What are some obvious and/or some not-so-obvious connections between geometry and sports? ~

The shape of the baseball diamond

The entire basketball court has geometry everywhere.

When you sit at just the "right angle" while watching women's volleyball, you can see "acute" "obtuse" "point" or two  (if you know what I mean).  For those who want to do higher math, create a geometric series using the given "circles".   One series can represent the distance the "circles" travel when falling, and another can represent the distance the "circles" travel when bouncing back up.  And it you don't get too carried away with the math, you might even glimpse a "closed curve" or two. 

I'm not particularly good at either one. Or interested, for that matter.

I can only see the physics. Sorry.

Pool. Lots of angles to figure out. 

Making a safe catch in cricket. I suppose it also works with baseball. A ball coming off a bat will always travel in the shape of a parabola (offset slightly by wind and air resistance but this effect is less noticeable than with, say, football or soccer due to the density of the object), and a fielder unconsciously solves the equation in his or her head to put his or her hand in the exact right spot to catch it before it hits the ground.

Curling: I have watched but never played it. The scoring instructions' diagrams I saw, resembled something from a geometry text-book.

Bowling (green): precise aim and force in dead straight lines. The bowls themselves are not spherical but have two, opposing, slightly flattened faces which with their mass, gives them a gyroscopic effect like a flywheel.  

Snooker and Billiards: inertia, momentum and the laws of reflection.

Any ball game: any projectile including a thrown or batted ball follows a parabola.

Clay-pigeon shooting: tracking a projectile on a parabolic trajectory, at velocity changing by square laws; though the spread of shot raises your chance of hitting it.

Sailing: resultants of triangles of forces, plus the properties of the aerofoil.

;;;

While more games than sports, Skittles and Darts:

Skittles needs careful bowling aim and force to avoid the balls simply going through the gaps between the pins, and to knock over isolated pins on the second and third throw of the hand. Further, skittle-alleys are never exactly the same length as each other, so if playing in a league team, being an expert on your home alley may not guarantee success in away games. 

Darts players become adept at mental arithmetic consisting almost entirely of factors and subtraction.

(Someone once told me of a cruel trick inflicted by good darts players of bad morals on tyros by playing for money or drinks, but offering to double the novice's score each round. Since the winner is the one who finishes first by leaving exactly 0 to throw, and there is no 0 on the board, the naïve beginner may make impressive progress early in the game, but cannot win.)