Golf and luck
Given a player's talent, I routinely think of the results of a series of basketball free throws as "luck". That is, if the player has worked to become an 80% talent, whether he makes the current shot (80 percent chance) or misses it (20 percent) is just random, as if he flipped an 80% coin.
Some people don't like that idea ... they feel that because it's all within the player's control, it's wrong to think of it as "luck" or "random". I don't agree, but I won't argue that here. What I want to do here is try out a different example, one that I can use instead of free throws, that maybe we can all agree on.
So ... how about golf shots? Those aren't completely under a player's control, because of wind.
A difference in wind speed of only about 2 m/s (4.5 mph) is said to affect the ball's distance by around 15 meters (49 feet) (.pdf). That's pretty big. Pros sink 20-foot putts only 14 percent of the time, as compared to 38 percent for 10-foot putts ... and that's only a 10 foot difference, not 49 feet.
Now, you could argue that golfers should take the wind into account when swinging. And they do. But, wind changes while the ball is in the air, and it's literally impossible, from the ground, to predict how the wind will change. If 2 m/s wind is 15 meters of distance, we can guess that 0.2 m/s of wind is 1.5 meters of distance. If there's an unpredictable 0.2 m/s change for half the time the ball is in the air, that's 2 to 3 feet. That's still a fair bit. Moving a putt 2-3 feet closer is a big deal, especially when you're already close.
Or ... suppose a golfer gets a hole in one. It's reasonable to assume that if the wind had been even slightly different, in any direction, the ball wouldn't have gone in.
When does the ball go in on a tee shot? Consider where the ball would have landed if there were no hole. Let's say that if that spot is, maybe, 12 inches behind where the hole would be (in the line of trajectory), and four inches left to right, it would have gone in. That's 0.33 square feet. Let's round it up to 0.5.
If the wind makes an unpredictable difference of, say, 3 feet each direction, that's a circle of radius 3, or about 28 square feet.
28 divided by 0.5 is 56. So, because of wind, there'd be only a 2% chance the ball would go in if you did the exact same swing again.
That is: if you get a hole in one, you hit a 50-to-1 longshot, by luck. That's even if you're a perfect golfer in every respect.
Of course, the better a golfer you are, the more holes-in-one you're going to get. The argument is not that it's *all* luck -- the argument is that there's *some* luck.
Holing your tee shot is like winning the lottery. I'm not a very good golfer, but my lottery ticket might still come in someday. Tiger Woods, because of his skill, holds several thousand tickets, so he'll get lucky much more often.
"Iron Byron" is a machine that swings a golf club, exactly the same way each time -- or at least, as close to "exactly" as a machine can get. But the balls it hits don't land in exactly the same place. This site says that, after multiple swings, the pattern of balls was 15 feet by 8 feet for cavity-back clubs, and "about 1/4 the size" for the club they were developing.
For the purposes of this discussion, that's close enough to the 3-foot radius I guessed at.
You'd think what the machine did would be the limit of human performance. Of course, you might think humans can be more precise than machines, which seems unlikely -- but feel free to argue it if that's what you think. Keep in mind, though, that the human is always a different distance from the pin, and has to adjust his swing every shot! On the other hand, the machine doesn't have to figure out how hard to swing, because it doesn't matter.
So the human has to be *more* perfect than the machine, to get the same results.
Both these arguments -- theoretical, and empirical -- seem to imply that non-human forces have an effect on a golf shot, an effect that's significant enough to affect who wins a tournament. In other words, that there is at least some "external" luck in golf.
For those of you who disagree that there's luck in free throws, does this argument convince you that there's luck in golf shots? If someone hits a hole in one and wins a PGA tournament by two strokes, would you be comfortable agreeing that luck had a lot to do with it?
If not, why not?