Welcome back to Hack a Stat! This post is a statistical analysis to find an answer to this question: how much does players’ height influence basketball? Players’ heights during the last season are available in League Average stats!

ITALIAN VERSION

## Introduction

This analysis was born from my thoughts: I suppose Milano needs another wing next to Micov for the next year (I wrote at the end of the 2017/2018 season). I think a player in spot 3 with good defensive skills can help Milano, both to reduce Micov’s usage and to guarantee better defensive skills. So I asked myself: is it possible to assume this need from the numbers? This question triggered a chain reaction that led to something more: so this post will focus on how much the height influences the results and the game, especially the defensive one.

Why the height? Because what differentiates the roles are the dimensions, therefore height and weight. In today’s basketball, the role differences with respect to height have weakened, but you can still rely on it to divide the players into the various roles: the guards are around 190cm tall, the wings are around 200cm tall, while the big men are 210 / 215cm tall.

## Average height and weighted average height

Let’s start with this basic data: the following chart shows the average height of the sixteen Euroleague teams.

But this is a simple arithmetic average that does not provide any information: in those numbers, there are players’ heights who played rarely. To overcome this it is useful to weigh the importance of the height based on the total minutes played: in this way the margins of error of the starting data are reduced, as not only the player’s height is taken into account, but also his actual usage. By calculating this weighted average, the following results are obtained:

As you can see, Panathinaikos is the team with the lowest arithmetic average, but by weighing the values on the minutes it passes from 16th to 11th. Milano moves back four places. Here is the chart that shows only the weighted heights:

Olimpia, Maccabi, Efes have therefore used “short” players most of the time; they are three teams that were at the bottom places at the end of the regular season. Immediately afterwards, however, we find CSKA, the winner of the Euroleague regular season. This suggests that height does not affect the outcome that much. And in fact, intersecting the weighted height with the winning percentage we obtain the following graph:

Although the line shows us a slightly positive trend, the team distribution is very heterogeneous. In fact, the trend line is not very inclined, meaning that the correlation between the two data is not so marked. For example, Milano and the Red Star have diametrically opposite average heights, but almost equal W%. In short, it seems that the average height does not affect the results.
I wanted to check other correlations. The next step was to cross the weighted average of the heights with the Pace:

In this case, we already have a more marked tendency: if a team is small, it is probably that it likes to run. Of course, the game speed (as well as the player’s speed) is influenced by many other factors, but Maccabi and Fenerbahce, who ranks one opposite the other, show us that there is a correlation between the two data. This graph therefore gives us an interesting first idea: if you have a team in which the most used players are small, it would be appropriate, except in special cases, to increase the pace.

The chart that intrigued me the most was that relating to the team’s Defensive Rating, given that a player’s height influences more his defensive than offensive contribution. A greater height than the guarded opponent leads to some advantages: it allows the defender to cover more space, allowing him to limit the opponent’s vision. Furthermore, there is a dimension so far not mentioned, but which is strictly related to height: the wingspan. In today’s NBA, wingspan is highly considered, even more than height. Having a wide wingspan allows the defender to better guard the opponent. With a large wingspan, players can switch without running into mismatches. In modern basketball, in fact, many switches are made.
Taking the image of Leonardo’s Vitruvian Man, one notices that the height is equivalent to the wingspan: this is true, but obviously there are exceptions.

Some studies have calculated the relationship between the two measures: we are very close to 1, but the wingspan is slightly higher than the height (0.5-1% more). Then there are the particular cases like Leonard or Durant that have a wingspan greater than their height. In any case, given the lack of these values, we assume that the two are equivalent. Having said that, we intersect the weighted average height (which will therefore also be the weighted average wingspan) with the Defensive Rating:

Also in this case, there is no correlation. Red Star and Olympiacos both have a high weighted height value, but very different Defensive Ratings.

The graphs presented so far show a weak influence of the height on different values, but nothing so striking as to justify a need for the teams to have tall players.

## Backcourt height influence

To further improve the analysis I thought of calculating the weighted average heights of the backcourt (point guard, shooting guard and forward) and of the frontcourt (power forward and centers). So here is the graph showing the weighted heights of the backcourt (blue) and frontcourt (green) of the sixteen Euroleague teams:

It is no coincidence that we tend to find the worst defenses on the left side of the graph (therefore with the short backcourt), while the best ones on the right side. Having a tall backcourt means having a perimeter defense that grants less space and makes things more difficult for the opponent; moreover, it allows defenses not to grant mismatches once switches have been made. We resume the scatter plots shown above, but this time we only use the weighted height of the backcourt: we start by intersecting it with the Winning Percentage.

The last two teams in the ranking in the worst corner, the top three in the best corner: no, it is no coincidence. Having a tall backcourt helps to win.
Returning also to the graph relating to Pace, we find a trend that confirms again the considerations made with the weighted height:

Maccabi in the upper left, Fenerbahce in the lower right: even considering only the backcourt weighted height, the chart provides the same indications of the previous one.

Finally, the chart that I consider most important: the one about the defense, in which we intersect the backcourt weighted average height with the team’s Defensive Rating.

The trend line is strongly inclined, meaning that with a tall backcourt (and therefore with a wingspan wider than the average) it is easier to have a good defense. It is good to underline it: clearly the defensive skills of the players also clearly affect, but nevertheless the height is clear that it helps.

## Frontcourt height influence

The frontcourt height instead has less influence on the Defensive Rating. Here is the graph showing it:

A very heterogeneous distribution. CSKA has the shortest frontcourt, but it is one of the first defenses. Real Madrid is also one of the best defenses, but with an average height.

In my opinion, there are two main reasons that lead to this spread: firstly, power forwards now play more outside the area than before. This means that beyond a certain limit, the height becomes a weak point more than an added value: it’s harder to play defense for a tall guy in those zones. The small ball is essentially this: adding a fourth backcourt player in place of one of the two big men and taking advantage of the more agility of this line-up. This phenomenon partly explains the negative trend of the chart, since the opponent is forced to lower his line-up to make up for the different athleticism.
The second reason is that by now the centers are not only required to be tall but also quick and these two characteristics do not always get along. High and static centers nowadays are struggling to keep the current pace and this reason also explains why the more you move to the right, the easier it is to come across high Defensive Ratings.

## Conclusion

So how much does height influence basketball? As can be seen from the various charts, in modern basketball having a high backcourt (and therefore very likely with wide wingspan) guarantees some defensive advantages such as greater contested shots, more deflected passes, and space limitations, as well as not to grant mismatch after the switches. Obviously the backcourt height is not enough to create an efficient defense but it is clear that it helps a lot.
The frontcourt is also influenced by the average height, but in this case, there are other factors (speed, defensive readings) that are more crucial than the height itself.

This post ends here. We have found the answer to the question: how much does height influence basketball? See you soon, your friendly neighborhood Cappe!