"Obstacles don't have to stop you. If you run into a wall, don't turn around and give up. Figure out how to climb it, go through it, or work around it." Michael Jordan

Hi there!

The basketball is one of the most popular sport in the world. Can be considered a complex sport, due to a large variation of dynamic and continuous actions, like sprints, jumps, combinations of movements and situations of game that demand speed, endurance, strength and dexterity. For that, the most requirements are the individual players skills and the constitutional factors such as the body height.

An important outcome of the game is the gaining possession of the ball on rebound. The rebounding affect the most parts of the game, and can be an indicator of many things about your players and your team, as how hard playing, team focus, shooting effectiveness, etc. Due to that, several studies as been conducted to know more about the factors that can determine the rebound skills.

For this post we used a sample based on 508 NBA players in the current season (2018/2019) scrapped from the NBA Advanced Stats ( https://stats.nba.com/).

Let's see what data tell us, namely, is there any relationship about the number of rebounds and the body height of a NBA Player?

The height and rebounded balls percentage relationship was examined by using Pearson's correlation coefficient and revealed a strong correlation coefficient (r=.554, p= 0.000 < 0.05) this indicates that higher the height of the players the greater is the percentage of offensive rebounds.

This fact is aligned with theory that consider the most best rebounders the most higher players, although there are exceptions.

This results are quite interesting and also make us wonder if there is any association between the height of the player and the position that the NBA player adopts in field. Let's see in a greater detail next!

## Is the height associated with the position that the player adopts in the Basketball field?

There is five field positions that are adopted by basketball teams. They are the point guard (PG), the shooting guard (SG), the small forward (SF), the power forward (PF), and the **center (C)**.

In theory, there is a strong relationship between body composition and positional roles in elite basketball.

In the NBA, the center (C) players are the tallest on the team. This position has been traditionally considered one of most important. This is a player responsible for keeping the opponent from shooting by blocking shots and passes, and also important on gaining rebounds.

The **power forward (PF)** play a role similar to that of center (C). He is noted for his mid-range jump-shot, shot blockers and also gaining rebounds.

Shooting guards (SG), are players typically taller than point guards. Many bigger shooting guards also can play as small forward. The shooting guards should be a good ball handlers.

**Small forwards (SF)** are shorter than power forwards and centers but taller than either of the guard positions. Typically it's a shorter, quicker and leaner player. Is considered to be perhaps the most flexible of the main basketball positions.

**The point guards (PG)** are usually the shortest players on the team, they increases team efficiency and generally have a high number of assists.

That said, what does the data tell us?

By looking to the columns percents indicate that center (C) players are more likely to be tallest (greater than 84 inches) than Shooting guards (SG), Small forwards (SF) or point guards (PG) - see that almost 72% of the players that measure more than 84 inches are in this position. And ~ 69% of the PG are in the shorter position ( < 77 inches). This seems to be aligned with what we said previously.

Let's check if this suspicious is statistically significant. To answer that in a first stage, we will used the **Chi-Square Test of Independence**.

The hypothesis of the Chi-Square test are:

- Ho: There is no association between the height category and the player's position.
- Ha: There is an association between the height category and the player's position.

With the Chi-square test, we will confirm if the variables are associated or not. This test show a X^2 = 547.042 and a p-value = 0.000. The p-value allows us to determine if we accept or reject the null hypothesis. In our case, p-value < 0.05, so this means that we reject the null hypothesis, and we can state that exists an association between the players position and their height.

At this point we’ve established a relation between height and the player's position. Let’s see what correspondence analysis can contribute to our understanding of it.

Simple correspondence analysis is typically applied to a two-way table of counts and explores the dimensions underlying the relation between the rows and columns. Is closer to exploratory techniques such as factor analysis than it is to predictive models such as regression.

Simple correspondence analysis attempts to account for the relation between the row and column variables by assigning optimal scores to each row and column category along the underlying dimensions. If two rows (or columns) have similar percentage patterns, they will have similar scores on the dimensions, while if the rows (or columns) differ their category scores will differ. These category scores are the basis of the perceptual map, which places the row and/or column categories in a space, derived from their relationship.

The perceptual map is a graphical method used in conjunction with statistical techniques to visualize relationships and differences in data. It involves plotting the scores of individuals or groups with values for variables or variable categories in a space derived from the specific statistical analysis. It can be used to view the relative locations of categories of height of the players and their adopted position in a low dimensional (two-dimensional) plot.

Looking to the table above and to the tip that the Quark Analytics Portal give us, we can see that the dimension 1 dominates the solution with 64.33% of the variation. For this reason we will view the categories on the plot focus most on this dimension. We can also see that together the Dimensions 1 and 2 explain almost 94% of the total inertia (this is also know as the retention of the solution).

Projecting the height categories in the axis along with the positions adopted, we see that the center (C) players are close (more likely) to the higher height (84 +) . Also, we can see that the point-guards (PG) are close to smaller height (< 77 inches) this is aligned with the theory that they need to be shorter in order to increase the team efficiency and the number of assists. The players on the shooting-guard (SG) or small-forward (SF) positions both are close to the range 77 to 80 inches. Interesting to notice that the power forward (PF) play a role similar to that of center (C) is also close to the higher heights and far from the other positions.

These results are aligned and confirm this way that, all categories seems to be according with mentioned theoretically.

With the first part of the analysis we can conclude that players with most height are normally the bests at gaining rebounds. When attacking, this players can easily gain position inside the paint/lane zone, which allow them to gain offensive rebounds or score points, and when defending, they can gain defensive rebounds or avoid opposite team players to score points. And it seems that the higher heights are associated with the players position are center (C) and power forward (PF).

For the other hand, players with less height are best at dribbling the ball, because of their lower center gravity, and are great game distributors. This players position are point guard (PG) and they are really fast and can do high speed movements and sprints, and also they assists a lot other players. They are the "brain" of the team.

For last, players with average height are good at linking game play, between the game distributor player and players inside paint/lane zone. This players usually are also good at shooting at 3 points line, and when attacking they use blocks, on opposite team players, to allow team mates to gain position to score points. This players position are shooting guard (SG) and small forward (SF).