Tuesday, December 18, 2012

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.

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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.

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"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.

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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?

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At Wednesday, December 19, 2012 8:58:00 AM,  aweb said...

I'm a pretty good golfer, and I can't imagine any golfer arguing against the idea that luck is the primary driver of any hole-in-one (I still haven't had one...) or similar hole-out. Long putts would be the same.

I think people don't like the luck argument for free throws because it is possible to perform at such a high percentage, that it seems like luck has less to do with it. I can shoot free throws at about 75-85% (not in game conditions), and if you could freeze time right after I release each one, I could give you a pretty good estimate of make probability - that is, I know when I've definitely (95%+) made one, and I know when I definitely missed one (<5%), and could probably do a good good guess in between too. The "luck" involved seems entirely under my control, even though I can't decide when I'll make a perfect stroke and when I'll make an awkward one, no matter how hard I concentrate or how much I practice. Of course, there are people who can make 99%+ of free throws (not in-game), so again, it seems even less like luck.

In golf, I can tell you when I've definitely missed an iron shot (>99%, only chance is a lucky bounce off an unseen rock/sprinkler), but even a shot which seems "perfect" has a <1% chance, so it always seems lucky.

It's human nature to blame yourself for failing at something that seems possible to do perfectly (free throws), and credit luck when something rare occurs, even though they are opposite sides of the same coin. I'm not sure where the breakeven spot is for crediting luck mentally...much less than 50% I think. Getting a hit in baseball doesn't seem lucky at the time, so probably below 30% at least.

At Wednesday, December 19, 2012 9:43:00 AM,  BMMillsy said...

The Iron Byron thing is very neat, thanks for that link Phil.

I always considered Tiger Woods the greatest, most dominant athlete in any sport namely due to the reasons you list here. His ability to minimize randomness on a golf course during those wonder years goes above and beyond anything we have seen in any other sport. The minimization of luck was the best argument (I thought) I could come up with for why he was better than the likes of Bonds, Ruth, etc.

I never really ran into anyone that said "there's no luck involved" before, but I'm sure they exist!

At Wednesday, December 19, 2012 11:07:00 AM,  Nate said...

I think that 'luck' and 'talent' aren't necessarily the best terms.

Let's assume - for the sake of discussion - that there's some technique out there that's superior to what players are using today. (For example Rick Barry's underhand method.) Now, do we call players' using the standard overhead technique bad luck, or bad talent?

There's certainly a luck factor, but it's not at all clear how big it needs to be.

At Thursday, December 20, 2012 12:12:00 AM,  Steve said...

Really enjoy the discussion of the proportions of luck and skill in results. I've been reading Michael Mauboussin's new book "The Success Equation" and it is entirely concerned with this topic (see here: http://www.amazon.com/The-Success-Equation-Untangling-Investing/dp/1422184234/ref=sr_1_1?ie=UTF8&qid=1355979742&sr=8-1&keywords=michael+mauboussin)

@ Aweb - I think there is also a physiological limit in terms of shooting a free throw (or hitting a golf/tennis ball etc.). The body simply cannot process what the mind is telling it to do without introducing some variation. The amount of variation can be minimized by intense and prolonged practice (hence your 80% rate, Steve Nash's 90+% and my 45%) but even the most skilled athletes will still top out short of 100%.

All time FT % leader Mark Price ran off 3 seasons from 90-91 to 92-93 at 95%, but even he missed some. His career percentage is just over 90%. With

At Thursday, December 20, 2012 9:11:00 AM,  aweb said...

@ Millsy - Tiger's best runs are a great example of how much luck is involved in golf too. Tiger for several years was always the best player in the tournament, by a fair margin (I think his stroke averages were 1 better than the next best some years, a massive gap in golf). Yes, it was almost unprecidented for him to win 50% of the time, but he also lost while being the better player 50% of the time. On a tournament basis, I think it's fair to say luck in golf is worth 3-4 shots a tournament even for the best players, and probably much more than that. Wind is only a part of it, and there are ball striking techniques to minimize the effects of the wind as well.

Minimizing luck's influence is crucial in golf, because you are far more likely to lose a stroke to 40 feet of distance (bunkers, water, trees, etc..) than you are to gain a stroke (hole-out, coming close enough to gain significant putt make %). Announcers in golf are often obsessed with this, always talking about "perfect shots" that are 15-20 feet away from the hole. Knowing how to best minimize luck's influence is an important golfing skill for top players.

@Steve - that's why I mentioned "not in-game" for the top end - fatigue and pressure certainly lower the top performance available. Three pointers are similar at a lower level - in game, 55% or so seems to be about where players top out for a single season, but in shooting practice, I think a lot of the best guys can make 70-80%.

The inherent mind-body variation is part of what I was getting at with things seeming under my control, even when they aren't. External factors always seem like luck when they don't go as expected.

@Nate - I don't think using the wrong technique is bad talent or bad luck, it's just the wrong method. High jumpers pre-flop technique weren't less talented, they just hadn't optimized that talent. That's "bad luck" in a larger historical sense, but not the same type of bad luck we're discussing here, IMO.