The thought occurred to me the other day that participants in major team sports are called players. We have baseball players, basketball players, football players, volleyball players, hockey players, polo players, badminton players, and so forth. On the other hand, in the more solitary game of golf, we have golfers.
When I began considering the matter more systematically, I decided that it isn’t the solitary vs. team distinction that is important so much as what we call the activity. Golfers golf, but people do not baseball or football or hockey or tennis.
In other words, if the name of a sports activity can be a verb, more likely than not, we call someone engaging in it by the name of the activity suffixed by er. Thus, we have golfer, bowler, curler, swimmer, sailor—this was once sailer, apparently, which now has a different, but related meaning—pole vaulter, etc. On the other hand, we generally don’t have baseballers, footballers, or hockeyers. In team sports, however, we do have pitchers, catchers, fielder, passers, blockers, etc.
Cricketer might seem like an exception, but it turns out—Americans might not know this—that cricket can be a verb. An actual exception is footballer, a name unlikely to be applied to an American football player but something an Australian would call a football player, or, as we would say, a soccer player. (Soccer is not used as a verb, and a soccer team does not consist of soccerers.) If football is ever used as a verb, it must be rare indeed.
I suspect that one could find other exceptions to my general rule. One who races horses is not a horse racer but a jockey (not a jockeyer), someone who jockeys. People engaged in bobsledding are bobsledders, of course, but the person who pilots the sled is a pilot. A person riding a bicycle can be a bicycler but is more likely to be called a bicyclist. One who engages in gymnastics—one doesn’t play gymnastics—is a gymnast.