You're exactly right, in some sense: it's worth it to go for an extra ball if your expected points are higher if you do.

Assume that with our extra ball we play the strategy we would've played this ball instead, say. (I.E. this is the last extra ball available through this route)

Then our points for the go-for-extra-ball strategy are

Points(going for extra ball)+P(get extra ball)*Points(not going for it)

while our other strategy gets us

Points(not going for it)

Thus, we should go for it if

P(get extra ball) > 1- Points(going for extra ball)/Points(not going for it)

Where "Points(going for extra ball)" are the expected points on the ball where we try to get the extra ball, which is usually much smaller than whatever else we could be doing--if we drain while doing so. If we don't, though, we can add the points from the "standard" strategy thereto.

Um. That implies that Points(going for it) ~= Small number + P(get extra ball) * Points(not going for it). If we assume that scoring is linear, or doesn't carry from ball-to-ball, that implies after some algebra that we go for it if

P(get extra ball) > 1/2 * (1 - points we get while getting extra ball / points(not going for it))

Which means if you can get an extra ball more than half the time, you should drop whatever else you're up to and go after it.

(Apologies for the math, I'm a math dork)

Sure. "Expectation values" are tricky things to estimate, hence the conclusion at the bottom: if you're 50% to get the extra ball, on average you'll do better going for it.

Note that I'm completely ignoring extra balls for score, because I've never liked games set-up that way.