The vertical jump is defined as the highest point that the athlete can touch from a standing jump, less the height that the athlete can touch from a standing position. The measurement of the jump is flawed if the athlete is permitted to take one or more steps before jumping, as the athlete will convert some of the energy developed in the step taken into the force of propulsion that generates upward lift. Basketball has numerous legends and other urban myths concerning the seemingly superhuman leaping ability attributed to certain players; one such player, former University of Louisville star Darrell "Dr. Dunkenstein" Griffith, was reputed to possess a 42 in (1 m) vertical leap. It is likely that the average National Basketball Association player 6 ft 6 in (1.97 m) or shorter has a vertical leap of between 25 and 30 in (0.63 and 0.75 m); taller and heavier players will usually not be able to jump as high.

Among the hundreds of lessons I learned during my youngest child’s first year of life was this: If you earnestly pursue dunking after your athletic peak years of 18 to 30, give or take, it can be done. You can enjoy what it feels like to dunk. You can even feel it more purely than I did, maybe without needing a lob from a friend, and hopefully without all the hand damage. But you should expect a long, frustrating, demeaning war of attrition that pits mind, body, spirit against the most oppressive, unrelenting opponent of them all: gravity. The sun rises and sets, the tides creep in and out—even taxes and death seem negotiable nowadays—but gravity remains constant, forever pounding our shoulders, stooping us shorter as we grow gray, never letting up—no matter what NASA tweets.
Because of the possible combinations of starting and finishing hands, and raised-legs, there are many variations on the basic under-the-legs dunk—more so than any other.[17] For example, in a 1997 French Dunk contest, Dali Taamallah leapt with his right leg while controlling the ball with his left hand, and once airborne he transferred the ball from his left hand, underneath his right leg to his right hand before completing the dunk.[18] NBA star Jason Richardson has also pioneered several notable variations of the between-the-legs including a lob-pass to himself[19] and a pass off of the backboard to himself.[20] Independent athlete Shane 'Slam' Wise introduced a cuffed-cradle of the ball prior to initiating the under the leg transfer and finishing with two-hands.[21] While a number of players have finished the dunk using one- or two-hands with their backs to the rim, perhaps the most renowned variant of the dunk is the combination with a 360°, or simply stated: a 360-between-the-legs. Due to the athleticism and hang-time required, the dunk is a crowd favorite and is heralded by players as the preeminent of all dunks.[citation needed]

Keep that in mind, and progress slowly. A mini basketball is a little more challenging than a tennis ball, but it's easy to palm and that helps. See if you can get high enough to get your hand over the rim--almost up to your wrist--so you can stuff the mini ball. If you can't throw it down with a little authority, a bigger basketball won't be any easier.
A great summary of what it takes to improve vertical jumping ability Joe. There is definitely an art and science to optimizing vertical jump height. I actually just completed a huge post on the topic of How To Jump Higher which your readers may find complements this post nicely. It is a long read (12000+ words) but for those of your readers who want to learn more about the art of jumping they may find it helpful. Keep up the great work!

The way Arthur J. Daley and the other spectators at the Y felt when Fortenberry dunked—that’s how fans at the Oakland Arena felt on Feb. 12, 2000, when Vince Carter shoved his forearm into the rim and swung there by his elbow. What only the initiated noticed about Carter’s dunk was that if you froze him during his approach, he looked like Bob Beamon. Carter long-jumped some 12 feet, right foot leading the way, before landing for a nanosecond and blasting off into his two-footed ascent.
An important component of maximizing height in a vertical jump is attributed to the use of counter-movements of the legs and arm swings prior to take off, as both of these actions have been shown to significantly increase the body’s center of mass rise. The counter-movement of the legs, a quick bend of the knees which lowers the center of mass prior to springing upwards, has been shown to improve jump height by 12% compared to jumping without the counter-movement. This is attributed to the stretch shortening cycle of the leg muscles enabling the muscles to create more contractile energy. Furthermore, jump height can be increased another 10% by executing arm swings during the take off phase of the jump compared to if no arm swings are utilized. This involves lowering the arms distally and posteriorly during the leg counter-movements, and powerfully thrusting the arms up and over the head as the leg extension phase begins. As the arms complete the swinging movement they pull up on the lower body causing the lower musculature to contract more rapidly, hence aiding in greater jump height.[5] Despite these increases due to technical adjustments, it appears as if optimizing both the force producing and elastic properties of the musculotendinous system in the lower limbs is largely determined by genetics and partially mutable through resistance exercise training.[6][7]
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