Defensive Distribution Analysis

Analyzing the defensive side of the ball is a greater challenge due to the fact that fewer statistics are available with regards to defense.  Steals, blocks, rebounds and fouls do not tell the whole story of how a player contributes, whether it is on the ball or helping teammates.  A great on the ball defender doesn't always get steals to reflect his on ball defense and a great help defender doesn't always get blocks to reflect his help defense.  Until I can get my hands on better defensive data, this is my effort using the standard readily available defensive statistics.  


Measuring defensive efficiency, or defensive points per possession, using the standard deviations of various defensive statistics provided rather simple results.  Lineup data was used and standard deviation variables were created for personal fouls, steals, blocks, and defensive rebounds based on the percentage in each category that each of the five players in a lineup accounted for.  

Defensive efficiency was predicted using lineup per possession statistics in personal fouls, steals, and blocks as well as defensive rebounding %.  Each of these categories increased with a more even distribution or lower standard deviation.  As a result, for the positive statistics of rebounding percentage, steals and blocks, as the standard deviation decreased giving us a more even distribution, defensive points per possession also decreased, as much as 4, 9 and 1 point(s) per 100 possessions, respectively.  In the case of personal fouls, a negative statistic, the reverse was true; as the standard deviation of personal fouls increases, personal fouls per possession and defensive points per possession decrease.  

So what do these results mean and why do I refer to these results as simple?  They are simple because they essentially mean that we want everyone in a lineup playing defense.  We want everyone rebounding, everyone playing strong defense on the ball and getting steals, and everyone contesting shots and getting blocks. 

Obviously when players are getting steals and blocks successfully, they aren't fouling, and ideally, players are getting those steals and blocks efficiently without fouling, so why is a wider distribution of personal fouls beneficial for a defense?  Perhaps this means we want a player or two in a lineup getting fouls when a steal or a block isn't a realistic possibility.  These fouls are likely skewed towards players in the paint, lending itself to a higher standard deviation, where fouling is preferred to allowing easy buckets on dunks and layups.

2011 NBA Finals - Series Recap

• As I predicted with confidence before the Finals, the Dallas Mavericks won this series with their superior team game and shooting ability.  Although I was wrong about their team game having the advantage in Game 1, where Miami's defense proved to have the advantage before Dallas adjusted, Dallas successfully adjusted and got better with each game in getting good looks with greater frequency as they had become accustomed to throughout the postseason and Miami's defense failed to readjust.  This was particularly apparent in the last two games where Dallas' offense was extremely efficient.  Whereas James was able to single-handedly slow down Chicago's offense by blanketing Rose, he was not able to do so against a Dallas team that played better team basketball than anyone else in the playoffs.  
• This series was a win for team basketball, where the whole is greater than the sum of the parts.  Dallas players consistently made each other better and got each other good looks.  Catching and shooting an open jumper is always better than getting a jump shot off the dribble through isolation and Dallas clearly valued this idea.  Dallas, when they weren't shooting good catch and shoot looks, focused on a few very specific things that played to the greatest strengths of the players doing those things, including isolation in the high post for Dirk with the threat of either taking outside shots or attacking the rim, some plays in the post for Marion, a few shots for Terry on pull-up mid-range jumpers off a couple hard dribbles, and Barea attacking the rim.  These are things all four of those players do very well and Dallas was disciplined in staying with those strengths, and getting shots for each other, particularly through the threats of Dirk, Terry and Barea.  
• When James signed with Miami, he expected multiple championships, starting right away, thinking that since he was so close to a title with Cleveland, that adding Wade and Bosh guaranteed that.  He made the mistake of thinking that the whole is equal to the sum of the parts and they relied on their individual talent more than they focused on bettering each other with team play.  They got close with their talent and athleticism mostly through their defense, but their half court offense left lacking.  Miami certainly shared and moved the ball well at times, but they failed to do so with anywhere near the discipline and consistency Dallas did, and often fell back on isolation plays and contested shots.  Clearly, they have a little more work to do, specifically as it relates to teamwork. 
• The changes that were keys to Dallas winning the series:
• Carlisle's decision to start J.J. Barea and get him even more opportunities to attack the basket, correctly expecting him to convert on the attempts he was failing to convert on early in the series.  This not only allowed Stevenson's defense to come off the bench, preventing their defense from being top heavy with Chandler, Marion and Kidd already starting, but it also opened up things for Jason Terry, who handled the ball more and attacked the rim with more time with Barea off the floor, rather than just trying to catch and shoot over James.  
• Terry's adjustment after starting this series slow was another key.  His veteran leadership and ability to take some pressure off Dirk offensively was invaluable to Dallas.  He really found his rhythm in the last two games, shooting 19 for 28, where he and Dallas were at their best offensively.  Playing less with Barea, who is most effective with the ball in his hands, also enabled this adjustment by Terry. 
• Carlisle's decision to replace an ineffective Peja Stojakovic in the rotation with the hard-nosed Brian Cardinal was very important as well.  Stojakovic had great success in the Western Conference Playoffs, particularly against the Lakers and Trail Blazers, but against the athletic Thunder and particularly the bigger, stronger, faster Miami Heat, he struggled.  Cardinal stepped up, hit a couple shots from beyond the arc, made good passes, and generally played disciplined team offense and most importantly, played great, hard defense.  
• As for the four Dallas players that started every game in the NBA Finals: 
• Dirk was Dirk. He hit open shots, got to the line and also made some tough shots for most of the series.  His ability to play in the high post, something he wasn't nearly as effective doing a few years ago, also allowed him to create good opportunities for his teammates.  He keyed the Dallas comeback in Game 2 that reversed the momentum Miami had in the series, when every half court possession went through Dirk and they scored on 11 of their last 12 possessions.  
• Jason Kidd made his presence felt most on the defensive end in addition to hitting some timely threes throughout the Finals. After some early problems with turnovers and moving the ball, he settled down, made the right passes and helped facilitate the offense as he always has.  His effort on the defensive end truly showed how much he wanted this title after 17 years in the league. 
• Shawn Marion was a rock throughout this series.  He played great defense, guarding both James and Wade, and played great offense in the paint.  He finished inside, played within himself offensively, and got his hands on a lot of loose balls on both ends of the floor.  He redefined himself, and even though his numbers in Phoenix were better due to being inflated by his role in a high-paced Phoenix offense with Nash, he played the best team basketball of his life in these playoffs and was an indispensable piece of the team basketball Dallas plays. 
• Tyson Chandler filled the role of defensive leader with his energy and length.  Offensively, he filled the role of getting his hands on rebounds, earning himself and his team offensive boards and second chances, and he finished around the basket when called upon to do so.  
• These key changes and the way Dallas plays disciplined team basketball show that Rick Carlisle is without a doubt one of the best basketball minds and coaches in the league. Credit to Cuban for bringing in Carlisle (and also for their forward thinking in making 82games.com founder Roland Beech a part of the coaching staff). 
• Eric Spoelstra lost the coaching battle in this series, but he lost it to an amazing coach, and as a result is probably getting more flack than he deserves.  Although he hesitated in taking Bibby out of the lineup, Chalmers was consistently getting more minutes, and he may have simply been playing Bibby more with Anthony and Chalmers more with Haslem, clearly feeling that they were most effective in those combinations rather than necessarily feeling  that Bibby was better and should start.  He certainly says all the right things in interviews and in what we see from the looks into the locker room and huddle, and shows his knowledge of the game, but if I can only have one criticism, I fear he is not assertive enough with James and Wade, who often seem like they feel they can do no wrong.  James in particular continued to make some of the same mistakes throughout the series, and though most of this falls on James himself, Spoelstra needed to be assertive and hard on James to help correct some of his poor play and decision-making.  James has enough yes men and Spoelstra shouldn't be another one.  Some of his talk after the Finals was focused on how the media is unfair to James.  Though that may be true, that is not what James needs to hear to become a better player.  He doesn't need more excuses and certainly not from his coach.    Spoelstra is certainly a very capable coach and he, like the players, will only grow from this experience, and I hope Miami keeps him on and doesn't disrupt the chemistry the team has between the coaching staff and players that got them to the Finals in their first year together.  Firing Spoelstra would be a very short-sighted decision.  
• For the Miami Heat players, James, Wade, Bosh and Chalmers were the key contributors.  In reverse order: 
• Chalmers proved to be the only capable point guard for Miami and separated himself from Bibby.  This was apparent early in the series, and Eric Spoelstra took a few games too long to make the change from Bibby to Chalmers.  In fact, it appears from the rotation in Game 6, that he made this change not solely because Chalmers was outplaying Bibby, but because House gave him confidence with his play in Game 5 that he could count on him off the bench, and eliminated Bibby from the rotation entirely.  
• Chris Bosh started slowly in this series, but turned it around after hitting the game winner in Game 3.  His play in Game 6 and his reaction after losing showed he wanted it more than anyone else on the team.  Unfortunately, he didn't do enough to make it happen.  He didn't call for the ball in the post enough, and he didn't get in the ears of James and Wade to get them to look for him more as he was hitting everything in Game 6.  
• Dwyane Wade was the best Miami player offensively throughout this series.  He was also very strong defensively.  With the exception of Game 6, he was great in every game, including the minutes he played in Game 5 when he suffered a hip injury.  He was able to get to the rim better than James, and showed greater skill and feel for the game in creating opportunities for himself, which is why he was the focus in the 4th quarters of this series.  Wade could have done a better job scoring on mid-range jump shots as he has for so long, but with all the attention on James' 4th quarter disappearing acts, he probably didn't dominate the ball in the half-court as much as he maybe should have and didn't look for that mid-range shot with anywhere near the frequency he has in the past.  
• Finally, LeBron James was disappointing offensively throughout most of the Finals.  It was well documented that he completely disappeared in the 4th quarters of the series.  He not only didn't take control of the ball, but he stood around and watched and did nothing to make his teammates better in crunch time.  He stood idly by and completely failed his team offensively.  When his shot wasn't falling and he wasn't getting anything outside of easy transition opportunities, he forgot that he could create for his teammates.  Credit Dallas' team defense and Marion in particular for stifling James, who was never able to consistently create opportunities for himself and his teammates.  James also has to work on improving his offense without the ball.  With his physical skills, there is no excuse for him not to be great in just about every aspect of the game, including his offensive play without the ball.  
• An extra note about LeBron James.  He certainly isn't a sympathetic figure, not only due to "The Decision," the manner in which he left Cleveland, and his statements before the season ("not five, not six, not seven..."), but his actions and statements after losing this series and some in the past.  A little humility would go a long way for him not only in that regard, but also in allowing him to realize what he needs to do to become a better player.  As a basketball enthusiast, I hope and expect him to hold himself accountable for this failure and be motivated by it to put in the focused hard work in the off-season necessary for him to come back as a much improved player, within the team concept and individually.
• It is only appropriate to finish this post with a congratulatory note to the Dallas Mavericks, Mark Cuban, Rick Carlisle and the Dallas coaching staff, Dirk Nowitzki, Jason Terry, Jason Kidd, Shawn Marion, Tyson Chandler, J.J. Barea, and the rest of the Dallas Mavericks players and organization on a job well done and winning the 2011 NBA title by playing the game the right way on both ends of the floor; as a team, by making each other better, resulting in a whole that is even greater than the sum of its very good parts. 

Observations from Game 6

• Just as they had in the last few games, the Dallas offense showed that they had figured out how to get good looks against Miami's athletic and active defense after starting slow through nearly two full games.  With good looks coming often, Dallas converted them (with the exception of Nowitzki in the first half, who uncharacteristically couldn't find the bucket), whereas in the first two games, where the good looks were at such a premium, the added pressure of hitting when the opportunities were there resulted in some uncharacteristic misses.  
• On the other end of the floor, Dallas continued to focus on trying to keep Dwyane Wade and LeBron James out of the paint, something that cannot be done completely, but Dallas did a good job limiting it as much as possible particularly in the 2nd half.  In limiting Miami's looks in the paint, and staying disciplined on offense, Dallas made this game about hitting jumps shots on open looks, playing significantly in their favor.  Credit their team defense and Carlisle for utilizing the zone effectively.  Dallas again limited their turnovers offensively, allowing them to limit Miami's transition offense defensively.  
• Apart from a 3 minute stretch in the 2nd quarter when Miami went on a 14-0 run, they simply did not match Dallas' consistent effort and discipline on every possession, leading Dallas to generally get better shots than Miami.  Dallas led almost the entire second half after Miami's 5-2 run to start the half and take a one point lead with about 11 minutes left in the 3rd quarter.   
• Neither team could hit their free throws, both shooting around 60%.  It was likely just the result of randomness, but perhaps it was the pressure of playing in an elimination game in the NBA Finals.       
• Individually, first, Brian Cardinal deserves his just due, as does Carlisle for recognizing Stojakovic's ineffectiveness and replacing him in the rotation with Cardinal, who not only hit the open three when he was asked to do so, but, more importantly, was active and effective on defense.  Despite only taking three three-point field goals in the series, and making one in each of the last two games, he was still a threat, succeeding in spreading the floor just as Stojakovic does, but was a completely different player than Stojakovic defensively, particularly in his help defense in getting in the way of the strong and athletic James and Wade.  Though his personal numbers don't show it, there is a reason why he led the team in +/-, matching Shawn Marion with +18 in just 12 minutes of play.  Team basketball won this championship, and Cardinal is a great example of the team concept and played his role and within himself perfectly.  
• The keys to Dallas' victory tonight, as well as in Game 5, were J.J. Barea and Jason Terry.  Barea's success in getting in the paint throughout the series finally resulted in some made baskets as he had done the rest of the postseason prior to the first few games in the Finals.  More credit to Carlisle and the Dallas coaching staff for putting Barea in the starting lineup and bringing Stevenson's defense off the bench, contributing to three straight victories for Dallas.  Barea struggled making shots early in the series, but the Dallas coaching staff recognized his success in getting in the paint and they increased his opportunities, where made baskets were sure to follow.  Jason Terry was just phenomenal.  He stepped up and knocked down shot after shot while getting himself good looks.  After being slowed by James early in the series, he did not back off and played more aggressively, driving towards the rim on the catch without a moment's hesitation, which in turn opened up some opportunities for him outside.  His reaction to adversity early in the series showed his veteran leadership. 
• Although Nowitzki couldn't find the basket in the first half, Dallas did a good job keeping him involved in the 2nd half, and helping him find his rhythm with a shot and make on their first possession of the half.  His shots down the stretch helped seal the victory.  
• Jason Kidd hit a couple big 3s when called upon to do so, but more importantly,  just as he did all series, contributed nothing but positive things on the defensive end and was a key piece to slowing down Miami's offense.  What he can still do defensively at 38 years old against some of the best athletes in the game is just amazing.  His hands are as good as anyone's and he is one of the smartest players around on both ends of the floor.  
• Shawn Marion, similarly, played great defense again and was effective in his role offensively.  Marion redefined himself in Dallas as a player who strictly scores around the basket, taking advantage of his athleticism and ability to get up quickly.  Long gone are the days where he shoots the three.  The great team player he is, he has left that to the many capable players on Dallas and added value by focusing on what he does best on the team with his activity in the paint.  
• Tyson Chandler, limited by foul trouble, was still efficient offensively, and as has been his focus throughout the series, rebounded well, got his hands on a lot of balls, and disrupted Miami with his length. 
• DeShawn Stevenson hit some big 3s in the first half, providing Dallas a cushion that they would need with the run Miami went on in the 2nd quarter.  Though I am not a fan of jawing and tough guy behavior generally, his scuffle with Udonis Haslem and Mario Chalmers completely stopped Miami's momentum in the 2nd quarter and gave Dallas time to regroup.  Credit him for not fading in response to Miami's big run.  
• Ian Mahinmi also stepped up and contributed off the bench, getting a couple offensive rebounds, working hard on defense and making a couple shots including a big one at the end of the 3rd to add to Dallas' momentum and another early in the 2nd quarter where he looked like Nowitzki on a step back one-footed fadeaway at the end of the shot clock.
• For Miami, James played a good offensive game and finally hit some outside shots, though he focused on his strength of scoring while going towards the basket and in the paint.  He can maybe be faulted for still not taking enough shots and not being even more aggressive, but credit Dallas' defense for limiting his looks in the paint.  James was disciplined in focusing on getting his looks inside, and until the very end of the game when he took two three-pointers, every shot he took after the first quarter was in the paint, but for one (a made shot from the free throw line).  The main problem was that he didn't get more of those looks.  It also is worth noting that while Wade, Bosh and Chalmers each had a positive +/-, James was the worst on the team in that regard with astounding -24. 
• Wade regressed in this game offensively, taking about half his attempts from outside and missing all but one of those, while making most of the shots he took inside.  Credit Dallas' defense for limiting Wade as much as they could from getting into the paint.  Wade did a good job getting his teammates involved in the 1st half, where he had all six of his assists.  However, in the 2nd half, given his success inside and difficulty from the outside, Wade failed to use the threat of his drive to create good shots for his teammates and did not have a single assist.
• Chris Bosh continued his good shooting over the last few games of this series, fueled by the game winning shot in Game 3.  He was shooting extremely well, inside and out, and Wade and James should have looked to create for him more with their outside shots not falling.   
• Chalmers played another good game, creating for his teammates and playing solid defense.  He also was fairly effective shooting the ball, although he struggled from beyond the arc, only making one of six before making an inconsequential three with 16 seconds remaining.
• Off the bench, Udonis Haslem and Eddie House were effective, with House making his entire contribution in the first half and book-ending Miami's 2nd quarter run with a pair of threes, and Haslem working hard on defense and the boards.  
• Ultimately, Miami failed in Game 6 where Dallas succeeded in Game 2.  In Game 2, when Dallas had their backs to the wall and down 15 in the 4th quarter, they focused, played disciplined offense and got good shots while playing disciplined defense and forced Miami to shoot from outside, to which they kindly obliged.  Miami buckled in big moments when down in the 4th quarter.  One particular sequence of possessions for Miami stood out with under 9 minutes remaining and the score 87-77: Wade dribbled the ball off his foot on one possession, on the next, James drove and took a good shot on a short jumper off the glass, but missed terribly under the pressure rather than attack the rim and try to get a layup or get to the line, and then Wade took a bad three after Barea had put Dallas up by 12.  Also, after Bosh cut the lead to seven with a three-point play, Chalmers got a steal with about seven minutes left and rather than pull the ball out and get a disciplined good shot, he forced the issue and tried to attack against Kidd with Chandler helping, missing a significant opportunity to cut the lead to four or five and add to their momentum with plenty of time remaining
• Miami's big two just did not step up to the moment after falling behind by near double digits late in the 3rd and in the 4th quarter, and they wilted under the pressure with 11 costly turnovers and some bad misses late between them.  They will hopefully grow and learn from this adversity and improve as a team on the whole and under pressure going forward, but as of now, the better team, the Dallas Mavericks are the reigning NBA Champions.  

Observations from Game 5

• As much as Game 4 was about defense, Game 5 was about offense.  Both teams did a great job of getting good looks on a high percentage of their possessions and converted on those opportunities. 
• Dallas has gotten more and more comfortable and gotten a higher percentage of good shots with each game, with Game 5 being their best offensive game yet.  However, defensively, they allowed Miami to create many easy opportunities which allowed them to shoot 53% from the field overall despite shooting under 40% on jump shots. 
• J.J. Barea and Jason Terry were the keys for Dallas in this game, as both stepped up, played aggressively and made big shots, including the good shots they've been making all postseason along with some tough contested shots.  Both attacked the basket, taking some pressure off their outside shooting, which benefited as a result.  Barea also created a number of easy shots for Nowitzki.  
• As noted above, Miami did a great job creating many easy opportunities, only a few of which were in transition.  However, with the exception of Mario Chalmers and Mike Miller, they shot very poorly from outside, highlighting the importance for them to get easy opportunities inside the paint.  Excluding Chalmers and Miller who went 7 for 11 from outside, the rest of the team shot around 30% on jump shots. 
• LeBron James was more active this game, but again disappeared in the 4th quarter.  His activity before the 4th quarter was certainly in part a product of Dwyane Wade's injury and absence during the 2nd and 3rd quarters.  Like the rest of his team, he was much more successful going to the rim and shot poorly from outside.  He must be looking forward to returning home, where he has had more success with his shot. 
• Chalmers had another solid game and came out with a great first half, but did not take a single field goal attempt in the second half.  He continues to outplay Mike Bibby on both ends of he floor.  I have been wondering how long it would take Spoelstra to start Chalmers, and he is finally doing so tonight in Game 6 with Miami facing elimination. 

Observations from Game 4

• This game was all about defense.  Dallas' defense was particularly impressive as far as making Miami work for shots just as Miami has done to them all series.  
• However, defensively, Dallas struggled early rebounding the ball, allowing Miami to get some easy buckets off 9 first quarter offensive rebounds, allowing them to keep the game close early on with 8 of their 21 first quarter points on second chances.  
• Also keeping the game close was Dallas failing to convert numerous open looks.  Specifically:
• Nowitzki missed a few open looks in the first half after starting 3 for 3, a few shots around the basket and a few more open jumpers in the 2nd half, including an open 3-point attempt to end the 3rd quarter and another open look from beyond the 3-point line after an offensive rebound with just over three minutes left in the 4th quarter.  He even missed his first free throw of the NBA Finals.  Although his shot wasn't falling, Nowitzki did a great job getting to the line and attacking the rim late, getting two key layups. 
• Jason Terry, had a better game due to being more aggressive and attacking the basket, something Dallas desperately needed him to do, but he also missed a number of open looks, particularly late in the game.  He missed a mid-range shot just past the free throw line with nobody near him with under three minutes left and an open 3-point attempt with less than a minute left on a pass from Dirk that could have made the win much easier.  
• J.J. Barea, starting in place of Stevenson, was again successful in getting penetration, but again failed in putting the ball in the basket consistently.  He missed a couple easy layups in the first half.  Dallas seems to want him on the court with Kidd early to give the team a penetrating threat in the hopes of getting some ball movement when they can't find success doing so with Dirk in the high post or off the pick and roll.  With Barea on the court less with Terry as a result, Terry was forced to be more aggressive driving the ball, where he had some success.  
• Stevenson provided a spark off the bench, not only by being the only Maverick to hit his three-point attempts consistently (although he short-armed a wide open look from the corner with a minute and a half left in the game), but by providing some defense off the bench.  With some of Dallas' best defensive players in Chandler, Marion and Kidd starting, starting Barea over Stevenson was particularly successful defensively as it gave Dallas some defense coming off the bench. 
• Overall Dallas shot just 4 for 18 from beyond the arc, and this is not a team that takes many bad three-point attempts, so they are simply not knocking them down.
• Although Miami won the battle on the offensive glass, Tyson Chandler again stepped up on the offensive glass after being shut out in that regard in Game 1.  With Dallas missing so many open looks, his ability to get his team second shots was critical. 
• Kidd was again tentative offensively, missing both of his open looks, both from three, and leading the team with four turnovers, but continues to make plays on defense, including a good hard foul preventing an easy basket by Wade to tie it at 82, leading to a missed FT.
• Marion returned to the level of efficiency that eluded him in Game 3, and was a steadying presence offensively, scoring 16 in just 26 minutes, many in isolation when Dallas needed him to make those plays most.    
• For Miami, Wade stepped up again and making big plays on both ends of the floor as he has done all series.  Not enough can be said about Wade's play in this series, so I will just leave it at the fact that he has clearly been the best player in the series thus far.  
• With Dallas missing shots, what allowed them to stay close enough to make a run was James' passive play offensively, where on his limited attempts he mostly settled for contested jump shots over attacking the basket.  Credit Dallas' defense, but James can certainly make a more concerted effort to get to the rim.  This hurt Miami offensively more than anything tonight. 
• Bosh stepped up tonight, clearly more confident after making the game winning shot in Game 3.  He attacked the basket and made some easy shots inside, got to the line, and even made half his shots outside the paint.  He did however fumble a pass on a key play that resulted in a Dallas transition layup to take the lead in the 4th quarter.  
• Chalmers has shown he is clearly the better player between he and Bibby and tonight was another example.  Despite only shooting 1 for 5, he created good shots for his teammates and was effective defensively as well.    
• Despite falling behind by 9 points in the 4th quarter, Dallas was the more successful team as far as getting good looks at the basket.  However, it was their defense this game that gave them room for error on their failure to convert open looks offensively. Game 5 is a must win for Dallas and they will need to bring the same intensity defensively and convert on those same open looks they failed to convert tonight to ensure that they don't go back to Miami needing to win 2 games.

Observations from Game 3

• Miami's active and athletic defense is still making it difficult for Dallas to get open looks anywhere near the consistency that they did in the Western Conference Playoffs.  It isn't news that James in particular is making things very difficult for Terry.  Dallas is scoring field goals almost exclusively from the outside as Miami is ferociously contesting everything at the rim.  Nothing is coming easy for Dallas, particularly when they go away from Nowitzki.  
• Although Nowitzki scored 34 points, in my opinion Dallas did not use him enough, particularly before the 4th quarter, to start the offense, force help, and get ball movement to get his teammates open shots.  The talk after the game was that Nowitzki needs help, but the best way Dallas can get shots for the rest of their players is still through Nowitzki, whether he starts with the ball in the high post or gets it through the pick and roll.  He provides the only real advantage offensively for Dallas that requires Miami to help, allowing others to get free.  
• Haslem made it very difficult to get Nowitzki the ball, particularly in the 4th quarter, fronting him effectively and denying the ball. 
• Barea is still able to get penetration, but unless he starts to finish at the rim, he won't be a big enough threat to get his teammates open.  Stojakovic in particular needs the chaos that Barea is capable of creating in order to get the open shots he hit so consistently in the Western Conference Playoffs.  
• The lack of ball movement is also hurting Terry, who hasn't had many catch and shoot opportunities and is having to take more shots off the dribble in an effort to create shots for himself.  
• Offensively, Miami did a phenomenal job attacking the rim.  But for a few three-point attempts by Bibby, a made open baseline jumper by Haslem, a missed contested baseline jumper by Wade, and the last second made heave by Chalmers, every shot by Miami in the 1st quarter was made towards the rim or in the paint.  After going away from that strength during Dallas' comeback in Game 2, Miami clearly came out with a purpose at the start of this game of taking shots at the rim. 
• Wade was particularly aggressive, getting to the rim at will, especially in the 1st quarter.  One play, of many, by Wade that stood out was in the 2nd quarter.  Unlike in the the 4th quarter of Game 2, when Dallas went on a run (9-0 in this game), Miami got Wade the ball, who attacked the rim for a layup to stop the bleeding.  This showed focus on their part that they lost at the end of Game 2. 
• It was obvious from the beginning that to stop Wade, Dallas was going to have to play better team D and not leave whomever was guarding him on an island.  Though Kidd stepped up individually as a defender, it took a team effort to slow him down, which Dallas did a better job of in the 2nd half.  With both Wade and James able to attack the rim so well, there is only so much Dallas can do to help.  
• Chandler came up big with 7 offensive boards and made a number of aggressive defensive plays in the paint as well.  With Haywood injured, Dallas will need more of this from him. 
• For the first time in the series, Marion did not step up and have a solid game.  This probably made the difference in the game, along with Haslem's ball denial in defending Nowitzki, though Mavericks fans will certainly point to the missed call on Chalmers' first quarter heave at the buzzer.  He missed some easy shots and wasn't as effective on the boards as he has been thus far.  I expect him to step up in Game 4.  
• Stojakovic came in and Dallas ran a play for him in an effort to get him going and he made an open shot off a screen from the baseline.  However, despite his best efforts on both ends of the floor, he is still proving to be a liability defensively while still having trouble finding good shots.  During his 6 minutes on the floor, Dallas scored 11 points fewer than Miami. Unless Dallas can get him open shots with consistency, he will continue to see very limited minutes. 
• As suspected, this series is coming down to Miami's defense against Dallas' offense, and so far, despite close games probably decided by randomness more than anything, Miami's defense is winning that battle as Dallas is having to work extremely hard for every point, while Miami is finding easy opportunities at the rim.  The fact that these games have been close is a testament to Dallas' superior jump shooting ability.  

The Comeback through Dirk

• After avoiding Dirk during stretches, Dallas' possessions were dominated by Dirk in their comeback during the last 7 minutes of the game after falling behind 88 - 73.  Possession by possession:

• 1 - Dirk got the ball, attacked, was fouled in the act of shooting, but wasn't given shots.  After the call, they went through Dirk again and he got Marion a good opportunity on a layup, which me missed. 
• 2 - Dirk got the ball from Kidd, attacked, and found Terry for an open made jumper.  
• 3 - Transition layup by Terry off a missed 3 by Miami. 
• 4 - Terry earned a trip to the line, making both, after receiving a pass from Marion who got the ball in transition.  
• 5 - Offense went through Dirk again, who attacked, found Marion, who immediately used the space created for him from the help on Dirk, attacked the rim and made an easy shot.  
• 6 - After an initial penetration by Terry, Kidd found Dirk, who attacked again, drew Bosh, which led to James sagging, and found Kidd for a wide open 3. 
• 7 - Dirk received the ball in the high post, was doubled, made the easy pass to Kidd, who made the easy pass to Terry who took two dribbles past Chalmers and made a mid-range jumper.  
• 8 - Dirk sets a high screen for Terry, Bosh stepped out, Dirk released towards the baseline, Terry found him and Dirk made the relatively open but still contested mid-range jumper he's made all postseason.
• 9 - Dirk gets the ball outside the three-point line with just 8 seconds left on the shot clock, rushes a contested shot, which is blocked, followed by a desperate missed shot by Kidd.  This was one of only two empty possessions in the last 7 minutes of the game for Dallas.   
• 10 - Transition layup by Dirk to tie the game after a possession where Miami took two contested three-point shots and Dallas fortunately came up with the ball after Haslem was stripped after a 2nd offensive rebound on the possession and tried to save the ball as he fell out of bounds. 
• 11 - Terry starts with the ball, gets the ball to Dirk, who hits an open 3 thanks to a screen from Tyson Chandler. 
• 12 - Dirk got the ball in isolation and scores the winning layup after being overplayed by Bosh, who was certainly worried about the pull-up mid-range jumper. 

• Aside from two plays by Terry in transition or immediately following initial transition, every possession went through or ended with Dirk.  In the two possessions that Dallas failed to score on, in one, Marion missed a good layup opportunity created by Dirk, and in the other Dirk did not receive the ball until 8 seconds were remaining on the shot clock (though my feed went black until there were 15 seconds left and it didn't appear that Dirk had touched the ball, so I can't be sure).  Point is, Dallas is most successful when the offense runs through Dirk, and as long as they take care of the ball and move it effectively when he is doubled, and hit the open shots that are created, they will play very efficient basketball.  Stretches where Dirk doesn't touch the ball, or poor passes are made after Dirk is doubled are when Miami had the most success creating turnovers and getting in transition. 

• During the same stretch to end the game, Miami missed 9 contested outside shots on 8 different possessions, James missed a layup on one and got to the line and made two free throws on another, on another Bosh turned it over and Chalmers made one open three-point shot to tie the game after Dallas had already taken the lead after a 20 - 2 run. 

Observations from Game 2

This was a tale of two games in one.  One comprised of Mavericks possessions where they continued to feel the pressure of Heat's athletic D, made rushed and difficult passes, took rushed shots, and turned the ball over, and Heat possessions where they scored easy transition buckets off turnovers with the superior foot speed of Wade and James and were efficient in the half-court game with Wade getting to the rim at will; and another game comprised of Mavericks possessions, many of which occurred during the last six minutes of the game, where they settled down, went methodically through Nowitzki, made easy passes and made open shots as a team, and Heat possessions where they were forced to play half-court offense after good Mavericks possessions, where they surprisingly went away from Wade attacking the rim, which he was extremely successful doing in the first half.  

For Dallas:

• Nowitzki was more aggressive when he got the ball, particularly early (despite still missing shots that he has been making this postseason ) and very late when he finally looked composed and confident when taking shots and made the shots his team needs him to make, while also creating for his teammates with the threat of his offense.  
• The Mavericks went away from him for much of the 3rd and early 4th, a surprising mistake that resulted in him not taking any more possessions on shots and free throws than he did in Game 1, before force feeding him the ball when they most needed him leading to the 17 point turnaround in the last 7 minutes of the game.  They also started the 3rd quarter especially slow, and didn't go to him until after Carlisle called a timeout, before mostly going away from him again until the final run.  More on this later. 
• The Mavericks turned the ball over 18 times and were particularly sloppy during some stretches.  Credit the Miami defense for this, but Dallas composed themselves late in the game, didn't allow Miami's pressure to rush them into bad passes, and they didn't turn the ball over at all in the last 7 minutes.  
• Dallas won the battle of the boards.  On the offensive end, after getting outrebounded by 10 in Game 1, Dallas outrebounded Miami by 5, while limiting Miami to 6 offensive boards.  On the defensive end, Dallas outrebounded Miami by 6 rebounds.  
• The Mavericks ball movement was more successful going through Nowitzki than on penetration through the pick and roll, although he was a little sloppy with the ball, resulting in five turnovers.    
• Kidd particularly struggled and was uncharacteristically sloppy.  Although, he has been the only other Maverick aside from Stevenson to hit multiple 3s with efficiency.  Both Kidd's playmaking and the team's three-point shot-making need to improve for Dallas for things to be a little easier on them going forward. 
• Barea seemed to be the only Mavericks guard able to get anywhere against the Miami defense with penetration.  He got a few good shots and created for his teammates, but even he struggled, going 0 for 5 after starting very aggressively and going 2 for 2. And despite creating some good shots in the first half for his teammates, they didn't result in points as they missed on those few open opportunities.  
• Terry finally stepped up late in the 4th quarter, making key baskets to start the Mavericks comeback, and at least threatening to penetrate before getting the ball to Nowitzki, but he started slow, continuing to miss open looks, particularly his two open looks from the beyond the arc early in the 2nd quarter. 
• Marion again played consistently good basketball, making positive plays on both ends of the floor, the only Mavericks player to do so for both games in this series. 
• Chandler stepped up his effort in Game 2, particularly on the offensive glass, where he was non-existent in Game 1.  
• Stojakovic was again a non-factor and defensive liability.  When he's on the floor, the Mavericks need to find a way to get him open looks and he must knock them down.  Otherwise, he's certainly going to do them more harm than good.  
• Stevenson made some big open three-point shots in the first quarter, making up for the complete lack of made three-point shots from Terry and Stojakovic.   

For Miami:

• It all starts with Miami's defense, which was great for most of the game and forced Dallas into a lot of bad possessions and turnovers, leading to easy baskets in transition due to their athleticism.  
• Miami again made more three-point shots, three more, but it took them 13 more attempts and they only shot 30% from beyond the arc.  A few of those attempts were questionable forces during Dallas' game-winning run to end the game.  
• Wade was absolutely unstoppable going to the rim.  Why the team went away from this late in the 4th quarter is a mystery.  It may have been partly Dallas' defense, but it didn't seem that Miami tried to get Wade going inside the arc during the final stretch.  He also ran past the Dallas defense for multiple transition plays in the 3rd and 4th to help extend the lead to 15.  
• James continues to impress with his ability to hit difficult contested outside shots almost as well, if not better than he does open shots, including making a contested three-point shot near the end of the first quarter, after missing a wide open three-point shot from the top of the arc despite traveling to get his feet set.  However, those same contested shots did not fall late in the game.   
• Bosh was poor from the field again, and had a costly turnover late in the game with Miami leading by four.  He has certainly disappointed in his first finals appearance.  
• Bibby, stepped up big and played his role by hitting open 3s, making 4 of 7, after going 0 for 4 in Game 1.
• Anthony made life difficult for Dallas offensively around the basket, blocking 3 shots and contesting many more.  He played his role, but again did not pose a threat offensively, as expected. 
• The bench for Miami wasn't much of a factor.  Chalmers shot poorly from outside, but made a big wide open three-point shot to tie the game at 93.  Miller and Haslem were disappointing, shooting 1 for 6 combined.   

Observations from Game 1

• Miami's defense certainly stepped up to the task.  They did a fantastic job limiting Dallas' ball movement and closing out on shooters.  Their athleticism narrowed the passing lanes Dallas has been used to this postseason.  
• Dallas came out tentative to start the game.  It appeared that Dallas shooters certainly felt the pressure of not only the NBA Finals, but of the active and athletic Miami defense, missing shots they have made in the previous series as the open looks came at a premium, resulting in some rushed shots on even open looks. 
• Specifically, Dirk Nowitzki and Peja Stojakovic in particular missed shots they have made throughout the playoffs.  Jason Terry and J.J. Barea also missed some shots similar to those they have made throughout the playoffs.  Haywood even missed a dunk.  
• Miami also did a great job on the pick and roll, rendering Barea ineffective.  He will certainly have to step it up going forward if the Dallas bench is to have the success they have had the rest of the postseason.   
• Dirk Nowitzki was not as aggressive as he has been the rest of the postseason and as a result may not have earned some of the calls he got during the Western Conference Playoffs.  More importantly, his lack of aggression resulted in fewer uncontested opportunities for his teammates through the ball movement that starts with him in the post.  His lack of aggression may have hurt Dallas more than anything offensively within their control (read: not including Miami's defense). 
• The biggest difference may have been the 10 more offensive boards Miami grabbed than Dallas.  All four of their bench players grabbed at least one offensive board.  
• Despite only shooting 38.8% from the field (35.2% inside the arc), Miami probably did a better job moving the ball than Dallas did, getting two more assists as a result despite averaging 5.6 fewer in the playoffs.  
• Miami not only took more three-point field goals but they made more, shooting 45.8% (11 of 24), with LeBron James leading the way with four including a fadeaway over Tyson Chandler to end the 3rd quarter.  Dwyane Wade added two himself.  It is hard to expect them to keep this advantage throughout the rest of the series.  

2011 NBA Finals

Thanks to EvanZ from the APBRmetrics forum and The City, I might have the data I need to apply my analysis to a number of Miami Heat and Dallas Mavericks lineups soon.  But, in the meantime, I wanted to provide my suspicions on which team adheres more to the theories I have provided here.  

This blog is all about team chemistry and no team has played better team basketball than the Dallas Mavericks.  They create an advantage, either through Dirk in the high post or the pick and roll, followed by good decisions on passes and shots, resulting in easy uncontested shots.  Granted, the defenses each team has faced were not the same and the analyses on this blog have been limited to the offensive side of the ball, so take this with a grain of salt.  

First, looking at the distribution of two-point field goals, where a wider distribution has proved beneficial, I anticipate that the Mavericks have the advantage.  Dirk Nowitzki takes by far the largest chunk of the team's two-point field goals, with Shawn Marion and J.J. Barea chipping in with some shots around the basket, Jason Terry taking less than a handful of open mid-range jumpers and Tyson Chandler throwing in the occasional dunk or put-back.  The Miami Heat, on the other hand, have Lebron James, Dwyane Wade and Chris Bosh taking a similar number of two-point field goals.   

Unless the Heat can find someone to stop Nowitzki without help, the Mavericks will continue to be able to start the offense through Nowitzki in the post, force help, move the ball, and get open three-point shots by any of their very capable three-point shooters.  Similarly, the Heat will also have to slow down the pick and roll to slow down the Mavericks ball movement.  I look forward to seeing how much the Heat use James on Nowitzki as he may be the only one with the strength and athleticism to make things hard enough on Nowitzki to limit the need for help defense. 

When it comes to three-point field goal attempts, where more attempts and a more even distribution predict an increase in offensive efficiency, it isn't even close.  With great three-point shooters like Nowitzki, Jason Terry, Jason Kidd, and Peja Stojakovic, not only do the Mavericks take and make more three-point field goals, they do so at a better percentage, and I anticipate that the statistics will show that they have a more even distribution of three-point attempts among the five players in their lineups.  James, Wade, Mike Miller, Mario Chalmers, Mike Bibby and James Jones all take three-point attempts, but the latter four split much of their time, and Wade, Bibby and Miller all have shot under 25% for the playoffs.  Also, the Mavericks take higher quality, uncontested three-point attempts, on catch and shoot opportunities due to superior ball movement partly explaining their higher efficiency beyond the arc, where observation tells me that many of the Heat's three-point attempts are contested shots taken by James and Wade, or on broken plays or transition, which may be hard to come by against the savvy Mavericks defense.

As far as shooting from the field goes, the Mavericks have shot about 2% better from two and over 6% better from beyond the arc during these playoffs. 

When it comes to getting to the line, where a more even distribution predicts greater offensive efficiency, despite Nowitzki's domination at the line during the playoffs, at first glance the Heat appear to hold the advantage when it comes to distribution, as James, Wade and Bosh all get a good number of attempts each game, taking about 24 between them during the playoffs.  That said, the rest of the Heat take about 5 attempts per game.  Joel Anthony earned 2.1 attempts per game, James Jones, who didn't play much against the Bulls, has earned 1.1 attempts per game in the playoffs, while nobody else on the team has averaged an attempt per game in the playoffs.  Although no one on the Mavericks comes close to the attempts Nowitzki has earned in the playoffs, they have more players who get to the line each game, evening the distribution some  Terry has averaged 3.7 attempts, Chandler 3.1, Brendan Haywood 2.5, Marion 2, Barea 1.8 and Jason Kidd 1.5.  These are game averages, a far cry from giving us an idea of how the attempts are spread among players in the lineup.  Nevertheless, there may not be a significant difference between the two teams when it comes to the distribution of free throw attempts.  

With offensive rebounding, where a more even distribution predicts an increase in offensive efficiency, it is the Heat that have more players contributing in that regard, with James, Wade, Bosh, Anthony and Udonis Haslem all averaging an offensive rebound or more a game.  Zydrunas Ilgauskas also rebounds well offensively, however it remains to be seen whether he will see the floor in this series, as the primary lineup he played in during the playoffs was absolutely destroyed by the opposing lineups and he failed to see the floor against the Bulls.  For the Mavericks, Chandler, Marion and Haywood dominate the offensive boards, with Nowitzki and Kidd chipping in just over half an offensive board a game.  It appears that the Heat have a more even distribution, giving them the advantage, but despite that, both teams have averaged the same number of offensive rebounds per game in the playoffs.  So, despite the fact that the Heat have more bodies who attack the offensive glass, it appears the Mavericks offset that with the superior offensive rebounding ability of guys like Chandler, Marion and Haywood. 

As far as distributing the ball goes, because it is hard to see much of a difference on first glance at the distribution of turnovers (where a number of players on each team contribute to similar team totals), it comes down to assists, where a more even distribution predicts an increase in offensive efficiency.  For the Heat, James and Wade dominate the ball and in turn the assists, averaging 5.5 and 4.1 assists respectively.  No one else on the team has averaged over 1.5 assists during the playoffs, with point guards Chalmers and Bibby averaging 1.5 and 1.2 assists per game, respectively.  This makes for a higher standard deviation; a negative in this analysis, and the team as a whole has averaged just over 15 assists per game as a result. 

For the Mavericks, although Jason Kidd has accounted for a large chunk of the team's assists during the playoffs at 7.7 per game and focuses almost entirely on facilitating the offense apart from when he is wide open for a three-point attempt, Nowitzki, Terry, Barea and Marion all average over two assists per game at 2.7, 3.2, 3.5 and 2.1, respectively.  With Dallas' ball movement and likely higher percentage of shots on the catch and shoot than off then dribble, this is not a surprise.  It appears the Mavericks have the advantage here as well. 

So, on first glance, the Mavericks appear to have a significant advantage on the offensive end, which is reflected by their playoffs offensive rating of 113.00 and the Heat's playoffs offensive rating of 106.74 (see www.basketballvalue.com), which will require a significantly superior effort by the Heat on the defensive end to overcome, something they absolutely could be capable of.  That said, with the Mavericks showing the ability to step up during stretches defensively, particularly in fourth quarters against the Lakers and Thunder, and Marion and Chandler in particular playing inspired defense, I will go out on the limb and take the older, wiser, underdogs in the series with confidence and in Game 1 tonight, where the Mavericks hold an advantage with their team play, ball movement and ability to get uncontested shots.   

True Distribution Analysis with 2-Point FG replacing All FG

As suspected, replacing the field goal data with two-point field goal data found a stronger relationship between the standard deviation of the percentage of two-point field goal attempts taken by each player in the lineup and the lineup OPPP than was found between the standard deviation of the percentage of all field goal attempts taken by each player in the lineup and the lineup OPPP. 

This graph illustrates that increasing the standard deviation of the percentage of two-point field goals attempted by each of the players in a lineup can increase the lineup OPPP by as much as 3 points per 100 possessions, more than found with respect to field goal attempts generally.  


Interestingly, the coefficient for the standard deviation of the percentage of two-point field goals attempts with respect to the dependent variable of lineup two-point field goals made per possession was negative, while it was positive with respect to the dependent variables of lineup three-point field goals made per possession and lineup free throws made per possession.  This indicates that while a greater distribution of two-point field goal attempts predicts a greater number of three-point field goals made per possession and to a lesser extent a greater number  of free throws made per possession, it also predicts fewer two-point field goals made per possession.  

True Distribution Analysis

To best analyze how the distribution of various roles influence offensive efficiency, we want to do so independent of the sum.  This means reducing the per possession numbers of each player to a percentage of the team or lineup total, which is realistic with lineup or by position data, as opposed to the original data set comprised of players not on the floor together much of the time.

Season lineup data was used in this analysis.  By position data was found to be unconducive to the analysis of the distribution of roles or statistics, for a few reasons.  Most importantly, the same player can account for statistics at multiple positions throughout a game.  Also, by position data combines multiple players at each position, each of which may bring a different set of skills.  As a result, this makes it difficult to determine how the roles and statistics are actually distributed.  For example, three-point attempts may be taken by only the guards in a starting lineup, but by only the forwards in a second unit.  Although the three-point attempts are broadly distributed in each lineup, when the statistics of the two lineups are combined, the distribution looks even.  This wasn't as much of a problem with the prior analysis as the standard deviations analyzed were not sum independent; sums that weighed heavily into the results.  With lineup data, we are able to look at specific players, with specific skills, which is ideal for studying the distribution of roles. The true distribution analysis for offensive efficiency is below.  

Field Goal Attempts

The analysis shows that a wider distribution of field goal attempts can make a difference of as much as 1.7 points per 100 possessions.  This may not appear too significant, but when considered with the results regarding the distribution of three-point attempts, where an even distribution proves beneficial, we can conclude that a wider distribution of two-point field goal attempts has a greater effect than the distribution of overall field goal attempts suggests. 

Three-Point Attempts

Unlike the previous results, this analysis shows that a more even distribution of three-point attempts can increase offensive efficiency by 12 points per 100 possessions.  This implies that the previous results regarding three-point attempts were influenced more by the total three-point attempts than the distribution of those attempts, indicating that offensive efficiency increases as three-point attempts per possession increases, but that a more even distribution of those attempts is preferred.  So, not only do we want skilled three-point shooters taking many shots, we want many of them spread around the floor.  


Free Throw Attempts 

The analysis shows that a more even distribution of free throw attempts can make a difference of as much as 10 points per 100 possessions.  This implies that the previous results regarding free throw attempts were influenced more by the total free throw attempts than the distribution of those attempts, indicating that offensive efficiency increases as free throw attempts per possession increases, but that a more even distribution of those attempts is preferred.  Lineups with multiple players capable of attacking the rim and earn free throw attempts are more efficient than those that get most of their free throw attempts from a player or two.    


Offensive Rebounds

This analysis shows that a more even distribution of offensive rebounds can increase offensive efficiency by almost 3 points per 100 possessions.  This indicates that lineups with multiple players capable of grabbing offensive rebounds are more efficient than those with a player or two that get most of the lineup's offensive rebounds.  
   
Assists

Unlike the previous results, this analysis shows that a more even distribution of assists can increase offensive efficiency by 6 points per 100 possessions.  This implies that the previous results regarding assists were influenced more by the total assists than the distribution of assists, indicating that offensive efficiency increases as assists per possession increases, but that a more even distribution of assists is preferred.  
  
Turnovers

Unlike the previous results, this analysis shows that a wider distribution of turnovers can increase offensive efficiency by 15 points per 100 possessions.  This implies that the previous results regarding turnovers were influenced more by the total turnovers than the distribution of turnovers, indicating that although offensive efficiency increases as turnovers per possession decreases, a wider distribution of turnovers is preferred.    

NCSSORS Follow-up

After NCSSORS, I had the opportunity to further discuss my research with Dean Oliver, author of Basketball on Paper, and former Director of Quantitative Analysis for the Denver Nuggets, who kindly provided data more ideal for my analysis.  Rather than using season data for the top five or eight players in minutes played to predict offensive efficiency for the team, season lineup data and game by position data was used in the follow-up analysis.  This data fully accounts for the offensive efficiency being analyzed (OPPP), which appears on the Y-axis in all graphs. 

SEASON LINEUP DATA

Using season data rather than game data takes into consideration all opponents faced, rather than a specific opponent, giving us individual data points less affected by defenses that may be outliers, weak or strong.  Lineup data also focuses on specific players rather than the contributions of multiple players to a single position as by position data does, making it easier to pinpoint the skills of that player as opposed to those of multiple players accounting for the statistics accumulated at a particular position during a game.     

Using lineup data in the analysis shows a stronger relationship between the standard deviation of three point attempts per possession and offensive points per possession than in the original analysis.  Going from the lowest standard deviations in the sample to the highest made a difference of nearly 7 points per 100 possessions.    

In their recent series against the Los Angeles Lakers, the Dallas Mavericks showed great success taking many threes and focusing most of the attempts on a player or two in each lineup, with Jason Terry, Jason Kidd and Peja Stojakovic (who have only played 18 possessions together through 10 games in two playoff series) taking the great majority of them.  Dirk Nowitzki also took and made three point attempts, but he mostly played to his greatest strength in taking mid-range jumpers that are difficult to stop, forcing the defense to help, leading to many uncontested three point attempts for the others.  Particularly in Game 4 against the Lakers, the Mavericks played the game plan of draw and kick to perfection, with the offense almost exclusively starting with Nowitzki’s mid-range or post-up game or with Kidd, Barea or even Terry penetrating off screens, forcing rotation that just could not keep up with the ball. 

The relationship between the standard deviation of free throws attempted per possession and offensive points per possession was also stronger using lineup data.  17 points per 100 possessions separates the lowest standard deviations from the highest.  Needless to say, having a player (or two) who can get to the line at will provides a significant advantage.  It certainly hasn’t hurt the Oklahoma City Thunder this year with Kevin Durant and Russell Westbrook.  James Harden also gets to the line at a high rate for the Thunder, providing another option that can attack the rim and earn free throw attempts. 

The relationship between points per possession and the standard deviation of offensive rebounds is not a strong one, though lineups that have a lower standard deviation of offensive rebounds per possession still score about 1.6 points per 100 possessions more than teams with a greater standard deviation of offensive rebounds.  Determining whether this is a result of more offensive rebounds being available as a result of more missed field goals requires further analysis.  

The category of assists is where the most significant advantage can be found, where a higher standard deviation of assists per possession predicts in increase of as much as 20 points per 100 possessions. 

Since turnovers are a negative stat, the relationship found is a negative one.  Like with assists, the primary ball handler generally leads his team in this category.  If that player limits his turnovers, clearly a good thing for a team’s efficiency, the standard deviation will decrease.  Here you can see that from one end of the spectrum to the other, decreasing the standard deviation of turnovers per possession can make a difference of as much as 16 points per 100 possessions.    

GAME BY POSITION DATA

Game by position data accounts for what a team gets out of each position for the duration of each game.  It takes into consideration the contribution of every player that played in that game rather than a specific group of five as is the case with lineup data.  The following graphs represent how the stated standard deviation variables influence offensive points per possession.   These results reflect those from the lineup analysis, with the exception of offensive rebounds, where the relationship reversed.  In addition, the standard deviation of field goal attempts per possession proved significant in this analysis as well, although just slightly, with a more even distribution of field goal attempts per possession predicting an increase of up to 0.8 points per possession.  

This graph illustrates that when observing game by position data, increasing the standard deviation of three point attempts per possession predicts an increase of as much as 17 points per 100 possessions.

This graph illustrates that when observing game by position data, increasing the standard deviation of free throw attempts per possession predicts an increase of as much as 13 points per 100 possessions.

Unlike the previous results, this graph illustrates that when observing game by position data, increasing the standard deviation of offensive rebounds per possession predicts an increase of as much as 1.2 points per 100 possessions. This does not represent the strongest relationship, similar to the negative relationship found in the original and lineup, so the change is not a great one, and in either case, the distribution of offensive rebounds does not have a strong relationship with offensive efficiency.  

This graph illustrates that when observing game by position data, increasing the standard deviation of assists per possession predicts an increase of as much as 20 points per 100 possessions. 

This graph illustrates that when observing game by position data, decreasing the standard deviation of turnovers per possession predicts an increase of as much as 8 points per 100 possessions. 

NEXT

The standard deviation of per possession numbers used in the above analyses are affected not only by the distribution of those categories, but also by the aggregate team per possession numbers in those categories.  For example, if Team A averages twice as many assists per possession as Team B, but those assists are similarly distributed between the five players on the floor, with 60% going to one player, and 10% each going to the other four players, the standard deviation variable for Team A will be twice that of Team B, and Team A will score more points per possession, all else being equal, as reflected above.  The same goes true for free throws attempted.  This applies to turnovers as well, though with the opposite effect.  


Given this, in addition to looking at the distribution of various statistical categories, this analysis lends insight into the influence of the aggregate as well, which is more obvious with respect to certain per possession statistical categories like free throws attempted, assists and turnovers than it is with field goals attempted, three-point field goals attempted and offensive rebounds.  When the relationships found above are consistent with the assumed relationship between the per possession total in a particular category and offensive points per possession, the affect of the distribution of those statistical categories remains unclear.  To exclusively analyze the distribution of roles or categories independent of the total, the total must be removed from the analysis.  Reducing each player's per possession totals into a percentage of the team per possession total and using the standard deviation of those percentages in the analysis instead of per possession values, will better predict the influence of distribution alone.  This analysis and the implication of those results with respect to the above results will soon follow.