Throughout the night, the body goes through 90-120 minute cycles of REM, or Rapid Eye Movement, sleep. During these stages, muscles are completely relaxed and do not move, while dreams generally occur. Through an entire night of sleep, especially during these REM cycles, seemingly countless processes take place, effecting both the mind and body.
The first benefit to the mind is memory consolidation, which is essentially the concreting of skill, information, and muscle memory. So, if you are working on your basketball skills, without sufficient restorative, deep sleep (periodic one-hour naps are not considered deep sleep) is required (howsleepworks). Also, focus and decision making are notably hindered the following day, and extreme sleep deprivation is proven to cause mental effects equal to being legally drunk (CBS). Finally, sleep deprivation can lead to higher cortisol levels, a hormone that considerably raises stress in most humans.
Effects on performance are also very significant. HGH, or human growth hormone, is released as one sleeps (Sparta). HGH is associated with the regeneration of muscles at a cellular level, which means that recovery and muscle synthesis peak during sleep. It has also been proven that not only does a lack of sleep disallow the body to recover from the previous day's workout(s)--which in effect builds muscle, skill, etc--but the next day's as well. Additionally, it puts one at risk for higher fatigue in the following days (NSF).
In a renowned study by Stanford researcher Cheri Mah, the sleep of 11 elite college basketball players was extended. By the end, "the players ran faster 282-foot sprints (16.2 seconds versus 15.5 seconds) than they had at baseline. Shooting accuracy during practice also improved: Free throw percentages increased by 9 percent and 3-point field goal percentage increased by 9.2 percent" (Mah). This can also be viewed through an NBA lens, where players and teams such as the Golden State Warriors and Andre Igoudala are taking sleep analysis to the next level. Research is actually "beginning to show correlations between sleep debt and statistical production, and some studies have begun to connect the dots between sleep and injury rates" (CBS). For example, Igoudala's stats with eight hours of sleep did the following:
+29% in points/minute
+9% in free throw percentage
+2% in three point percentage
-45% in fouls committed
-37% in turnovers committed
Obviously, there is a strong correlation there between decision-making, motor skills, and basketball skill.
Sometimes, it is difficult to get a full, good night's sleep. So, how can you?
Primarily, alter your environment to your advantage. Studies have shown that a dark, quiet, and cool environment results in better and more sleep (according to ninds.gov, "people lose some of the ability to regulate their body temperature during REM, so abnormally hot or cold temperatures in the environment can disrupt this stage of sleep"). Also, eating inflammatory foods, "such as those containing trans fats or those fried in toxic, hydrogenated oils," prior to bed may harm sleep quality (CBS).
Other ideas include sticking to a relatively regular sleep schedule--going to sleep and waking up at around the same time every day--as well as tracking sleep as a means to ensure proper sleep, the number of which alters for all, but is generally above 8 hours. Without these 8 hours, you lose the most important part of the night! "REM sleep, necessary for cognitive repair and decision-making, occurs in the latter stages," generally the last two hours of an 8-hour night of sleep.
You can track your sleep with apps such as sleep cycle, or wearable devices such as Jawbone technologies (jawbone.com/support/articles/000008210/tracking-sleep-up24).
In the words of former Navy Seal turned NBA sleep advocate Kirk Parsley, "we live in a culture that doesn't value sleep. It's often associated with laziness, lack of motivation, all sorts of negative connotations for somebody who sleeps excessively -- and all sorts of accolades and idolization for people who claim to sleep three or four hours a night. You have to get past that prejudice." Even LeBron James, Kevin Durant, and more attribute much of their success, especially in recovery from thousands of minutes played, to sleep.
So, as long as you're working sufficiently on your skills and performance, sleep can take your game to the next level.