This is a definition problem.
Since I am from Greece I think of these words from the greek grammar's and etymology's perspective.
According to the ancient greek etymology, âthlos “contest, struggle” (
source)
Pool doesn't seem like a struggle to me, but it is a contest...
Even by modern etymology, "(άθλημα είναι) η ατομική ή ομαδική δραστηριότητα που αποσκοπεί στη γύμναση του σώματος και περιλαμβάνει συχνά τον ανταγωνισμό για την επίτευξη καλύτερων επιδόσεων" (
source), which loosely translates to "athlema is the individual or group activity that aims to excessive the body and frequently includes competition to achieve better performance" (sorry for my mistakes)
So I guess it is half and half again.
To me, pool players aren't athletes. Pool is not a sport in my mind. BUT, I can't deny that other activities, that I can see similarities with pool, are (and were) considered sports. Archery is the best example I have. Archery does not include running or other movements that are considered as "athletic", but require extreme precision and very good eye-arm co-ordination. Archery was in the Olympics since the beginning, so if it was good enough for them, who am I to argue otherwise?
I guess it's a matter of where do you draw the line. As others pointed out, a healthy body sure does help being precise.. but it's not a requirement.
I guess pool is 50% sport.