So, the main reason why a lot of people have the habit of wearing a watch while playing - is simply this, taking off the watch, there is a high risk of loss. I can tell you, a lot of watches disappear in locker rooms at country clubs. Who knows, maybe the steward boys have keys to all the lockers? This isn't a very satisfying answer. The military mentality is also to carry as much as you can on you - and the watch was seen as a very personal tool. In the 1930s, this was the dawning of wristwatches and time when men still often wore pocket watches - and they would even wear pocket watches while playing many sports!