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If you would like to see the full formula click here. Beware. Clicking on that link can cause brain injury. Being that the formula is a tad complicated, we thought an explanation was in order.
The main theory behind total offense created is to include anything and everything that an individual player can affect on the offensive side of the ball. That results in four main components: scoring, teammate boost, assists and other factors.
Essentially, you can argue that there are two components to every shot: the creation of the shot and the execution of the shot itself. Sometimes a player controls both of these components, but in some situations, multiple players are involved.
For example, consider this scenario: Chris Paul penetrates and brings Blake Griffin’s defender over to stop him. Paul dishes the ball to Griffin, who throws down the dunk for two points.
In that situation, Paul created the shot, and Griffin made it. Most metrics will give two points to both of them, essentially double-counting the basket. Only two points were scored though, not four. Therefore, we're splitting the credit evenly between the distributor and the finisher.
The field goals that a player made were split up into two categories: unassisted and assisted. Players received full credit for unassisted field goals as they served as both shot-creater and shot-maker, but only half credit for assisted ones. This applies to both two-pointers and shots from behind the three-point arc.
One of our major objectives was to account for the impact a player has on his teammates. Players who are asked to generate offense are often faulted for being “high-volume” scorers, but the impact such players have on the game can be immense.
We looked at how a team's effective field-goal percentage—a weighted metric that gives more value to three-pointers—changed when the player in question was on and off the court. If the four teammates joining the player shot more effectively while he was on the court than the average five teammates did while he was on the bench, then the player received a positive "teammate boost."
The amount of field goals that teammates shot while the player was on the court also influenced this part of the metric. An equal change in effective field-goal percentage is more valuable when more shots are taken than when fewer shots are lofted up at the basket.
Just like in the scoring component, all credit for assists was split between the person who made the pass and the person who finished the play. After all, every assist results in an assisted field goal; it's impossible for an unassisted bucket to use an assist.
Players also received more credit when assists led to three-pointers, as those shots are worth an extra point on the scoreboard.
Players received positive boosts for free throws made and offensive rebounds. However, not every offensive rebound is equal.
Those boards were weighted according to how successfully teams used possessions. An offensive rebound is more valuable on a team that averages 1.1 points per possession than it is on a team that averages 1.0 points per possession.
The same theory applies to missed shots from the field and turnovers, both of which counted against players in this formula.
However, all missed field goals aren’t lost possessions. Many times, teams score on missed field goals. In fact, the tip-in is one of the most efficient shots in the game, and literally none of those happen without a missed shot.
As a result, missed shots were more detrimental to the cause on teams that were less effective on the offensive glass.
The last factor was free throws missed, which obviously count against a player.
Some of the content for this description was provided by Adam.
We were greatly helped in compiling our data from a number of websites. Hoopdata gave us the number of assists which led to three-point shots. Basketball-reference gave us shot details from the various parts of the court as well as per 48 minute stats. NBA.com's Advance Stats helped us to determine what the team did while a player was on and off the court.