Just as there's a general factor of intelligence, coaches tend to talk as if there is a g factor in sports. In America today, they tend to call it "athleticism."
The way the word is used can be a little surprising: e.g., eye-hand coordination is not considered part of athleticism. Quarterback Michael Vick has "athleticism" but Peyton Manning, despite his superior throwing ability, does not. Cornerbacks have lots of athleticism, but placekickers do not. Centerfielders have athleticism but third basemen do not. Willie May had athleticism, Brooks Robinson was a great fielder. You might recall Brooks Robinson diving flat out over third base to spear a ferocious one-hopper, then scrambling to his feet to fire a throw to first base, but, well, that's just not athleticism.
Breaking it down, it appears that "athleticism" consists of footspeed, leaping ability, agility, ability to improvise unexpectedly (e.g., fake left, go right), ability to react, and hitting ability (in the football sense, not the baseball sense). One reader says "athleticism" is used to mean "lower body springiness."
One interesting question is whether "athleticism" exists as a general factor much like g in IQ. I sometimes wonder if it's not just a euphemism for "black."
Anyway, anyone interested in "multiple athleticisms" vs. "a general factor of athleticism" could take a look at the data from NBA and NFL Draft combines. For example, here are the numbers on the 2007 NBA draft hopefuls on two kinds of leaping ability, bench press, lane agility, and 3/4 court sprint. You might be able to extract something interesting here, although range restriction is severe -- all these guys would beat you 20-2 in a one-on-one game.