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.

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.

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