NBA Real Plus-Minus

ESPN just came out with a new advanced metric called Real Plus-Minus (RPM). It is intended to be a perfected form of the normal plus-minus stat, which measures the gains or losses of points while a given player is on the field. The issue with the original plus-minus stat is that it doesn't factor in the impact of the other players on the court at the same time as the given player, so mediocre players who play alongside superstars will often excel in this stat as much as their superior teammates.

Nothing has been revealed about the actual calculation of this stat yet, but it allegedly factors in numerous variables on both offense and defense to calculate the number of points a player contributes to or takes away from his team per 100 possessions. Although it's difficult to do anything to calculate using this metric because the algorithm is not given, we can use the already-calculated RPM numbers to compare and contrast different teams.

Comparison of the Oklahoma City Thunder and the Miami Heat based on the RPM of starters:

OKC:

Russell Westbrook: 4.09

Thabo Sefolosha: 0.37

Kevin Durant: 6.77

Serge Ibaka: 3.10

Kendrick Perkins: -3.19

Total: 11.14

MIA:

Mario Chalmers: 1.48

Dwyane Wade: 2.13

Shane Battier: 1.60

LeBron James: 8.11

Chris Bosh: 3.75

Total: 17.07

Interestingly, Nick Collison, a backup big-man for the Thunder, is the sixth-best player in the NBA according to this statistic with an RPM of 5.81. Collison is the same height as Kendrick Perkins, whose RPM is a lowly -3.19; if they inserted Collison into the starting lineup for Kendrick Perkins, their RPM total for starters would be increased to 20.14! 

Although this stat is new and certainly imperfect to some degree, it does bring the value of some underrated players to light. Maybe this switch would improve OKC and make them even better than the defending-champ Heat.

Source:
http://espn.go.com/nba/statistics/rpm/_/sort/RPM

11.2 Vectors In Space

This section is about the properties of vectors in 3-D space. The component (regular) form of a vector is
v = <v1,v2,v3>. As we know from earlier chapters, a vector is the difference between a terminal and initial point. Since this is in three dimensions, the three numbers inside the angle brackets are the differences between the x-values, y-values, and z-values, respectively, of a terminal and initial point.


Length of a vector: ||v|| = squareroot(v1^2 + v2^2 + v3^2)

• This equation makes sense, as the length of a vector would be the distance between its initial point and its terminal point. Each vn value is the difference between the x-, y-, or z-value of the terminal and initial points, so this length equation is the same as the basic distance formula we all know and love!

11.4 Lines and Planes In Space

In this lesson, we learned how to find the parametric and symmetric equations of a line in a 3-D space and how to find the angle and distance between two planes. In this blog, I'm going to focus on planes. The basic equation is:

a(x-x1) + b(y-y1) + b(z-z1) = 0

In this equation:

• a,b,c are the x, y, and z components of a perpendicular (normal) vector. n = <a,b,c>
• x1, y1, and z1 are the coordinates of a point on the plane.
• x,y, and z are variables. 

Many problems will give hints and ask you to find the equation of a plane. In the following example, a point on the plane and a perpendicular vector are given:

Cool 3D Shapes