The document analyzes the effects of height and wingspan on shooting ability in the NBA. It defines variables like height, wingspan, field goal percentage, and 3-point percentage. Regression analyses find that height positively correlates with field goal percentage but negatively correlates with 3-point percentage above average height. Wingspan shows negative but insignificant correlations with 3-point percentage and percentage of shots from 3-point range. The only significant finding is that increased wingspan decreases free throw percentage. Lack of data limits the statistical significance of the analyses.

1. Jonathan Mcfaul<br />Econ424<br />The Effects of Height and Wingspan on Shooting Ability in the NBA<br />This paper will use statistical analysis to find out the effects that a player’s height and wingspan have on their shooting ability. While the term “shooting ability” can mean different things to different people, I interpret it to mean a player’s consistency and shot making ability in different situations, and I will use Field Goal %, 3 Point %, and Free Throw %, to give an indicator of and discuss it. Height has long been considered a detriment to shooting ability. When you think of the best shooters in the game today, you would consider mostly Point Guards, Shooting Guards, or Small Forwards(i.e. shorter players) before thinking about front court players like Power Forwards or Centers. I expect the results of the analysis to support this commonly accepted notion. <br />My real question is regarding the effect that wingspan has on shooting ability. The first time I thought about this topic is thanks to Guard J.J. Redick, who is the only player that I’ve seen in the NBA who measures out to have a shorter wingspan than height. According to various internet sources, the average human will have a wingspan pretty similar to their height, perhaps slightly longer. Wingspan is often thought to be a huge help in basketball(easier to block shots or steal the ball on defense, harder to have your shot blocked on offense), which is why it is one of the measurements taken at the official NBA Pre-Draft Camp. Because of this, one would consider that the average wingspan of an NBA player would be much higher than that of the average human, much the same that the average NBA height is much higher. This makes J.J. Redick’s proportions seem that much stranger. However, Redick is considered one of the best shooters in the game, and this discovery made me think that it might not be a coincidence.<br />Our first step in this experiment is to define the variables:<br />-28575301625<br />heightinches: A player’s height measured in inches without shoes on.<br />wingspan: How much longer a player’s wingspan is than his height(Inches) <br />maxvert: Maximum Vertical Leap<br />fga: Career Field Goal Attempts per game<br />fgPercent: Career Field Goal %<br />ftPercent: Career Free Throw %<br />_3Ppercent: Career 3 Point Shooting %<br />_3PAs: How many 3 Point Shots a player takes per game<br />Percent3s: The percentage of a player’s shots that are 3 point attempts<br />The next thing we need to do is give ourselves parameters for the data. All of the physical measurements came from draftexpress.com and all of the shooting statistics from espn.com. I decided to record only players with at least five years experience in the league because players come in at different ages and develop at different speeds, but you would expect a player who has been in the league for at least five years to have evened it up(A better way to do it would be to only take a player’s averages from ages 25-30, considered their prime, but unfortunately, draftexpress.com only has measurements from 2000 on, so there would not be enough data). Another requirement was that a player must play at least 15 minutes a game for their career as I used all career stats of the players to account for variability. Lastly, my requirement for Three Point Attempts per game is that the player must average at least .5 attempts to have that statistic recorded because any less and it would be hard to consider the player a significant shooter.<br />So after putting together the data set, the first thing I did was provide a basic summary of the data.<br />38100131445<br />Taking a look at the means of each of the variables, it is interesting to note the average wingspan for an NBA player is over 4.8 inches longer than their height!<br />Our first regression analyses are the effects of height on field goal % and 3P%:<br />-9525139065<br />We can see that fgPercent is positively affected by height. That is, for every inch taller a player is, his field goal percentage would increase by .71504. We can also see that this is statistically significant as the p-value is 0.000(Statistical significance will be defined at 95%, requiring a p-value of less than .05). However, this is not a good indicator of shooting ability as Field Goal % includes dunks, layups, and other shots close to the hoop. Taller players tend to shoot more of these shots, which would explain the correlation between height and Field Goal %.(An example of this is Shaquille O’Neal, who although lead the league in Field Goal % for many years of his career, would never be considered a good shooter)<br />Taking a look at 3P%:<br />-5715095250<br />Although not statistically significant, it seems strange that the taller a player is, the better his 3 Point % is. The ability to shoot a 3 pointer is definitely an indication of shooting ability, so why does this seems to show the tallest players as the best shooters? Let us do two more regressions that might clear this up:<br />-57150158115<br />-47625-457200<br />When we divide 3 point % between players that are above the average height of 77.90517 and below it we get a more commonly accepted idea. Although still not statistically significant, probably due to not enough observations, we can see that height only improves 3 point % up to a certain height. Once you are past the average height, every additional inch decreases 3 point % by .9065054.<br />Moving on to wingspan, our first look will be at the effect of wingspan on Field Goal %:<br />-9525234315<br />Though it is not statistically significant, it is close, as the p-value is .068. We can see that this indicated a 1 inch increase in wingspan is met with a .4219784 increase in Field Goal %. However, like it was stated earlier, this could have more to do with the player being able to finish around the basket easier, not because of shooting ability.<br />If we look at the effect of wingspan on 3 Point %:<br />-9525-333375<br />Although not statistically significant, this would indicate that a 1 inch increase in wingspan is met with a decrease of -.259884 in 3 Point Shooting %.<br />Another thing we can look at is the percentage of a player’s shots that are 3 Point Shots. The players who have a higher percentage can be considered “3 Point Specialists”, as more of their shots are 3s than anyone else. This would seem to indicate a higher shooting ability:<br />center152400<br />Although it is close, it is not significant. However, it does indicate that for every inch shorter a player’s wingspan is, the % of his shots that are 3s is 1.63632% greater.<br />Another measure of shooting ability would be free throw %. Free throw % would appear to be a great indicator of shooting ability as there are no other variables that can factor in. Everyone has to shoot them from the same distance, without time restraints, and without a defender. Let’s take a look at the effects of wingspan on free throw %:<br />-9525-66675<br />As we can see from the above image, every inch increase of the wingspan is met with a decrease in Free Throw % by .852847%, and it is statistically significant. We can be 95% confident that increasing wingspan decreases Free Throw %.<br />We can see the different trends from the results that seem to indicate that wingspan has a detrimental effect on shooting ability, however due to the lack of statistical significance, the only one that we can have 95% confidence in is its negative effect on Free Throw %. The main problem is that there is not enough data. Future investigation into this subject would need many more observations. I was constricted by not having measurement data available to me from before the year 2000 and was only able to gather 87 observations, resulting in many of my regressions to not be statistically significant. <br />