I think that the 2 main factors behind the age distribution in professional sports are:
1. Athleticism declines with age and athleticism is a major contributor to being good at sports. You can see this in the pattern of which players do stick around into their 30s—they are often players who have a role that is less dependent on athleticism (e.g. in the NFL kickers, punters, quarterbacks, and long snappers, in the NBA very tall big men) or star players who were much better than baseline in their prime so they continued to be useful even when they weren’t as good as they used to be. (Injuries are a component of this—one way that a person’s athleticism can decline is if they get an injury that they never fully recover from; also older people tend to recover more slowly from injuries and playing through a nagging injury is another way of having reduced athleticism.)
2. Option value for young players: Young players can get a chance on a professional franchise when there’s uncertainty about how good they are or will become, based on the possibility that they will turn out to be good enough to be useful. Players who are out of the NBA or NFL in 2 years are usually players who were never quite good enough to play at that level, but who got a brief chance to be on a roster (or multiple rosters) based on the hope that they were before it became clear that they weren’t good enough.
I think that the 2 main factors behind the age distribution in professional sports are:
1. Athleticism declines with age and athleticism is a major contributor to being good at sports. You can see this in the pattern of which players do stick around into their 30s—they are often players who have a role that is less dependent on athleticism (e.g. in the NFL kickers, punters, quarterbacks, and long snappers, in the NBA very tall big men) or star players who were much better than baseline in their prime so they continued to be useful even when they weren’t as good as they used to be. (Injuries are a component of this—one way that a person’s athleticism can decline is if they get an injury that they never fully recover from; also older people tend to recover more slowly from injuries and playing through a nagging injury is another way of having reduced athleticism.)
2. Option value for young players: Young players can get a chance on a professional franchise when there’s uncertainty about how good they are or will become, based on the possibility that they will turn out to be good enough to be useful. Players who are out of the NBA or NFL in 2 years are usually players who were never quite good enough to play at that level, but who got a brief chance to be on a roster (or multiple rosters) based on the hope that they were before it became clear that they weren’t good enough.