# Stats glossary

In basketball there are two very important -although ill defined- metrics, these are the possessions and the plays. 3StepsBasket gives a clear definition for both of these terms as they are both crucial for better understanding basketball numbers and many of the metrics we use in this page.

## Definition: Basketball possession

A possession is every sequence of events created by a team until either they score a basket (including free throws) or they lose the ball. For example, the following group of events makes one possession:

• [Team A] Foul drawn (non-shooting foul)
• [Team B] Foul committed
• [Team A] Missed 3FG
• [Team A] Offensive rebound
• [Team A] Missed 2FG
• [Team B] Defensive rebound

As you see we grouped everything together until "Team B" managed to get the ball with a defensive rebound. A main take away is that one possession may contain multiple scoring attempts.

## Definition: Basketball play

A play is every possible scoring opportunity (including non-shooting fouls) that a team has. Based on this definition, a possession consists of one or more plays. Following the example above, here are the plays that took place during the possession.

• First play
• [Team A] Foul drawn (non-shooting foul)
• [Team B] Foul committed
• Second play
• [Team A] Missed 3FG
• [Team A] Offensive rebound
• Third play
• [Team A] Missed 2FG
• [Team B] Defensive rebound

## Definition: Offensive rating (or offensive efficiency)

A very strong and widely used metric is the offensive rating (ORTG), which tries to capture the ability of a team to score each time they get the ball. The formula is: ORTG = 100 × (points scored)/(possessions). The points scored and the possessions are usually the total amount during one season, unless stated otherwise.

## Definition: Defensive rating (or defensive efficiency)

Similarly to the offense we can define the defensive rating for the defense which is an indicator of the defensive quality of a team. The formula is: DRTG = 100 × (points allowed)/(possessions). Again the points allowed and the possessions are the total amount during one season, unless stated otherwise.

## Definition: Net rating (or net efficiency)

Net rating is the difference between the offensive rating and the defensive rating. That shows how much more (or less) a team can score compared to their opponents. NETRTG = ORTG - DRTG.

## Why ORTG, DRTG and NETRTG are important?

When analyzing the offensive or defensive quality of different teams the easiest metric to use is the points scored or allowed by the team. This can be in the form of points per game, points per shot attempt or even the field goal percentage.
All of the above are valid metrics, although they are prone to the following systematic errors:
Points per game get higher for teams that had to play over-time. Also, they don't take into account the speed of the game (high pace most likely will give more points).
Points per shooting attempt and the field goal percentage tell us half the story. A team that shots well has good chances to put the ball to the basket; but what about a team that doesn't shot good yet they grab many offensive rebounds, or they don't commit turnovers?
Offensive or defensive rating focus on this simple question: "how many points a team scores every time they have the ball?". It doesn't ask how do they score (for example by shooting efficiently or by getting many fouls). All it matters is if the team can somehow put the ball to the basket. You can find visualizations of such metrics in the charts page of each league.

## Rankings

Many player and team ratings are calculated by comparing the team's or the player's statistic with the rest teams/players of the league. This is a common technique in statistics and a pretty easy one to understand. For example, when we calculate the scoring metric we sort the players by points per game and they get their ranking based on how high they are placed on this sorted table.
Bellow we give brief explanations for all metrics used to define the quality of basketball teams and players.

## Player metrics

• ##### PPG (points per game)

The player's average points per game

• ##### BH (Ball handling metric)

BH = percentile(2*(average player assists) - (average player turnovers))

We chose this metric to define the ball handling ability of the player because on average an assist yields around 2 points for the player's team while a turnover yields around 1 for the opponents. That's the reason we multiply the assists by 2 while keeping the turnovers as they are.
It worths mentioning why we don't use the metric assist/turnover ratio. That's because as a calculation it is of minor mathematical importance since it doesn't give information about the frequency a player passes and on top of that we should always handle divisions by zero separately which makes the metric unstable.

• ##### MTW (Mixed teamwork)

This metric tries to capture the player's contribution to the team by using the following data:

MTW = percentile((percentile of A) + (percentile of B))
Where
A = (team points difference with player on) - (team points difference with player off).
B = The "winning" frequency for the player's team when the player is on the floor.

• ##### MTD (Mixed team defense)

Here we measure the defensive skills of each player by using the following data:

• A = The points per possession of the player's opponents while the player is on the floor.
• B = sum of individual data (as per game averages): steals, defensive rebounds and blocks.

MTD = percentile((percentile of A) + (percentile of B))

• ##### Player overall rating

The result of this metric is visible as the "red stamp" in the players' page. It is based on all other players' metrics, namely the scoring, ball handling, defense, rebounding and teamwork metrics. Players who ranked higher in most of these categories will enjoy higher placement in the overall rating as well.

• ##### eFG% (Effective field goal percentage)

eFG% = 100*(FGM+0.5*3FGM)/FGA

Effective field goal percentage adjusts FG% to account for the fact that 3-pointers count half time more than 2-pointers.

• ##### TS% (True shooting)

TS% = 100*PTS/(2*(scoring attempts))

True shooting percentage measures each player's shooting efficiency.

• ##### AST% (Assists rate for players)

AST% = 100*AST/(TEAM_FGA-FGA)
* TEAM_FGA stands for the team field goals only during the time the player is on the floor.

Assist rate shows the percentage of the teammate's field goals assisted by a player while on the floor.

• ##### AST% (Assists rate for teams)

AST% = 100*AST/POSSESSIONS

• ##### pAST (Points assisted)

Points assisted is the number of points produced by the assists of a certain player.

• ##### TOV% (Turnovers percentage for players)

TOV% = 100*TOV/(scoring attempts+TOV)

Turnover percentage is the player's turnovers per 100 individual plays.

• ##### TOV% (Turnovers percentage for teams)

TOV% = 100*TOV/POSSESSIONS

• ##### RPG (Rebounds per game)

The player's average rebounds (offensive and defensive) per game.

• ##### ORB% (Offensive rebound percentage)

ORB% = 100*ORB/(TEAM_ORB+OPPONENTS_DRB))
* TEAM_ORB stands for the team's offensive rebounds, grabbed only during the time the player is on the floor. Similarly we define OPPONENTS_DRB for the opponent's defensive rebounds.

Offensive rebound percentage estimates the percentage of available offensive rebounds a player grabbed while he was on the floor.

• ##### DRB% (Defensive rebound percentage)

DRB% = 100*DRB/(TEAM_DRB+OPPONENTS_ORB))
* TEAM_DRB stands for the team's defensive rebounds, grabbed only during the time the player is on the floor. Similarly we define OPPONENTS_ORB for the opponent's offensive rebounds.

Defensive rebound percentage estimates the percentage of available defensive rebounds a player grabbed while he was on the floor.

• ##### TRB (Total rebounding rating)

TRB = percentile(DRB% + ORB% + RPG)

• ##### USG% (Usage rate)

USG% = 100*(scoring attempts + TOV) / (plays participated))

Usage rate is the percentage of the team's offensive possessions a player used while he was on the floor.

• ##### Pace

Ball possessions per 48 (for NBA) or 40 (for Europe games) minutes of play.

• ##### FTrate (Free throws rate)

Number of free throws per 100 field goals.

## Team ratings

• ##### Team overall comment (stamp)

This is based on the wins, defeats, points for and points against of each team. Obviously the more wins and the more points scored one team have, the higher they are ranked.

• ##### Team players - roles comments

In the teams' pages we display the roster by splitting the players based on their strengths.

• Best: The players of the team that have a very high overall rating (see player's ratings).
• Floor chief: Players with very high ball handling rating (see player's ratings).
• Shooting good: Players who can hit from down-town, it only depends on the number of three-pointers they hit per game.
• Easy baskets: Players with an exceptionally high percentage in two-pointers.
• Defense first: Players with very high defense rating (see player's ratings).
• Team first: Players with very high teamwork rating (see player's ratings).
• Crew: Players with no significant strengths.
• Bench: Players that on average play very few minutes (ranked in the bottom 10% based on playing time).

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