Nichols and Dimes

Innovative Basketball Research

How the Shooting Abilities of Shooting Guards, Power Forwards, and Centers Affect Offenses

Not too long ago I ran a couple of studies measuring the effectiveness of three-point shooting ability for point guards and small forwards.  The general idea wouldn’t be complete without a look at the remaining three positions.

Using the lineup data at, I’ve split the lineups into three groups: those featuring a player from each position who shoots 40% or better on threes, those featuring one who shoots 30% or less, and the remainder.  For each group, I’ve calculated the average Offensive Rating.  In addition, the lineups are split between those at home and those on the road.  The results for shooting guards are in the graph below:

And here are the frequencies for that position:

The results for shooting guards are very similar to those of point guards.  Not surprisingly, having a player at those positions with the ability to shoot accurately from long distance greatly improves the success of your offense.  One thing that is different is the frequencies.  As you can see above, not too many shooting guards shoot less than 30% on three-pointers.  However, the frequencies for shooters above 40% aren’t too high, either.

Up next are the power forwards.  For this position, I had to alter the criteria a little bit.  To ensure adequate sample sizes, I had to change the definition of great shooters to those above 38% on threes, and poor shooters to those below 28%.  It’s a minor change, but it’s fair because of the relative lack of big men who can shoot well from the outside.

At home, it doesn’t seem to matter if your power forward can shoot.  The four categories are essentially identical.  On the road, it appears that your team gets a significant boost if your power forward can shoot threes at a higher rate than 28%.  He doesn’t have to be spectacular in this area; he just needs to be adequate.

Finally, let’s take a look at the centers.  I had to make yet another change for this position.  Even fewer centers can shoot three-pointers accurately, so I removed the cutoff points altogether.  Instead, I classified centers as shooters or non-shooters.  The difference was whether or not the player had a large amount of three-point attempts.  Of course, by changing the criteria from accuracy to attempts, I changed the dynamic.  However, given the scarcity of great-shooting centers, it was necessary.

The center results may not be directly comparable to those of power forwards because of the different criteria, but they appear to be the inverse.  On the road, it doesn’t matter if your center likes to shoot from the outside.  At home, however, it is beneficial.  Either way, the differences aren’t significant enough and the sample sizes too small for me to make a definitive statement.

So there you have it.  To recap:

  • For point guards and shooting guards, it is beneficial for your offense to have players at those positions that can shoot threes effectively.
  • For small forwards, it is best to have a player closer to average (between 30% and 40%).  This may be the result of sharpshooting small forwards being specialists that are weak in other areas.
  • For power forwards, it all depends on the location.  At home, it doesn’t matter how well he shoots threes.  On the road, it’s great if he can shoot them at 28% or higher.
  • For centers, the answer remains unclear.  There simply aren’t enough great shooting centers to reach a reasonable conclusion.

July 26, 2009 Posted by | Studies Using Lineup Data | Leave a comment

At Which Positions Are Bad Players the Most Detrimental?

In my last study, I looked at the importance of great players to a team’s success.  Today, I will be doing the opposite, instead focusing on the weaker players.  The methodology is the same, only I will be using players with an Adjusted Plus-Minus below -3 rather than above three.  For further details on my methodology, click on the article above.  Without further ado, here are the results:

And the home/away splits…

It appears the two positions you don’t want to be weak at are center and small forward.  On the other end of the spectrum, it appears you can manage a lot better with a bad point guard.  Of course, it’s best to have as many good players as possible, so ideally you don’t have to “deal with” anything.

At home, weak players at the guard position don’t appear to be particularly disastrous.  In fact, lineups featuring a point guard with an Adjusted Plus-Minus below -3 still on average tend to be better than their opponent.  On the road, it hurts much more to have a weak guard, especially a 2-guard.  Regardless of location, center and small forward are two positions where you can’t have a struggling player.

Just like I did with my last study, I’m going to look at two potential hidden issues.  The first is sample size.

There appears to be an adequate amount of bad players at each position to make this study valid.  Interestingly, there are more bad players at point guard than at any other position.  Originally I would have guessed centers would be the weakest.

The next step is to calculate the average Adjusted Plus-Minus for each position among those that qualify.  For example, if there are 20 point guards with an Adjusted Plus-Minus of -3.01, that position will look not as important because the players in the study really aren’t that horrible in the first place.  What do the numbers say?

With the exception of small forwards and possibly power forwards, the numbers appear to be pretty even across the board.  This further supports the evidence that having a weakness at small forward is a major problem.  Even though the small forwards in this study weren’t as bad as the other positions, they still had a more negative effect than any other position besides center.

Finally, I’d like to relate this back to my original study.  As you may recall, I suggested that small forwards and centers (especially on the road) are often the most important players to a team’s success.  Today’s results support that assertion.  Not only does having good players at these positions greatly improve your team, but having weak players at these positions worsens your team.  On the other hand, point guards appear to be much less important.  Both good and bad ones have less of an impact.

Like I said in the original article, these studies are by no means the final authority.  I only looked at two potential complications, and in reality there could be many more.  Further studies should isolate the positions further and perhaps explain in more detail why exactly certain positions appear to be more important than others.  I would also like to look at the results of previous years, which is something I may get into soon.

July 19, 2009 Posted by | Studies Using Lineup Data | Leave a comment

At Which Positions Are Great Players the Most Important?

Using the lineup data at, as well as the Adjusted Plus-Minus ratings, I’ve tried to figure out which positions are most crucial to a lineup’s (and team’s) success.  My method was pretty simple. I calculated the average net rating (offensive rating minus defensive rating) of all lineups featuring a player with an Adjusted Plus-Minus of greater than three at each position.  For example, if the average net rating for small forwards is five, then that means that all lineups featuring a good small forward (Adjusted Plus-Minus greater than three) beat the opposing lineup by an average of five points per 100 possessions.  The easiest way to understand this is to look at it graphically:

Let’s look at the home and away splits:

Overall, it appears that small forwards are the most important, followed by power forwards, centers, shooting guards, and point guards.  I’ve heard people suggest small forwards are crucial to a team’s success in the past.  Three of the remaining four teams in the playoffs last year featured a small forward as their main playmaker.  And as my study on the shooting abilities of small forwards showed, it’s best not to have a specialist at that position.  What you need is a player who can do it all because that position appears to be very important to your team being successful.

Things get especially interesting when you look at the home/road splits.  At home, small forwards still reign supreme.  However, the little guys essentially catch up to the big men in terms of importance.

On the road, though, it appears having a solid interior is crucial.  The importance of great guards is minimized greatly and centers and power forwards are well ahead of the rest of the pack.

Of course, there are a few potential concerns with this data, and I will explore two of them in this article.  First, as always, there’s the question of sample size.  Maybe point guards are just getting a bad rap because the sample size is too small and the ones that do qualify haven’t had that much success.  Let’s take a look at the frequencies of each position having a player with an Adjusted Plus-Minus greater than three among all lineups:

I would say the sample sizes are pretty big.  An observation I had was the relative lack of quality centers compared to other positions.  Perhaps the complaints about there being no good centers nowadays are valid.

A second concern might be the quality of players in each position among those that qualify.  In other words, if there are 20 point guards with an Adjusted Plus-Minus above three but they’re all at 3.01, it’s no surprise that they’ll look worse than the other positions.  To see if this is a problem, I calculated the average Adjusted Plus-Minus for each position among those that qualify:

Three of the positions (point guards, power forwards, and centers) are bunched together, one is clearly lower than the rest (small forwards), and one is clearly higher (shooting guards).  This evidence further supports the original conclusion I made that small forwards are the most important.  After all, we have the weakest group to choose from at that position yet they still have the most positive effect.  On the other hand, there are a lot of excellent shooting guards in the NBA, yet their impact is much less significant.  And still, I have yet to find an excuse for point guards.  They are often seen as the floor general and the player crucial to a team’s success, but remember who the two starting point guards in the Finals were (Derek Fisher and Rafer Alston).  Of course, there are still potentially hundreds of hidden variables that could have an explanation for why my data underrates them.

In a few days, I will follow up on this study by taking a look at the other side: bad players.  At which positions are bad players the most detrimental to a team’s success?  Not only will it be a unique compliment to this study, but it also may shed some light on why today’s results look like they do.  Stay tuned.

July 17, 2009 Posted by | Studies Using Lineup Data | Leave a comment

How the Shooting Abilities of Small Forwards Affect Offenses

The small forward position is one of the most critical positions in basketball.  In most cases, the other four positions have specific responsibilities that don’t change a whole lot from team to team.  However, the roles of small forwards are varied.  Some teams use them as scorers, others as ball-handlers, others as defenders, etc.  The goal of this study today is to determine the importance of three-point shooting ability in small forwards.

Using the lineup data at, I’ve split the lineups into three groups: those featuring a small forward who shoots 40% or better on threes, those featuring one who shoots 30% or less, and the remainder.  For each group, I’ve calculated the average Offensive Rating.  In addition, the lineups are split between those at home and those on the road.  The results are in the graph below:

27.01% of home lineups feature a small forward shooting better than 40% on threes, and 21.22% feature one shooting less than 30%.  On the road, those numbers are 26.56% and 21.62%, respectively.

The results are a bit surprising.  Least surprising is the fact that if your small forward is a liability from long range, your offense tends to suffer.  Clearly there is some benefit to being able to spread the floor.  What is surprising is the fact that lineups featuring a sharpshooter at the small forward position also tend to be worse (although only slightly).  Perhaps this reflects the fact that three-point specialists are often limited in other areas.

It appears the solution is to have a small forward who shoots somewhere between 30% and 40%.   Again, this isn’t because missing shots is in some way beneficial.  It’s most likely because the best shooters are the most likely to have the biggest weaknesses in other areas.

I don’t want to generalize too much, though, and there could be a number of hidden explanations for this.  For now, I’ll present the data and let you draw your own conclusions.

July 10, 2009 Posted by | Studies Using Lineup Data | Leave a comment

How the Shooting Abilities of Point Guards Affect Offenses

Although they all generally have the same duty (run the offense!), different point guards in the NBA possess a variety of skills.  Whether they are big or small, quick or fast, or aggressive or passive, they come in all shapes and sizes.  As it turns out, some of the game’s best shooters run the point.  Is the ability to shoot three-pointers well a key skill for point guards?  Today I’ll take a look.

Using the lineup data at, I’ve split the lineups into three groups: those featuring a point guard who shoots 40% or better on threes, those featuring one who shoots 30% or less, and the remainder.  For each group, I’ve calculated the average Offensive Rating.  In addition, the lineups are split between those at home and those on the road.  The results are in the graph below:

25.6% of home lineups feature a point guard shooting better than 40% on threes, and 30.05% feature one shooting less than 30%.  On the road, those numbers are 25.62% and 30.32%, respectively.

It appears as though the ability of your team’s point guard to shoot the three well is very important.  Overall, the difference is more than four points per 100 possessions.  Similarly, if your point guard struggles with his outside shot, your offense will struggle.

Beyond that, I don’t want to say too much.  It’s too easy to make bold statements without considering some of the underlying factors, so I’ll just present the data as is.  Feel free to draw your own conclusions, though.

July 9, 2009 Posted by | Studies Using Lineup Data | Leave a comment

Developing a Measure for Evaluating Coaches, Part I: Impact on Effort

Is there a method for rating head coaches in the NBA?  Perhaps just as important, should we even bother?  Some have said that coaches are all essentially equal, while others refute those claims.   Today will be the start of my first attempt at evaluating head coaches using statistics.

The rating system will assume coaches can have an impact on a team’s success in three ways: improving offense, improving defense, and increasing the effort level of players (As a side note: there are obviously many more than three ways a coach can impact a team, but these three appear to be the broadest and easiest to quantify).  In actuality, increased effort would be evident in offensive and defensive performance, but I have decided to separate it into its own category.  I have done this because out of the three categories, effort level may be the one that is the easiest to attribute to coaching, as opposed to the talent of the players.

Effort and hustle are extremely important for an NBA team, and perhaps they’ve become underrated.  While talent is necessary to be successful, it is quite easy to notice the difference in effort levels between dominant and terrible teams.  Part of this comes from the innate personalities of various players.  Some just make their living by working harder than their opponent.  But coaches can also have an impact, and today I will reveal which coaches appear to do the best job.

To come up with a rating, I will use three statistics.  The first is the sum of a team’s offensive and defensive rebounding percentages.  Rebounding is the result of effort as much as anything.  The second is the amount of offensive fouls a team draws.  Not every player will stand in the paint and take a charge.  The third stat is fouls committed during loose balls.  While committing fouls is never a good thing, it makes sense that teams that hustle more and go for more loose balls will inevitably commit more fouls in the process.  I have examined the data and the teams that are generally considered to play with the most effort do in fact commit more loose ball fouls on average.  Offensive fouls drawn and loose ball fouls are then adjusted for pace.

Once I have the three statistics, I calculate a team’s z-score in each category.  I combine the three z-scores and multiply by 10 to come up with a team’s effort rating.  As a result, an effort rating of 0 is average and scores generally range from -50 to 50.

Rebounding percentages and coaching information were obtained from  Offensive fouls drawn and loose ball fouls were obtained from  Because 82games’ data only goes back to 2002-03, that is as far back as my data goes.  For those that qualify, I’ve also included each coach’s rank among those with at least 3 seasons of data (31 qualified).  For teams that had multiple coaches in one season, I went with the coach that was in charge the most games.  To see the final numbers, go to:

There are a couple of things to keep in mind when looking at the data.  Like any simple study, it has some limitations.  Teams with good height are more likely to be good rebounding teams, regardless of how much effort they give.  Also, the data size of just seven seasons is relatively small.  That means that coaches who lasted just one or two seasons could have effort ratings that are greatly overrated or underrated.  It also means that coaches (such as Pat Riley) that got stuck on a few bad teams during the sample period will not look too great.  And finally, don’t forget that in the end, it’s the players who actually produce on the court.

The next steps are to estimate coaches’ impacts on offense and defense.  That will be coming in the future.

June 27, 2009 Posted by | Coaching Studies | Leave a comment

Player Projection: B.J. Mullens

Mullens has a lot of physical gifts.  He’s large enough to be a legitimate center in the NBA.  To go along with this size, he has solid athleticism and quickness.  This allows him to be a great finisher at the rim.  Unfortunately, Mullens never really put it together at Ohio State.  His production was inconsistent, to put it nicely.  Had he been able to come straight out of high school, he may have been a top five pick.  After one disappointing year in college, he’s just hoping to be taken in the first round.

How does BSPS think Mullens will do in the NBA?  Let’s take a look at his projected career averages per 36 minutes:

If nothing else, Mullens will be a pretty decent rebounder because he’s big and athletic.  However, his offensive game is so raw that he won’t be much of a scorer.  In fact, he’ll likely get less easy finishes in the NBA because of smarter defenders.  Besides the rebounds, there is very little to praise in that box score.

This is to be expected, though.  Mullens had a poor season and I doubt anyone would state otherwise.  However, he was just a freshman, and whichever team takes him knows they’ll be selecting a risky project.  I started this article by saying that Mullens has a number of physical gifts.  Those are real.  The question is whether or not he turns those gifts into actual production in the NBA.  Based on a small sample size, BSPS doesn’t think he will.

June 2, 2009 Posted by | Player Projections | Leave a comment

Player Projection: Austin Daye

Today I will be projecting the NBA stats of Austin Daye of the Gonzaga Bulldogs using my Box Score Prediction System.  Daye has not hired an agent as of May 30 so he still retains the right to withdraw from the draft.  If he chooses to stay, he will probably be selected some time in the first round.

Daye is a unique prospect because of the wide range of skills he possesses despite measuring in at 6’10.  He’s got a great shot from the outside but also possesses the athleticism to drive the ball to the basket.  In addition, he’s a good ball-handler for his size.  Finally, he’s a solid rebounder and shot blocker.

Despite his shot-blocking skills, scouts have questioned Daye’s defense.  Defense is half of the game, after all, so that is an area he must work on.  However, that might not even be his biggest weakness at this point.  Daye has a very wiry frame and if he doesn’t bulk up considerably he will not be able to bang down low with the strong big men of the NBA.

How does BSPS think Daye will do in the NBA?  Let’s take a look at his projected career averages per 36 minutes:

The box score above looks good but not great, but I think there’s some hidden positives.  Even though 15.41 points per 36 minutes isn’t a ton, BSPS thinks Daye will score in an efficient manner.  His good three-point shooting and knack for drawing fouls will boost his true shot percentage.  All Daye needs to do is become more aggressive and put those skills to good use.  If he can do that, he can be a fantastic scorer.

Being more aggressive would serve Daye well in a lot of other areas.  Based on his size and athleticism, he should be able to pull down more than 7.18 boards per 36 minutes.  It would also boost his assist and block numbers.  Daye must control this aggressiveness, though.  If that foul rate jumps any higher he won’t get enough minutes on the floor to make an impact.

Like many of the prospects in this year’s draft, Daye is far from a sure thing.  However, he has the size and skills to be a great player.  A simple change of his playing mentality might do the trick.

May 30, 2009 Posted by | Player Projections | Leave a comment

Finding the Achilles Heel of Each Remaining Playoff Team

As the number of teams still in contention for the 2009 NBA championship dwindles down, it’s important to note not only the strengths of each team but also the weaknesses.  All it takes is one major hole for another team to exploit and make you pay.  We’ve seen this happen countless times in the past.  So what is each remaining team’s biggest weakness?

Cleveland Cavaliers

Achilles heel: Depth

When you’re talking about a team as good as the Cavs, it’s really hard to find any weaknesses.  They’re pretty much good at every statistical category.  If I could nitpick and find one flaw, it would have to be their bench depth.  With Anderson Varejao now starting, the only bench player they have with a PER over 14 is Joe Smith.  Varejao, Big Z, LeBron, Mo Williams, and Delonte West are all great.  After them, there is a bit of decline in terms of talent.  But I should repeat: this isn’t a huge problem.  It’s just the best I can do.

Boston Celtics

Achilles heel: Offensive turnovers

In the regular season, the Celtics were the second best defensive team in the league and a strong sixth on offense.  This balance allowed them to stay dominant despite Kevin Garnett’s injury.  However, there’s been one area they’ve struggled in mightily all year: offensive turnovers.  In fact, on a per-possession basis, Boston was the third worst team in the league at taking care of the ball.  Who are the biggest culprits? Kendrick Perkins, Stephon Marbury, Tony Allen, and Leon Powe, to name a few.

Orlando Magic

Achilles heels: Offensive rebounding and forcing turnovers

For a team as good as the Magic, it’s a surprise that they rank towards the bottom of the NBA in the two statistics I mentioned above.  I’m especially surprised that a team with Dwight Howard can be so poor (third worst in the league) at collecting offensive boards.  If you investigate closer, you can see why.  The Magic’s two centers, Howard and Marcin Gortat, do a pretty good job of crashing the boards.  But Orlando also starts Rashard Lewis at power forward, and he has an offensive rebound rate well below average for his position.

Atlanta Hawks

Achilles heel: Defensive rebounding

One of the great things about the Hawks is that they’re so versatile.  Despite playing without a true center, they generally have good size and athleticism.  Thanks to having Josh Smith at the power forward spot, they can run with the best of them.  Unfortunately, you can’t run unless you grab the rebound first, something the Hawks struggle at (although they did just fine against Miami).  In the regular season, Atlanta’s defensive rebound percentage was seventh worst in the NBA.

Los Angeles Lakers

Achilles heel: Point guards

Derek Fisher is a solid vet who generally makes smart plays, but in terms of production he’s been lacking.  His PER of 12.1 shows how in many games he is quite a non-factor.  Thankfully his solid defense often makes up for this weakness.  Behind him on the depth chart, it doesn’t get much better.  Jordan Farmar has had plenty of ups and downs with the Lakers, and this season certainly qualifies as a down.  His PER of 9.9 is very low for a rotation player on a championship contender.  He shoots inefficiently and turns the ball over too much.  The Lakers must be careful: the Rockets have two good point guards in Aaron Brooks and Kyle Lowry.  Brooks has already shown what he can do.  It’s no surprise the Lakers have started to resort to Shannon Brown and Sasha Vujacic.

Denver Nuggets

Achilles heel: Offensive turnovers

Like the Celtics, one potentially fatal flaw for the Nuggets is their inability to take care of the ball.  Denver’s turnover rate is sixth highest in the NBA.  It’s not a shocking statistic, considering the fast and sometimes wild pace they play at.  However, it is a bit surprising considering that their floor general is Chauncey Billups, a very steady player.  The Nuggets with the highest turnover rates include Anthony Carter, Chris Andersen, Nene, and Dahntay Jones.

Houston Rockets

Achilles heel: Forcing turnovers

As always, the Rockets are a stellar defensive squad.  Their defensive rating ranks fourth in the NBA and they have defensive studs such as Ron Artest and Shane Battier on their roster.  In terms of holding the opponent to a low field goal percentage, gathering rebounds, and not fouling, they are great.  However, along with this steadfast approach comes a conservative attitude.  Guys like Shane Battier won’t gamble for a steal; they’ll stay in front of their man and force a tough shot.  In a way, this weakness may end up being one of their greatest strengths.

Dallas Mavericks

Achilles heel: Drawing fouls and forcing turnovers

In the 2006 Finals, there was a great deal of talk about the free throw discrepancy between the Heat and the Mavericks.  It is indeed true that Dwyane Wade spent a ton of time at the foul line (although partly thanks to Dallas’s willingness to foul Shaquille O’Neal and put Miami in the foul bonus early).  However, it is also true that the Mavericks have never been a great team at earning free throw attempts.  Three years later, it’s still an issue.  Jason Terry, Josh Howard, and Jason Kidd, three guys who don’t make a living at the charity stripe, run much of their offense.  Even the main man, Dirk Nowitzki, doesn’t get fouled a ton.  It’s simply not Dallas’s style.

May 7, 2009 Posted by | Commentary | Leave a comment

Euroleague Now Included in the Box Score Prediction System

Recently I explored the correlation between Euroleague and NBA stats.  My next step has been to incorporate Euroleague stats into my Box Score Prediction System.

I used the same process with Euroleague as I did with the NCAA.  I developed a formula that projects each NBA stat using Euroleague data and other variables such as height, weight, and experience.  These formulas were developed using multiple linear regressions.  The adjusted R^2 ( values for the different NBA stats are as follows:

FGA: 0.2971

FG%: 0.3004

3PA: 0.6834

3P%: 0.7729

FTA: 0.4111

FT%: 0.6887

REB: 0.8609

AST: 0.7202

STL: 0.5606

BLK: 0.7964

TO: 0.4538

PF: 0.5432

In the next few weeks, I will include projections of European prospects to go along with my projections of college players.  I have slightly less confidence about the Euro projections because the data is more unreliable, but the projections will still be useful.

All Euroleague stats were obtained from  NBA stats were obtained from

April 9, 2009 Posted by | Box Score Prediction System | Leave a comment