Shoot your shot! Basketball brings flash and fire to one of the most exciting team sports around. The 2023-2024 National Basketball Association (NBA) season brings together the best ballers in the world to battle it out to get into the playoffs and take home the Larry O’Brian trophy in the NBA Finals. Behind all the jams, 3-point bombs, and ankle-breaking crossovers is a plethora of math. Spark Math by Spark Education brings to you our popular series Math in Sports featuring the razzle dazzle of Basketball! Here is our blog “Math in Sports: Fun Basketball Math Facts for Kids”
A Quick Overview of Basketball
For our dear readers who may not be familiar with the great sport of basketball, here is an easy summary of the game. Basketball is traditionally played 5-on-5 on a full-length court with hoops on both ends. Teams score by shooting or dunking the ball into the hoop they are attacking while the defense does their best to stop them. The team in control of the ball, or the team with possession, is on offense and the team without is on defense (possession changes dozens of times in a game).
There is a 3-point line that runs in an arc around the hoop that is about 22 feet away. Shots behind that line count as 3 points and any shots within the line are 2 points. Games are divided into 4 quarters of 12 minutes each. The team with the most points when time expires is the winner.
Basketball teams usually have a Point Guard, a Shooting Guard, a Small Forward, a Power Forward, and a Center as their 5 players on the court. Guards are usually smaller in size and more agile, while the Power Forward and Center are taller and stronger. Some superstars, like LeBron James, can play nearly every position on the floor and be an offensive or defensive powerhouse.
Offensive Basketball Math
When we think of prolific scorers and offensive juggernauts in basketball, we think of players like Michael Jordan, Kobe Bryant, and more recently, Stephen Curry. Strong offensive players excel at shooting from 3-pt range, scoring off the dribble, and 1-on-1 isolation. They also make the players around them better by getting them open and making great passes to set their teammates up to score. Here are a few important offensive basketball terms you should be familiar with:
Fieldgoal (FG): A made basket by a player
Assist: Passing the ball to another player who then scores
Points: Scoring a basket and being credited for the points
Turnover (TO): A player losing the ball or having it stolen from them
Free Throws: When a player is followed in the act of shooting they receive to free shots from a designated area with no one trying to stop them
Points Per Game (PPG)
Points per game is an average of the points scored by a player usually taken over the length of a season. This is a raw measurement of the offensive potency of a player without taking into account things like efficiency. Despite that, the players that lead the league in scoring every year are usually the best all-around players. For PPG, we will look at the top 2 players in the league for MVP voting in Joel Embiid and Nikola Jokic.
Math You Will Need
- Addition
- Division
PPG is a stat that analysts track over the course of the season, updating after each game. For our example, we will calculate PPG over the course of the entire 2022-2023 regular season.
For Joel Embiid, we will use addition to add together the points he scored in each of his games. This number is 2,183 and he did this over the course of 66 games. We will use division to finish finding his PPG.
2183/66= 33.1 points per game
At 33.1 PPG, Embiid led the league and captured the scoring title.
For Nikola Jokic, we will follow the same procedure of first using addition to add together his points and then division to reach his final PPG.
1690 points/69 games= 24.5 points per game
This puts Jokic at number 11 at PPG for this season.
True Shooting Percentage (TS%)
True shooting percentage is a more advanced offensive stat that looks at a player’s efficiency with the ball. Specifically, it measures a player’s accuracy when accounting for 3 point shots, 2 point shots, and free throws. While Field Goal Percentage (FG%) is also a commonly used stat, it is a more simplistic overview of how often a player makes a shot without taking into account other details.
Players that are good 3-PT shooters might show a much worse FG% than players that do most of their attacking close to the rim because 3-PT shots are inherently a lower percentage shot than a dunk. TS% helps take into consideration different types of shots into a complete overview of accuracy. Let’s revisit Joel Embiid and Nikola Jokic for this calculation.
Math You Will Need
- Addition
- Multiplication
- Division
- Order of Operations
From our example before, we have the total points of both players, but we need a few more pieces to complete the puzzle. We also need Field Goals Attempted (FGA) and Free Throws Attempted (FTA). FGA simply refers to how many shots each player has taken over the season, while FTA will cover how many free throws each player earned.
Embiid attempted 1,328 field goals and 771 free throws. 2183 Total points
Jokic attempted 1,022 fields and 415 free throws. 1690 Total Points
We take these values and use a special formula to solve it.
We divide the players’ total points by this equation (2(FGA+0.44xFTA))
Let’s start with Embiid. Using order of operation, we know that we must start by looking at the equation in the inside parathesis and we start with the multiplication portion first before we use addition.
- (2(1328+0.44×771))
- (2(1328+339.24))
- (2(1667.24))=3334.48
- 2183 points scored/ 3334.48=0.654
- 0.654 x 100= 65.4% TS%
Now try calculating Jokic’s TS% on your own. Hint: This might help explain one of the reasons why Jokic was neck-and-neck with Embiid for MVP despite having nearly 10 points per game less than him.
Defensive Basketball Math
Prolific defenders are hard to come by in the NBA. The game is a 2-way sport and this results in a low number of defensive specialists because offensive liabilities are a big problem for teams. On top of that, defenders don’t get the limelight quite like offensive stars.
Let’s see what makes a good defender and how math can help us prove that. Defense can be a hard metric to look at because there aren’t as many clearcut important stats like offense has. We might have to look at some more advanced methods with some overtime math! Here are some terms you may want to know.
Steal: When a defensive player takes possession of the ball from the offensive team
Block: When a defensive player checks the shot of an offensive player causing a miss
Defensive Rebound: When a defending player captures the ball after a missed offensive player’s shot
Plus-Minus (+/-)
Plus-Minus looks at a player’s overall impact on the score when he or she is in the game. This is tied directly to how many points his team scores while he is in the game as well as how many points the opponents scores. All players start a game with a 0 +/- which is considered neutral.
Math You Will Need
If team A scores 2 points, all 5 players in play for Team A are now at a +2 for their plus minus. If there opponent Team B, then score a 3-pointer, Team A’s players all drop to a -1 plus minus. There is a defensive specific plus minus but that formula is a closely guarded secret (seriously!) so we cannot use that. The name of this statistic really gives away what math applications we will need for this one!
- Addition
- Subtraction
- Negative Numbers
We will look at this stat 2 ways. The first way will be the overall season +/- of a player and also a hypothetical example of a game being played. For the overall season +/- we will look at the NBA 2022-2023 regular season leader, Nikola Jokic of the NBA Champion Denver Nuggets
Points Scored by the Nuggets while Nikola Jokic was on the floor: 9096
Points Scored by other teams against the Nuggets while Jokic was on the floor: 8456
9096-8456=640
Jokic had a 640+
That was easy. Let’s calculate a simulated live plus minus. Your job is calculate the +/- Paul Wall from Team Red and Mike Jones from Team White
Quarter Starts
Paul Wall Enters the Game
Team Red Scores 2
Team White Scores 3
Team White Scores 1
Team Red Scores 2+1
Team White Scores 3
Mike Jones Enters the Game
Team Red Scores 1
Team White Scores 2
Team White Scores 3
Team Red Scores 3+1
Paul Wall Leaves the Game
Team Red Scores 2
Team White Scores 2
Team Red Scores 2
Team Red Scores 2
Quarter Ends
Let’s calculate Paul Wall’s and then you can try Mike Jones’ on your own.
2-3-1+3-3+1-2-3+4= -1
Paul Wall leaves the game with a +/- of -1. After the quarter ends, Team Red ends with a team +/- of +3. This might indicate that Paul had a slightly below average performance as his team ended up +4 higher without him on the floor.
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Basketball thrills hearts of millions around the world every year. Whether it is the NBA, International leagues, WNBA, or just in the school yard, basketball brings out the best in many fans and players. If you have a fan or a player, combine their favorite sport with math so they can learn more about the players they love. If you are looking for more math fun that can keep your child engaged and learning, check out Spark Math. Book a free trial class today for the most fun and effective way to math success.
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