Definition

SPA is an impact metric based on the change in win probability on a play-by-play basis.

Basic Events

We can attribute the impact of many event types to one or two players:

Event

Primary player impact

Secondary player impact

Free throw

The player shooting the free throws is
attributed with the change in win
probability.

N/A

Rebound

The player that rebounded the ball is
attributed with the change in win
probability.

N/A

Turnover

The player that turned the ball over is
attributed with the change in win
probability.
If a live-ball turnover, the player
that stole the ball is attributed with
an equal change in win probability.

Foul

The player that committed the foul is
attributed with the change in win
probability.
The player that drew the foul is
attributed with an equal change in win
probability.

Missed field goal

The player that missed the shot is
attributed with the change in win
probability.

N/A

Made Field Goals

There is one key event that is missing from the table above: made field goals. That’s because determining credit for a field goal can be a bit tricker. Let’s split all field goals into two buckets: assisted and unassisted. Unassisted field goals are simple: the player that made the shot is given credit. However, we need to determine what share of the change in win probability should be attributed to an assisting player. For this metric, we will use the following system for attributing credit:

\[a = \frac{p \cdot f \cdot 100}{o} - 1\]
  • \(a\) is the percentage of the change in win probability attributed to the assisting player,

  • \(p\) is the number of points associated with the field goal attempt,

  • \(f\) is the shooter’s field goal percentage from the area of the shot, and

  • \(o\) is the team’s offensive rating.

In short, we will be giving the assisting player credit for the percentage lift in points per 100 possessions driven by the shot they created.

Sequences

There is another corner case we need to address: sequences. A sequence is a combination of events that occur in the same time period. For instance, a shooting foul sequence will consist of the foul and free throw(s) in a single timestamp. We need to firmly define how much impact each player involved in the sequence should get. Below we’ve defined some common sequences:

Sequence

Events

Attribution

Offensive foul

* Foul
* Turnover
Offensive foul row dropped, player
committing the foul given blame.

Shooting foul (2PT FGA)

* Foul
* Free throw
* Free throw
Player committing the foul given
blame. Player shooting free throws
given credit.

Shooting foul (2PT FGA - Missed FT)

* Foul
* Free throw
* Free throw
* Rebound
Player committing the foul given
blame. Player shooting free throws
given credit. Unknown effect for
rebound.

Shooting foul (3PT FGA)

* Foul
* Free throw
* Free throw
* Free throw
Player committing the foul given
blame. Player shooting free throws
given credit.

Shooting foul (3PT FGA - Missed FT)

* Foul
* Free throw
* Free throw
* Free throw
* Rebound
Player committing the foul given
blame. Player shooting free throws
given credit. Unknown effect for
rebound.

Shooting foul (FGM)

* Field goal made
* Foul
* Free throw
Player committing the foul given
blame. Player shooting the free throw
given credit.

Shooting foul (FGM - Missed FT)

* Field goal made
* Foul
* Free throw
* Rebound
Player committing the foul given
blame. Player shooting the free throw
given credit. Unknown effect for
rebound.

Putback FGM

* Rebound
* Field goal made
Player getting the rebound given
credit proportional to the quality
of the shot taken (similar to
assist). Player making the shot given
rest of credit.

Putback FGA

* Rebound
* Field goal missed
Player getting the rebound given
credit proportional to the quality of
shot taken (similar to assist).
Player taking the shot given rest of
credit.

Shooting foul (Putback FGM)

* Rebound
* Field goal made
* Foul
* Free throw
Player getting the rebound given
credit proportional to the quality of
the shot. Quality of shot includes
expected value from free throw.
Player that made the shot and shoots
the free throw given rest of credit.

Shooting foul (Putback FGA)

* Rebound
* Foul
* Free throw
* Free throw
Player getting the rebound given
credit proportional to the expected
value from free throws. Player taking
free throws given rest of credit.

Shooting foul (Putback FGM - Missed FT)

* Rebound
* Field goal made
* Foul
* Free throw
* Rebound
Player getting the rebound given
credit proportional to the quality of
the shot. Quality of shot includes
expected value from free throw.
Player that made the shot and shoots
the free throw given rest of credit.
Unknown effect for following rebound.

Shooting foul (Putback FGA - Missed FT)

* Rebound
* Foul
* Free throw
* Free throw
* Rebound
Player getting the rebound given
credit proportional to the expected
value from free throws. Player taking
free throws given rest of credit.
Unknown effect for following rebound.

Note

In the table above, we’re defining “proportional” credit similarly to assists.