pointers than close shots (remember, though, that shooting fouls are not included, so in actuality he probably still takes more close shots), before the numbers revert slightly back to normal in the fourth.

Why would James do this?  There are a number of factors that come into play.  Fatigue would be my best guess.  It’s clear to everyone in the building that James is a superstar, so he not only must carry the offensive load but also deal with opposing defenses that are focused on stopping him.  It wouldn’t be shocking to find out that he settles for more outside shots as the game wears on simply because he doesn’t have the energy to keep taking the ball inside.  Another possible reason is opposing coaches growing tired of his easy buckets and stopping at nothing to prevent those later in the game.

Regardless of the reasons they occur, are LeBron’s in-game offensive adjustments beneficial for his team?  Let’s take a look at the efficiency of each shot type for every quarter:


The answer to my last question seems to be “no.”  Not only is he much more efficient at close shots than three-pointers throughout the game (something any basketball fan could tell you), but he actually gets progressively worse on threes as the game goes on.  In the first quarter, he’s quite efficient from long range, but by the end of the game he’s below average.  Meanwhile, his efficiency from close range remains about the same.   Yet for some reason, LeBron favors the three-ball more and more as the game progresses.

Fatigue could be a factor again, and we also must consider the interaction between these shot types.  James obviously must keep defenses honest, so abandoning the three completely despite it not being super-efficient would be a bad move.

Still, I think there’s a lot to learn from all this.  James is not shooting as efficiently in the fourth quarter as he is in the first.  The question is whether it’s because of poor decision-making, fatigue, or defensive adjustments.  Whatever the reason, it’s clear the Cavaliers would be better offensively if James could maintain his first quarter efficiency at all times.

The In-Game Changes of the Philadelphia 76ers’ Shooting Style
Aug 24th, 2009 by Jon Nichols

I’m going to look at the shooting styles of the Philadelphia 76ers in the same way I examined the Lakers.  I chose the Sixers because they are one of the teams at the extreme ends of the spectrum– they attempted the second fewest three-pointers of any team in the league last season and converted those shots at the lowest rate.  With the Lakers, we saw that close attempts and three-pointers were much more efficient than midrange shots, despite the latter being attempted the most.  Will we find the same results with a team that struggled from long range?

Thanks to the play-by-play data at BasketballValue, here are the Sixers’ shot attempt frequencies on average per game, at the per minute level:


I made one change from last time.  “Close” shots now only include dunks and layups (tipped shots are not included).  As we can see from the graph above, there are some substantial differences between the Lakers and the 76ers.  Although the overall shot preference order is the same, the Lakers take a lot more three-pointers.  In addition, the Sixers take almost as many close shots as they do midrange.  However, like the Lakers, their three-point attempts tend to go up as the game progresses at the expense of midrange attempts.  Let’s look at the efficiencies of each shot type:


Well, that’s just a mess.  There’s a simple solution, though.  Instead of doing it per minute, we can break down the data by quarter.  Here are the two graphs from above with the data calculated per quarter:



Here the data is much clearer.  Just like with the Lakers, the most efficient shot for the Sixers is the close attempt.  Also, despite a third quarter blip, and even though it is an obvious weakness of theirs, the Sixers are still much more efficient when shooting three-pointers than when shooting from midrange.  In fact, in the fourth quarter, the long ball is almost as valuable for them as is the easy bucket around the rim.

So what are the main differences between the Lakers and the 76ers?  Basically, Los Angeles is more active and efficient from beyond the three-point line.   This should not come as a surprise to many, as this is Philadelphia’s most obvious offensive weakness.  However, what is surprising is that the two teams aren’t very different from midrange.  Both favor that shot type the most despite it being their least efficient method.  The Lakers are slightly more efficient from midrange, but that should come as no surprise considering they feature a dominant post player in Pau Gasol.

As we learned from my last study, there is a correlation between post attempts and three-point efficiency.  Philly’s lack of a post presence last year and surrounding three-point marksmen may have been two of the biggest reasons their offense was not as great as the Lakers.  With the return of Elton Brand and the arrival of Jason Kapono, things should improve slightly for the Sixers.

But can it really be as simple as just taking more three-pointers?  The graphs above suggest this, but the answer remains uncertain for now.

Setting Up the Three: Which Shot Types Do the Best Job?
Aug 19th, 2009 by Jon Nichols

Before I move on with more studies on team shot types, let’s take a brief look at shot optimization.  As you can see from my Lakers study, L.A. takes a great deal of midrange shots despite it being their least efficient shot by a large margin.  On the surface, that certainly seems like a suboptimal strategy.

Perhaps, the thinking goes, midrange shots are efficient not because of how often they are converted but because of how they improve the conversion rates of other shots, namely three-pointers.  If you mix up your shot types, teams have to respect each one and can’t just prevent three-pointers.  Therefore, midrange shots improve the efficiency of three-pointers.

Is this true?  Let’s check the play-by-play data of BasketballValue to find out.  Below is a graph that features the relationship between the percentage of shots that are from midrange for each team and their three-point percentage (3PM/3PA, not the percentage of total shot attempts that are three-pointers):


As you can see, there is really no relationship.  If we were to draw a trend line, it would actually have a negative slope (the original hypothesis suggests a positive slope).  In addition, the p-value is .264, which means that slope is not even close to significant.  Basically, there is nothing going on between those two variables.

We should break it down further, though.  As you may recall, I include post shots in my midrange classification.  Those post shots in particular may do the job of setting up three-pointers.  Let’s take a look at a graph that compares bank/hook shots (two common post shots that are defined in the play-by-play data) with three-point percentage:


Although this isn’t a perfect representation of post shots, I think it’s the best we can do for now.  And you can see we’ve got something going on here.  The positive slope of the line has a p-value of .0682, making it significant at the .07 level.  The R^2 is still very low, but there does appear to be some sort of positive correlation.

What about dunks and layups?  After all, if defenses need to collapse the paint to prevent these easy buckets, this should lead to some open three-pointers.  Of course, many of these buckets come on fast breaks, so the data may be flawed.  Let’s look at the graph:


The trend line doesn’t seem to fit the data very well.  However, its negative slope turns out to be significant at the .1 level.  This is heavily influenced by a couple of outliers, though, so I wouldn’t make too much of it.  Regardless of whether or not the slope should be decidedly negative, it’s pretty clear it shouldn’t be positive.  One explanation for this lack of correlation is that some players just can’t shoot three-pointers, so they instead take it to the basket.  It’s not necessarily that inside shots don’t create openings on the outside.  We don’t know for sure, and the fast break problem can’t be ignored.

Finally, let’s take a look at the relationship between three-point attempts and three-point accuracy.  It may just be that taking more two-pointers allows you to be more selective with your threes, resulting in improved accuracy:


In reality, this is what we should expect.  If you’re better at shooting threes, you’re going to shoot more of them.  Therefore, the correlation is significantly positive.

In conclusion, the biggest thing to take from this article is the lack of correlation between midrange frequency and three-point accuracy.  However, when we narrow it down to shot types that are often taken from the post, there is something going on.  Post shots, but not all midrange shots, set up threes well.   Of course, none of this is a controlled experiment.  It may be that teams with good post players intentionally go after good three-point shooters, so confusing the correlation with causation would be a big mistake.

Tracking the Efficiency of Different Shot Types at the Team Level: Los Angeles Lakers
Aug 15th, 2009 by Jon Nichols

In my last article I took a look at how the Lakers mix up their shot attempts as games progress.  After posting my results at the APBRmetrics board, a common request was take a look at the efficiency of these different shot types.  Today, I will do just that using True Shot Percentage.

Using the same data and same methods as always, I’ve calculated the true shot percentage for the Lakers for each shot type.  This data was divided into each of a game’s 48 minutes, and the average results for all games are displayed below:

TS% by Minute

Midrange shots are generally the least efficient, and close shots are generally the most efficient.  However, the efficiency of three-point attempts for the Lakers fluctuates wildly.  This graph is a bit too hectic to make any sense of, so I’ve also broken the data down by quarter:

TS% by Quarter

This graph makes things much clearer.  Again, midrange/post shots consistently give you the least bang for your buck (although we can’t ignore their hidden positive effects).  For the Lakers, they are most efficient in the middle two quarters.  Close range shots are the most efficient for the Lakers in every quarter except for the third, in which three-point attempts reign supreme.  Of course, we can’t ignore the effects that each shot type may have on the others.

The other significant trend is that, for the Lakers, all shot types are less efficient in the fourth quarter than they are in the first.  Close range shots are consistently harder to convert, midrange shots rise then fall, and three-point shots bounce around pretty wildly.

What happens when we compare the efficiency of these shots to their attempts?  As a reminder, here is the graph showing their attempts per quarter:

Midrange shots are the most common attempt throughout despite being the least efficient.  I would imagine Lakers players and coaches aren’t stupid, so there must be hidden benefits to these attempts.  However, it’s clear that as the game goes on the Lakers move from a less optimal shot type distribution to a more optimal one.  Also, for what it’s worth, the decline in midrange shot attempts is smallest when they are shooting them the most efficiently.  Meanwhile, the Lakers shoot three-pointers the best in the third quarter and consequentially have the highest increase in attempts in the fourth.

The next step is to explore similar ideas with other teams, perhaps ones that are stylistically different than the Lakers.  Also, it would be interesting to see these results for individual players.

Exploring Shot Types at the Team Level: Los Angeles Lakers
Aug 13th, 2009 by Jon Nichols

In my last article, I suggested that knowing how an individual team changes the way it attempts its shots as a game progresses might be a valuable piece of information.  Today I will take a look at the Los Angeles Lakers.

To study shot types at the team level instead of at the league level, I’ve made two changes.  First, I’ve lumped the layup, dunk, tip, and putback categories into one called “Close.”  This will make the sample size large enough to draw reasonable conclusions.  Secondly, instead of totaling the Lakers’ amount of each shot type for every second, I will be doing it for every minute.  This will make the graph look much smoother, too.

Here are the Lakers’ total shots for the season per minute:

By Minute

Similar to the league-wide trend, the Lakers see their midrange/post attempts start high then decrease.  They also see their three-point attempts start low then increase, and their close attempts stay at a consistent level.  At the start of the game, it’s clear which shots they prefer.  By the end, it’s much harder to tell.  Also, coming out of halftime, the Lakers’ close shots spike first, followed by midrange shots, and then three-pointers.  It wouldn’t surprise me if the Lakers coaching staff at the half emphasizes getting shots near the basket to start off the second half.

Of course, this graph is a bit hard to make sense of sometimes because the data fluctuates so much.  To simplify it, I’ve broken it down by quarter:

By Quarter

This graph presents the data in a much clearer way.   With this graph the shot counts are calculated per game.  Here we can see that midrange shots consistently decrease throughout the game, while three-point shots have their biggest increases in the second and fourth quarters.

Overall, in terms of shot types, the Lakers don’t seem to be that unusual of a team.  They start with a lot of midrange/post shots, but by the end of the game their attempts of three-pointers have almost caught up.

Analyzing Changes in Shot Types Over the Course of a Game
Aug 9th, 2009 by Jon Nichols

Recently I explored how shot types change during the final two minutes of a game.  However, that only gave snapshots based on certain timeframes that I chose.  Looking at how those shot types change, second by second, is much more enlightening.  That is what I will be doing today.  For each shot type, I will calculate the total amount of attempts from every game this year for each second.

Let’s start with three-pointers.  From the last study, we saw that three-point attempts increase dramatically relative to other shot attempts in the last two minutes.  Is that a late-game surge only or do three-point attempts increase progressively throughout the game?  Here’s the data:


Outliers (which occurred at the end of each quarter) were removed from the graph for the sake of clarity.  As you can see, there’s a significant increase in attempts as the game goes on.  We also see a very rapid increase at the end of the game.  I won’t speculate as to why this happens, but it certainly is interesting.

In the last two minutes, three-point attempts increase mostly at the expense of midrange/post attempts.  Is this only a late-game trend, or does it gradually occur during all 48 minutes?  Let’s look at midrange attempts:


Two-point shots away from the basket appear to do the opposite of three-pointers.  They start at their highest frequency and gradually decrease as the game goes on.  In the final moments the decline slows, but that is because all shot attempts, regardless of shot type, increase in the final seconds.

Layups are the third shot type with a large enough sample size at each second in the game to make some sense of it:


Layups decline ever so slightly as the game progresses.  At the start of the game the trendline is at around 17, and by the end it is just above 15.  This difference is very small and can possibly be explained by one other change as the game progresses: fouls.  How do shooting fouls change over the course of a game?

Shooting Fouls

These fouls rise by about 2.5 during the 48 minutes, so it may be that layups just go down because shooting fouls (which will not show the shot type in the play-by-play) go up.  We don’t know that most shooting fouls are on layup attempts, but outside shooters are rarely fouled and dunks, tips, and putbacks are infrequent enough to not be much of a factor.

What about those dunks, tips, and putbacks?  I’ve put together graphs on all three shot types, but good luck making any sense of them:




In conclusion, teams don’t move away from midrange/post and towards three-point shots only in the last two minutes.  This appears to be a phenomenon that occurs from the very start of the game. Also, layups go down as the game progresses, but this may just be because of an increase in shooting fouls.

Although this information is interesting at the league-wide level, it may be even more helpful on a team-by-team basis.  If you knew how a certain team changes its style as the game progresses, it would be easier to game plan for them.  This is something I will look into studying in the future.

Banks, Hooks, and Fades Article Fixed
Aug 6th, 2009 by Jon Nichols

Just a quick note: some of you may have had trouble viewing the tables on the Banks, Hooks, and Fades article.  The article is fixed now.  My apologies.

-Jon Nichols

How Do Shot Attempts Change in the Last Two Minutes?
Aug 6th, 2009 by Jon Nichols

Using the play-by-play data at BasketballValue, I decided to see how shot attempts change in crunch time.  Do players take more three-pointers in the last two minutes of a game?  Are layups and dunks harder to come by?  Does desperation lead to more players crashing the offensive boards and tipping the ball in?  Today I’ll try to answer some of those questions.

Without further ado, here are the shot frequencies when there are more than two minutes remaining and when there are less than two:


As you can see, essentially nothing changes except for two types: three-pointers and midrange/post shots.  It appears teams take more long distance shots at the expense of less efficient and perhaps more difficult midrange shots.  Logically, this makes sense, especially when your team is trailing and every point appears to matter more.  If you’re down seven or eight points with little time left, you’re more likely to try to make up that difference in larger chunks.  Also, perhaps players know that on average three-point shots tend to be more efficient than long twos.  With the game on the line, they want to maximize their chances of having a productive possession.

There are a number of problems to consider when looking at this data, and today I’ll take a look at one of them.  Perhaps three point attempts only are high in the final seconds, when there simply isn’t enough time to get a shot off near the basket.

With that in mind, I’ve split up the final two minutes into four parts.  The results are below:


There are only thee shot types that have enough attempts in each timeframe to qualify: three-pointers, layups, and midrange shots.  As a general rule, with the game winding down, three-point attempts increase, layups decrease, and midrange shots bounce around a bit but also generally decrease.  When I didn’t split the final two minutes into chunks, it appeared layups did not decrease.  However, you can see that defenses tighten up on the inside as time runs out.  The only reason I can think of for why midrange shots spike in the last five seconds is because players don’t have time to get any closer.   There are also a lot of players like Dwyane Wade who will run the clock down to the final seconds and launch a midrange jumper at the buzzer.

The next thing to consider is the situation in which these shots were taken.  Narrowing it down to five-second intervals is nice, but it would be a lot more useful if we also knew the score and exactly how much time is remaining during each shot attempt.  That is something I will take a look at in the future.

Banks, Fades, and Hooks: A Look at the Ways Players Take Their Outside Shots
Aug 3rd, 2009 by Jon Nichols

In my last article I took a look at some of the league’s leaders in various “easy buckets” categories.  In other words, I found the players who had the strongest tendencies towards certain types of shots.  Today I will do the same thing with outside shots.

Let’s start with something simple: jump shots.  Which players have the most of their shot attempts come as jump shots?  Here are the top 20 (minimum 50 attempts):


Brevin Knight is small, even for a point guard, so it’s not shocking to see him top this list.  The top 20 includes a mix of big and small guys.  There are little point guards like Knight and Jason Hart, swingmen such as Richard Hamilton and Luol Deng, and plenty of big men.

Next is three pointers.  Although you don’t need the play-by-play data to calculate this information, I chose to do it anyways because it’s always enlightening.  Here are the top 20 (minimum 50 attempts):


We see a lot of names you would expect.  Guys like Donyell Marshall make their living with the long distance shot and the numbers reflect that.

Now it’s time to get more specific.  Here are the top 20 in fade away shot attempts (minimum 10 attempts):


Dirk Nowitzki is the leader of the pack by a wide margin.  His tendency to fade away along with his height make his jump shot nearly impossible to block.  The same can be said for Jermaine O’Neal and LaMarcus Aldridge, who also appear on this list.

Floaters are next.  They’re not exactly an outside shot, but they will be included anyway.  Here are the top 20 (minimum 10 attempts):


Most of the players on this list are point guards, who often have to float the ball over the outstretched arms of interior defenders in order to avoid having their shots blocked.  Mike Taylor appears to be particularly fond of this shot.  A few undersized big men such as Craig Smith and Antawn Jamison appear on this list as well.

I’ll finish off this article with two shots that are often taken from the post.  The first is the bank shot.  Here are the top 20 (minimum 10 attempts):


It’s no surprise Tim Duncan likes to face up his man on the post and use the glass.  His bank shot rate is considerably higher than Shaquille O’Neal’s, who has the second highest rate.  Either the Phoenix scorekeeper is confused about what a bank shot is, or the Suns teach their players to use the backboard often, because they have seven of the 20 players on this list.

Finally we have hook shots.  These come pretty much exclusively from the post.  Here are the top 20 (minimum 10 attempts):


If you’re guarding Dwight Howard, be ready for the hook shot.  Over 30% of his many field goal attempts are hooks.  The Big Cat is not far behind at 29.01%.  As you can see, the hook shot is a relatively common mode of attack for many big men.

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