Kyle: That's because people don't bother to prove the obvious. Are you honestly suggesting that if you take Golfer A and Golfer B to a variety of places on a golf course and ask them "how far to this?" and "how far to that?", and A is consnstently better than B, that's it's luck?
C'mon, man, that's beyond belief, and certainly beyond the waste of time required to study and prove it false.
Congratulations David, you've proven a coin flip.
The fact is, and this HAS been studied is that people can't deal with number much outside the first combination of simple primes - 2 and 3. Think of the orientation of dots on a die.
2x3 = 6. People can look at those dots and think six. Get much more outside of that and it's 1-6 in various combinations. A 3x3 square is not seen as a discrete "9" but instead as three 3s, for example.
On the golf course, the only standardized size is the cup and for the most part, the flagstick, be it 7 feet or 5 feet. We can easily estimate a 3 foot putt, and even up to 10 feet based on the size of the flagstick and relational. Get outside that, and the distance estimation becomes more and more varied until it's statistically insignificant.
As for your baseball and basketball analogies. Again, we are given discrete distances by which to gauge distance. The bases are 90 feet apart and most humans are able to double and triple that distance to gauge something up to 270 feet. We are then given the confines of the outfield as an outer limit. Same goes for Basketball... do you think that announcers constantly mentioning 17 foot shots are using the floor markings or their own skill at estimation.
Humans are wired to be able to divide and conquer given and upper and lower limit. And they'll divide into the fundamental primes: 1, 2 and 3.
This is the artilleryman's dilemma, and you better believe those guys were using math, calculation and distance gauging equipment back in the 18th century.
Familiarity with a golf course allows us to construct upper and lower bounds for distance gauging, but it's not a skill so much as rote memorization.
Stick the same golfers in an empty field and ask them to gauge distances and you'll see.