Maybe you can try extend wear contact lenses or GP contact lenses. I heard those contact lenses are available for wearing during sports activities. From this point, you will be safe to wear them while playing basketball. But regular soft contact lenses are not recommended using for sports for some reasons. So, you shall be careful when you choose contacts for wearing during playing basketball.
I do not recommend you to wear contact lenses. Although you do not want to wear eyeglasses, you can wear sports goggles with prescription lenses that will make you very cool and offer you vision correction and eye protection. If you do wear contact lenses during palyi9ng basketball, your sweat will affect contact lenses and your vision maybe get blurry, which may lead to some unexpected damage. So, you are suggested to wear sports goggles. They are very cool.
You can wear contact lenses while playing basketball. Because of their soft lenses, it will be safer than the normal eyeglasses. As you know that they have many advantages. First, it will not get infected easily. Second, they will not slide down your nose. Also, they can not make you get hurt like the eyeglasses which are easy to break. In other words, contact lenses can free you from some of the problems associated with eyeglasses. On the other hand, you should pay attention to your sweat which can do harm to the contact lenses.