Shooting Ability and Size
Everyone knows that, in general, guards are better shooters than centers. That means that bigger the size, poorer the shooting ability. In fact, a player only needs a good eye-hand coordination and average strength to be a great shooter. Thus, we can deduct that somehow size is negatively correlated with the coordination.
In this analysis, we want to explore the effect of height and weight on shooting sharpness. As our goal is to compare players according to their pure shooting ability, best way is to look to their free throw statistics as it is the only shot type of equal difficulty for everyone. Besides, with taking into account only free throws as dependent variable, we can at some degree get rid of the disturbing effect of fatigue, in-game distractions and pressure.
We used 2014-15 regular season free throws statistics of all NBA players with at least 10 free throw attempted. We classified them according to their height, weight and playing positions. Then we look both descriptively and statistically their free throw made percentages. The next three parts will cover descriptive graphs; but in the final part, we will give the results about the statistical relationships between shooting and height/weight while controlling the other. So that, we want to understand which one is the main reason that negatively effects the shooting ability.
499 players played in an NBA game last season. 427 of them attempted at least 10 free throws. James Harden led the league by far with 824 free throw attempted (second most is 654 by Russell Westbrook), and he made 715 of them resulting with .868 FT percentage. Only 13 players had over .900 FT % and 11 of them were guard. The other two players were Caron Butler (F, with 55 FTM of 61 FTA, .902 FT%) and Meyers Leonard (C, with 30 FTM of 32 FTA, .938 FT%). Jimmer Fredette led the FT% with .956 who made his 43 of 45 free throws. If we filtered out players less than 200 FT at total, Stephen Curry was the leader in this category with 308 FTM of 337 FTA and .914 FT%. Surprisingly the other three players were playing for the same team: JJ Reddick (183 of 203, .901), Jamal Crawford (227 of 252, .901) and Chris Paul (289 of 321, .900). After these some facts, let’s start our analysis now.
Position vs. Free Throw Percentage
We classified players onto 3 main playing positions: guards, forwards and centers (as it is in the all-star ballots). But we also add two mid-categories of guard-forwards and forward-centers. As expected, playing position creates the most visible distinction for free throw statistics. Numbers prove that guards are better FT shooters than all others and centers are worst.
Height vs. Free Throw Percentage
In NBA, majority of players have height between 6-6 and 6-9. Best shooting height size is 6-3 with the average free throw % of .827 and the worst is 6-11 with .671. Just note that, for our analysis, the height categories below 6-0 and over 7-0 are unreliable statistically as they covered so few players. For 7-2 size, there are only two players (with at least 10 FTA in the season) who are Roy Hibbert and Alexis Ajinca. Both of them surprisingly are very good free throw shooters. The following table and graph depict that as height increases, the FT% decreases.
Weight vs. Free Throw Percentage
Height and weight are strongly positively correlated. Thus, typically higher weight means lower free throw success according to previous information. In order to verify this fact, we collected players’ weights and classified them per 10 lbs. intervals; and look at their free throw made averages. For weight, majority of players are between 211-250 lbs. The negative effect of weight on FT% is clearly visible. Best shooting weight is 161-180 lbs. range and the worst is 261-270.
Weight/Height Relationship with Free Throw Success
Let’s start with simple correlations and look at mutual relationships between height, weight, position and free throw percentage (Position is in fact an ordinary variable, we numbered 1 to 5 for positions in this analysis.).
The following table shows that FT success is negatively correlated with others at %99 significance level. And also height, weight and position number have all strong positive correlation with each other unsurprisingly.
But this analysis is not helpful because we didn’t control the effect of others two variables while looking their correlations with FT success. And since there are strong positive correlation with height and weight, their correlations with FT Success is in fact spurious. Moreover playing position is actually a result of weight and height, it is not independent.
So, this time we did the partial correlation analysis, and we looked the relationship of two variables while controlling the effect of other. While controlling the height; weight and free throw percentages are again negatively correlated at %99 significance level. But on the other hand, while controlling the effect of weight; height and FT % are not correlated at all! Hence, it seems we discovered something meaningful here, which is, the shooting ability (or hand-eye coordination) is mainly affected with weight rather than height.
In order to validate this finding, we run another similar test: univariate analysis of variance (ANCOVA). Again we controlled the effect of height or weight and explored the relationship between the other with the free throw success percentage. The result was same. Height has no clear effect on FT% but weight has (negatively).
Finally, we selected out only players with the same height (6-9, the most crowded group) and filtered out the others. With this group, we split the data by half according to their weight and compared their free throw success percentage of these two parties. This is the independent sample t-test procedure, and it gives that between the players of exactly same height, if their weight differences result in significantly diverse free throw success percentages or not.
The result again confirmed that as the weight increasing, FT% decreasing. The flowing table displays for the players of 6-9, 33 players are greater than 237 lbs and their FT% average is .6439; in contrast the other group consisted of 34 players having less than 237lbs and with .7260 FT% average. And this is significantly higher.
To conclude, we applied the identical procedure this time while selecting same weight players, we split the data according to their height and compared their FT% averages. As it is seen the table below, although longer guys have lower FT% average (.6740), this is not significantly lower than the shorter guys (.7099) statistically (sig. value > 0.05).
All these analysis prove an important finding: the shooting ability is negatively affected by weight but not with height.