I'm 13 years old, and I'm 160 cm tall (that's 5 foot 3 inches for Americans). What do you think I will be when I reach age 16? I do quite a lot of sports too.
How tall is the average male supposed to be at age 16?
Height is affected by a large number of variables, making any prediction a guess. The main factors are your genes and the nutrition you have received. Therefore to make an educated guess at your adult height, I would need to know your mother's height and your dad's height. This would then give a rough estimate as to what height genes you inherited. One formula says to add your mom and dad's heights, add 13 cm (that's roughly 5 inches) and divide by 2. (Girls have to subtract 13 cm or 5 inches in this formula.) This gives you a rough approximation for your potential height. However, the formula is only accurate to plus or minus 13 cm (5 inches). That is quite a spread!
But nutrition plays a big part in your height. Even if you inherited genes that would take you to 183 cm (6 feet), if you did not eat well as a child, you would not necessarily hit your full potential. For example, in the early days of the United States, the average male height was 5 feet 9 inches (175 cm). The average is now 6 feet (183 cm). Most agree that the primary difference is that we eat better than people did in the mid 1800's. Hence, another factor that will narrow down your adult height is how much you currently weigh. Your current weight gives a rough idea about how well you have been eating. Adding it in to the height of your mother and father causes the estimate to be accurate to within 4 cm (1.5 inches) of your actual growth.
Prolong illness will impact your final height because your body is not able to absorb nutrients properly while you are ill.
Unfortunately, the playing of sports doesn't impact your height. It only affects your fitness and build.
One last thing is that you asked about your height at age 16. Few boys have finished growing by the age of 16. The normal age to start puberty is between 9 and 16 for boys and it usually takes 8 to 10 years to complete the physical changes. Hence, without knowing what stage of adolescence you are currently at, I can't predict where you will be at age 16. Most boys hit their maximum height growth rate about 13 to 14 years of age. Dr. Tanner divided adolescence into five stages. Stage 1 is before puberty and stage 5 is adulthood. Maximum height growth takes place in stage 3. If you are able to tell me what stage you are in, I might be able to give a more accurate guess as to your height at age 16.
All of that said, in the United States 160 cm (5 feet 3 inches) is the mean height for a 13 year old boy according to the Center for Disease Control and the National Center for Health Statistics. Assuming you remain at the 50th percentile, at age 16 you would be 173 cm (5 feet 8 inches).
See the Adult Height Prediction page to do your own estimates.