The place to start regarding this issue is that the right shoe can make a difference in your performance. However, the benefits of wearing the correct shoe are very limited. There is no magical glass slipper. A shoe is not going to allow you to jump higher or run faster than your muscles dictate. The idea of enhancing performance with the right shoe is better put into perspective by trying not to impair performance with the wrong shoe. The shoe definitely does not make the player. We have all seen pitiful athletes sporting Jordan's shoes. The following benefits should be considered when purchasing a pair of shoes.
1. HOW THEY FEEL AND HOW THEY MAKE YOU FEEL: If it is not comfortable just forget about it. A comfortable shoe is probably the most important consideration when purchasing footwear. If the shoe is uncomfortable and not shaped to your foot, or even the wrong size, it is going to be nothing but a distraction. You want the shoe to be snug fitting, but not smothering and constraining. The shoe should feel like an extension of your foot. Also consider how a shoe makes you feel. This is definitely an intangible but if the shoe makes you feel like an all star, the placebo effect (which is very real) is is going to give you a confidence boost. If you feel like a geek in your shoes, it is not going to help. Insoles can go a long way to add comfort to a shoe. Look for a firm but padded insole, preferably one that you can customize to form fit your foot. Stay away form the super cushy insoles made of gel. They will just make your foot slide around inside your shoe.
2. HIGH TOPS FOR ANKLE STABILITY MYTH: If you like high tops fine, but don't choose them on the basis of preventing ankle sprains or stabilizing a weak ankle. A high top is not going to prevent your ankle from rolling. That is a myth. If you have ankle problems get an ankle brace. You should also strengthen your ankle, as well as retrain with unstable surface training. A strong and reactive ankle is your best bet to achieve ankle safety, not high tops. Those will only give you a false sense of security.
3. LIGHTER SHOES HELP SPEED, QUICKNESS AND VERTICAL MYTH: Most shoes are 11 - 20 oz. (.6 - 1.2 pounds). Frankly the weight is not going to make a significant difference In your performance. You achieve more weight advantage if you go to the bathroom before you compete. There is always a newer, lighter shoe available. You may be able to feel the slight difference in weight, which may make you feel lighter and induce a nice placebo effect, but as far as physics are concerned, the additional few ounces are not going to make any performance difference. But if the shoe makes you feel light and fast, go for it.
4. THE WIDE VARIETY OF GIMMICKS: The wide variety of these kinds of special features in shoes has gotten a lot of athletes pretty excited for instantaneous results. Obviously these do not deliver or we would be seeing the amazing results all around us. The reactive ability of a jumper or sprinter does not come from their shoes. It comes through the entire muscle and tendon complex of the associated muscle groups which most definitely can be improved through proper training. Even if a shoe were capable of off the charts results, if your body is not capable of supporting the extra boost, it will all fail. There is no shoe that will turn you into an amazing leaper.
5. CARBON FIBER SHANK PLATE MARKETING TACTIC: Some companies tote a fiber plate in the sole so that your "toe off" is not weak. In theory this allows you to push with your entire foot and not have to worry about the role of your toes. This is a great concept, but shoes already have a large slab of padding and support on the bottom. The idea of additional support aside from the soles that all shoes have, is a marketing tactic that has virtually no impact on jump reach. The point is not to sound negative here. A great pair of shoes is a solid asset. But hundreds of special shoe gimmicks have come and gone. What is important is to realize is that the benefits from shoes are limited to comfort and the placebo effect. Instead, athletes need to depend upon a sound training program, not magic shoes, to make serious improvements. If the shoe fits, wear it. Than go out and engage in a training system that will in fact grow your vertical.