LeBron’s right, guys… the sleeves affect shooting

Those sleeves?

We mocked LeBron for his public disapproval of the sleeved jerseys, but they really do have a negative impact on field goal percentage.

Look, I don’t know who’s pushing these sleeved jerseys. They are so stinkin’ ugly that I can’t imagine fans are snapping them up at the outrageously inflated prices that teams and the NBA charge for replica merchandise. Maybe some guy at the NBA office is just tired of basketball being the only team sport where armpit hair is a routine part of the experience.

Anyway, here’s the “executive summary” that precedes a bunch of dry statistical explanations:

Based on a preliminary analysis of data from last season, sleeves were almost certainly responsible for a significant decrease in two point field goal percentage at Golden State. Sleeves were probably responsible for a less pronounced reduction in two point field goal percentage at Boston, and they appear to have had no meaningful impact on Orlando’s two point field goal percentage.

Conversely, the sleeves may have produced a small improvement in three point FG percentage which, however, did not offset the decrease in two point field goal percentage for Boston and Golden State, and barely offset the decrease with Orlando. Most of the terms in the table below are self-explanatory. One is not. Confidence level is the likelihood that the change in field goal percentage is not a coincidence.

Here are the numbers:

Conclusions

I came into this study assuming that the sleeves would have a negative impact across the board, and that the effect would be most noticeable with three point shooting. My assumption was that basketball players rely on finely tuned ‘muscle memory’, and that the restriction on movement imposed by these rather tight sleeves would alter the shooting motion enough to cause a noticeable decrease in long distance shooting.

However, the data clearly do not support that conclusion. An alternate hypothesis, assuming that this improvement in 3pt shooting holds up over time, as more data are gathered, is that the sleeves enforce a more ‘correct’ shooting form, which, if borne out, might suggest that a variant of this sleeved jersey would be beneficial for guards and wings to wear under a conventional jersey.

The conclusions that the data do support are that the sleeves almost certainly affect different players to different degrees, and that the effect is significantly different between two and three point shot attempts. This suggests that the restriction that these sleeves impose is more pronounced on shots taken near the basket, as there is no reason to suppose that the sleeves would exert a meaningful difference between “long twos” and three point shots, as the form used to shoot both is to all intents identical.

It’s possible that the sleeves are more restrictive on “big men”, either because they are not designed to accommodate the average “big man” physique, or because their range of motion while shooting the ball differs too greatly from a conventional jump shooter.

Based on the results returned so far, it’s my judgment that teams would be well advised to scrap the sleeves. When the best result is a thinly supported one point improvement for a lottery team (Orlando), the experiment, in my opinion, should be abandoned. Looking at 23 games of data from three very different teams, the evidence skews overwhelmingly negative.

The best argument for keeping the sleeves would be negligible impact for all three teams. The second best argument would be improvements in field goal percentage for a team or teams that would offset declines elsewhere. Neither of those scenarios played out. A team playing in sleeved jerseys, based on preliminary analysis, is at a disadvantage.

Methodology

(I put the conclusions before the methodology because you guys probably don’t want to read this)

Sample Sizes

In 2014/15 Golden State played 6 games with sleeves. These games were Saturday home games. Boston also played 6 home games with sleeves. These games were randomly distributed with respect to the day of the week and were tied to significant events in Celtics history. The Orlando Magic played 12 home games with sleeves. These games were also distributed randomly.

Boston’s sixth sleeve game (tied to the anniversary of “Havlicek Stole The Ball!”) was played against what was, to all intents and purposes, Cleveland’s bench. I did not include this game in the analysis as the Cavaliers all but forfeited it before tip.

For Boston and Golden State, each sleeve game was compared with four ‘adjacent’ home games. Where sleeve games were so close together that overlap would occur, I selected home games that were farther out, in order to have a “control” group that was four times larger than the sample being tested.

Since more than a quarter of Orlando’s home games were played with sleeves, I used all of their home games without sleeves as the control group.

Thus, the control and test groups were:
Golden State: 24 control, 6 test, 30 total (73% of all home games analyzed)
Boston: 20 control, 5 test, 25 total (61% of all home games analyzed)
Orlando: 29 control, 12 test, 41 total (100% of all home games analyzed)

Impact Formula

The impact in terms of points per game was obtained by this formula:

(average 2 point field goal attempts, all games) * (average deviation due to sleeves) * 2 (pts) * (probability that this result is statistically valid) + (average 3 point field goal attempts, all games) * (average deviation due to sleeves) * 3 (pts) * (probability that this result is statistically valid)

Results were rounded to the nearest integer.

Statistical Significance Testing

Results were analyzed using Welch’s t-test, a variant of the Student’s t-test which takes into account sample groups of different sizes. Hey regular RedsArmy.com readers. Are you still with me? Cool. You might enjoy this bit. The “Student’s t-test” has nothing to do with students. It was invented in 1908 by a guy named William Sealy Gosset, who was a chemist working for Guinness. Yep. That Guinness. Claude Guinness wanted biochemists and statisticians to help improve their product, and the t-test was developed as a cheap way to monitor the quality of stout. It’s called the “Student’s t-test” because Gosset published it under the pen name “Student” because Claude didn’t want his employees publishing the results of their research (NB: I summarized most of this from a Wikipedia article).

Anyway, the whole purpose of the t-test is to take two samples and determine if the differences between them are significant. I’m not going to go into the maths here, as you probably don’t want to know them. Suffice to say that this is a test that is used to, for instance, determine if a reduction in tumor size is just a statistical fluke or due to a cancer medication. Or in this case, to determine if these sleeves really are as bad as they look. It’s probably not as valuable of a contribution to our collective knowledge as cancer research, but hey, I’m doing the best I can with what I’ve got, okay?

The standard threshold used to declare the results of a t-test analysis as valid in the social sciences is 5% (that is, a 95% or better probability that the effect is not coincidental). According to the data we have for this analysis, that threshold is only met by Golden State. However, this isn’t a peer-reviewed publication and, in my opinion, the results are solid enough to justify rethinking something as trivial as sleeved jerseys, as the consequences of abandoning them are essentially meaningless. In other words, “better safe than sorry.”

Assumptions and Limitations

In order for the t-test to be valid, the underlying phenomena needs to follow a bell curve (that is, a normal or Gaussian distribution). Per game field goal percentage does tend toward a normal distribution in most circumstances.

I did not control for the quality of opponent in sleeved vs. non-sleeve games. It is my assumption that for Boston and Orlando, the difference is negligible. Golden State, on the other hand, was served up a most remarkable collection of patsies for its Saturday home games. Not once did the Warriors play a 2014/15 playoff team, and they actually played the Timberwolves twice.

My assumption with respect to Golden State’s below-average competition in sleeve games is that, if anything, it causes the effect of the sleeves to be understated. As supporting examples, the best two point field goal percentage Boston recorded in a sleeve game was against Philadelphia, and Orlando’s second best sleeve game field goal percentage also came against Philadelphia.

For Boston, I did not control for the rather incredible variation in personnel between games. My assumption, since the sleeves appear to affect players differently is that a high variability of personnel would mute, rather than amplify, the effect.

Only home games were analyzed, in order to eliminate any noise from a discrepancy between home/away field goal percentage. However, by analyzing only home games, there were occasions when the games in the control were some distance in time away from the sleeve games when Boston and Golden State games were analyzed.

A larger sample size could have been obtained by analyzing all home games for each team, but due to the significant changes in Boston’s roster during 2014/15, it did not seem wise to include full season statistics, given the fact that only one of the five sleeve games analyzed was played after the trade deadline. Golden State’s sample size was limited to provide a valid comparison to Boston’s.

Anyway, if you’re still with me, I’ve got the data all piled up in an Excel spreadsheet. If you’d like to have it, contact me via twitter, and I’ll get it to you. If you’re with 538, no, I don’t want to work for you. I don’t like your site or your philosophy of abusing formulas to make ridiculous claims. If you get the data and have the time to spend controlling for all sorts of things (like the opponents’ defensive rating, etc.), knock yourself out. I’ve already spent probably ten hours on this and I’ll stand by the validity of that effort, as limited by the caveats above.