Many physical therapists and professional basketball coaches believe that Kinesiology tape "is designed to facilitate the body’s natural healing process while providing support and stability to muscles and joints without restricting the body’s range of motion". The same belief is apparent in other sports such as tennis, athletics, gymnastics, but is less prevalent in soccer or swimming. I am not aware of any  evidence gathered from random clinical trials that corroborates the above belief, but if players using Kinesiology tape are able to participate in basketball and other sports and compete competently according to the perception of their coaches, then surely it is worth while using Kinesiology tape. 

Hi Charlie.

Here are some articles research that I think may interest you:

• Nakajima, M. A., & Baldridge, C. (2013). The effect of kinesio® tape on vertical jump and dynamic postural control. International journal of sports physical therapy, 8(4).
• Chaney, C., Hirayama, G. M., Mendoza, T. E., Schmitt, D. M., & Janini, S. (2015). The effects of Kinesio™ tape on vertical jump, 20-m sprint, and self-perception of performance in high school basketball players. Current Orthopaedic Practice, 26(4), 420-424.
• Wohltman, H. (2015). The Effects of Kinesio Tape on Sports Performance: Vertical Jump and Shuttle Run Performance in Women's College Basketball Players.

Please, upvote if you think that these information has been useful.

Interesting question, maybe tactile feedback from the skin can help reproducibility of U.E. movement via skin receptors. Here are some references that may provide you more information. Please see the following;

Kinesio® Taping in Stroke: Improving Functional Use of the Upper Extremity in Hemiplegia Ewa Jaraczewska and Carol Long Topics in Stroke Rehab, 2015

Influence of a compression garment on repetitive power output production before and after different types of muscle fatigue

William J. Kraemer et al. Research in Sports Medicine 1998

The Roles of an Upper Body Compression Garment on Athletic Performances

  David R. Hooper et al. J. Strength and Conditioning Research, 2015

These results demonstrate that comfort and performance can be

improved with the use compression garments in high level athletes is most likely

mediated by improved proprioceptive cues during upper body movements.