The Role of "Luck" in Playing Golf and Having Proper Expectations

[iacas]

On another site, talk rose of two performances in golf:

• Zach Johnson laying up on every par five but winning at Augusta National (and playing the 16 par fives in -12 for the week).
• Tiger hitting driver once in winning at Hoylake in 2006.

The topic actually started with the OP having watched an old British Open where a player played a par five by hitting a 1-iron, laying up with a 7-iron, and then hitting another 1-iron to the green. He lamented how "sad" it was that "course management" doesn't exist much these days.

Ummm, bullshit! Course management exists these days, perhaps more than ever. It's just not what people think of as "course management" because it's not employing the old ways of "managing" the course.

The second post mentioned Tiger in 2006. Someone mentioned playing a par five by hitting a bunch of 7I (for the tee shot, second shot, third shot). Somewhere down the first page, someone said "Great illustration of course management was Zach Johnson at the Masters in 07, where he laid up on all the par 5's." The same guy also said Jean Van de Velde had poor course management at Carnoustie.

No. It probably wasn't a "great illustration of course management." I said:

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Zach was lucky to have performed that well that week. Jean was unlucky to have gotten that bounce off the railing. Zach may have shot a lower score had he been a bit more aggressive, or maybe it was a once-every-15-years type of wedge/putting performance for him that week. He out-performed even his own wedge game that week.

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The same poster replied that "Although why is Zach lucky to win by relying on his wedge/putting game that week, but Tiger not considered lucky to have performed at the Open in 06 at Royal Liverpool not using driver but once? Both did something the rest of the field didn't and won a major."

I replied:

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Zach out-performed his typical performance that week by a good margin (and the weather, etc. depressed the performance of many others). Tiger was an other-worldly iron player, likely the best ever, so his performance was not nearly as far an outlier. And the ball still went 270+ off the tee with irons.

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The discussion goes on for quite awhile after that, with a few trolls trying to finally "beat" me at something (they're still winless), and a few others thinking I'm degrading Zach's performance that week, when in my mind I'm doing no such thing.

My problems with this way of thinking are, basically, that:

• Zach's performance is a very small sample size. Sixteen par fives. Four rounds of golf. If you ran multiple strategies 100 times each, and figured out the results, you could start to see which is the best strategy.
• Zach's performance is a major outlier. He could not have been expected to repeat such a performance very often. His performance relied on much more "luck" than Tiger's did.
• People are looking back at the results and ascribing "credit" when doing so would have to mean looking back at the years Zach employed the same strategy but failed to win the Masters.

Zach, likely employing a similar strategy in other years he played the Masters (a very weak field and the easiest cut to make in all of the majors), had these results:

• 2005: MC
• 2006: T32
• 2007: Win
• 2008: T20
• 2009: MC
• 2010: 42
• 2011: MC
• 2012: T32
• 2013: T35
• 2014: MC

After "validating" his "strategy" with a win, he proceeded to miss the cut in two of the next four, and never finish better than T20 (the year after).

So, how much did his "strategy" contribute to his win? How much did a combination of a better performance and a good bit of luck? What do I mean by "luck" in this sense?

I'll use the graphic from this post:

The graphic positions a Shot Zone that maximizes the chances of the player making a 2 or a 3 from where they lie. Ignore the title on the image, as that's for the other topic:

If you imagine the hole is cut near the brightest area near the middle of the green, you can see that this Shot Zone maximizes the chances of the player getting down in 2 or 3 shots. And yet… five balls end up in the water. A few balls end up in the rough, and some in the bunker.

Yet all the shots are in this player's Shot Zone. I say it's luck where any particular shot ends up. Skill is involved in reducing the size of a player's Shot Zone, as I illustrated in that same post:

Yet that player still dunks two balls! (They also make 2 or 3 with all of the others, basically.)

From the fairway in 2007, Zach averaged 20'9" from 100-125 yards and 17'10" from 75-100 yards. He was a little bit better in 2006, as his results in 2007 tailed off a bit after he won the Masters. He putted pretty well in 2006, too: he made 57.45% of his putts from 8-9' that year and gained 0.659 strokes putting that year (fifth).

Here's the thing, though: you can use the data to construct probabilities of any strategy winning out. You essentially take a strategy of "this club from the tee" and you plot maybe 1000 shots distributed in the way a player's Shot Zone is distributed. From there, you make another decision about where to aim, and from each of those 1000 points, you plot another 1000 points to figure out where they end up. (From there, you likely simplify it a bit and say "okay, from all the shots that ended up inside 3', call those one-putts, the shots from 8-9', give those to him at 60%, the shots in the bunker, call those 2.4 shots to hole out… whatever.)

And if you did that, you could figure out the truly optimal strategy. And the "strategy" could change per hole. Maybe going for a back-right flag on 13 makes sense, and never going for the green on 15 makes sense. Maybe going for the green on 15 always makes sense… if you keep the ball to the right and never chase a flag on the left. And so on. There are nearly infinite strategies one could employ, particularly if you add in weather, etc.

But then you've still gotta hit the shots.

And for any given shot, a player is going to have a Shot Zone. Better players will have smaller ones, but they're still going to be distributed around that Shot Zone. Good players have a somewhat normal distribution (bell curve) of shots in the Shot Zone - shots are more clustered in the middle, but it's also a function of being a smaller area, so that "PGA Tour average" is often not too far off from the "median" value, which as Mark Broadie says is a slightly better way of looking at things like this. The median describes a truly average shot, while the "mean" (or "average") can be pulled by a few exceptionally bad or good shots.

I describe where the actual individual shot falls as "luck." You could call it "randomness" too but most people consider "luck" to be good or bad, while "randomness" is often thought of as somewhat neutral.

For example, these shots are all examples of "good luck."

• You're aiming right of the hole location, but pull the shot to the left side of your Shot Zone.
• You're aiming right at the hole location, and hit a shot that ends up in the middle of your Shot Zone.
• You're aiming left of the hole location, and hit a shot to the right side of your Shot Zone.

In all three cases, two other results are "bad" or "less good" than the one above — hitting it right or centered when you're aiming right, hitting it left or right when you're aiming directly at it, or hitting it to the left or center when you're aiming left. They're not "bad" shots because they're all completely within your expected Shot Zone, but they are "worse" shots just by the luck of where that one dot falls in your Shot Zone.

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I'm going to quote a bit of what I wrote there now. The quoted text is someone else, and my text appears normally. Any asides I have, I'll put in [brackets]:

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I don't believe you gave your stance on if Tiger's victory at Hoylake was a great example of course management?

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I think you could figure out where I stand on that:

• The bunkers and the little bits (some of the taller rough, etc.) off the beaten paths at Hoylake were "bad."
• Tiger's long irons off the tees were still going 250-290+ yards.
• Tiger was so, so much better than even second place in SG:App (he was nearly 2x second-place Adam Scott that year).
• Thus, he was able to avoid the trouble without really increasing the distance he had to the greens, and he given that he was literally in a class by himself with the irons…

… his strategy was likely a good one.

Here's the thing: that answer wouldn't change if Tiger finished fifth because he hit the ball badly or got "bad luck." Y'all (many, not all) are looking back these two events — both wins, one involving Zach having freakishly good "luck" (i.e. outperforming his norm by a whole heckuva lot, while Tiger didn't out-perform his norm by nearly as much) — and saying "good strategy." But what about Tiger in 2006? Did he employ a "bad strategy" or did he just not play particularly great? Or did he get some "bad luck"? Also, what did Zach Johnson do in the future years, after he "validated" his strategy with a win? If a win says "good strategy" what about the years he MCed?

[At this point the person quoted Paul Azinger and Nick Faldo and maybe another person or two in talking about how brilliant Tiger's strategy was, or Zach's.]

Your quotes are all also looking back with hindsight. People before-hand [before Tiger's 2006 Hoylake win] were a little skeptical of his strategy, but they also really were still often under-estimating how good Tiger was with his irons.

You should know me better than to just throw a bunch of quotes out there. Those same people would also tell you (and have said) that the golf ball starts on the club's path and curves to where the face was pointing (incorrect ball flight laws), or they'd tell you "drive for show, putt for dough," or any number of other things. It's a logical fallacy, this appeal to authority… when in fact they were better players but that doesn't necessarily make them better at understanding the best strategies or how the golf ball flies or any number of other things within the golf sphere.

And the truth is, as I've said, that if you run the Tiger at Hoylake simulation 100 times with the strategy he employed, and 100 times with "hitting driver on two holes per round," and then another 100 times "hitting driver maybe four times per round," and so on… only then would you start to arrive at what the optimal strategy was. Because, again, we can't know. Maybe hitting driver 3x/round on certain holes would have led to the lowest average score for the tournament. Maybe he employed the optimal strategy. Maybe hitting driver everywhere would have actually been the best strategy. I'd say it's unlikely given the result, but Tiger is capable of winning while employing less-than-optimal strategies. He used to use The Memorial to work on his game… he'd draw the ball into a right hole location and fade it into a left one… with trouble left… and often win. He said in the press conferences afterward, or in the personal scrum after that, that he was just working on his game, because if he could hit the "wrong" shot and pull it off he knew he could trust it in the major in a few weeks.

Here's a story I've told before, but maybe not here:

I was giving a playing lesson to a young fella named Tim. We were on the eight hole of this course, which has a sort of island green. I had 150 yards (adjusted, as it's downhill a good bit), and I said "It's a 9I yardage but I'm going to chip an 8 because I don't want it floating around up in the air quite as much, and this will control spin a bit more with the steeper landing angle. The hole is way front right, so I'm going to aim center of the green and if I hit a good shot, I'll have a 25-footer or so for birdie. If I pull it, I'll have to work a little harder to two-putt from 45 feet or so, but I should be fine, and if I push it, I might be close and have a real chance at birdie." I hit the shot, immediately said "See, Tim, I pushed it" after the ball had just left the face. The ball hits the front right part of the green and rolls in for eagle.

Luck. The shot was completely within my Shot Zone/shot pattern, which is why I aimed where I did. It was skill to have a shot pattern that size from that yardage, but luck that I didn't hit the exact center of my Shot Zone. Had I pulled it and had a 45-footer, that too would have been luck - literally every shot in there is luck, because it's all coin flips (albeit with an almost infinitely sided coin depending on how precise you want to get with landing spots http://golfclubatlas.com/forum/Smileys/classic/smiley.gif ). Some of those shots will be closer to the hole, some will be farther out. The closer ones are more toward "good luck" and the bad ones more toward "bad luck."

I've said before that you can have a Perfect Putter set up at 20' and roll balls as exactly as you can and, on average, you might get 3 out of 10 to go in. Some will miss high. Some will miss low. But roll ten balls at a time and there will be runs where you get 1 and runs where you get 7 or 8. Zach had a run that week where he got 7 or 8 when the average is 10. Luck. Randomness. The randomness "fell" in his "favor" that week. Just as it did when I holed out for eagle in a playing lesson.

FWIW we had a good chuckle over that one, and because I'd told him all of that stuff, he knew it wasn't a "great shot." He knew I'd "missed" it a little. But he also knew I'd planned for it, and at some level expected it — not literally that specific miss, but I expected my ball to end up somewhere in my Shot Zone.

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Hole 13 he had only 213 yards to the hole from the middle of the fairway and choose to lay up to 75 yards to about 8 feet from the hole and made the putt. He was either tied or 1 shot behind the leaders at the time, couldn't tell exactly. But he was playing in front of Tiger who ended up with an eagle on 13. Peter Kostis and Feherty were very surprised and critical of him laying up from 213.

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Just because he birdied doesn't mean the strategy was "best." If he lays up 100 times and goes for it 100 times, then you can start to see which strategy would have been best.

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I also don't like the word luck for a strategy as no one else choose the route Zach did that week for the par 5's, I would say Zach had peak performance for his approach that week on the par 5's as that was the reason he won.

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Did I have peak performance in my playing lesson when I made eagle? Tiger eagled the one hole during the Hoylake victory (I think with a 4I in maybe the second round?): was that shot somehow "better" or "more peak performance" than the 3I from the hanging lie in the bunker at Hazeltine, despite the fact that the 3I didn't go in the hole?

(the video is stretched, which flattens out the lie in the bunker.)

Guys, very simply this: it's skill to have a Shot Zone of a certain size. It's luck where the specific, small sample size shots fall within a given tournament for the week. It's skill to give a lot of putts a chance to go in. It's luck how many of them actually fall in any given week. [Emphasis added here on TST, not originally.]

Zach's "performance" was way at the end of the bell curve that week because he hit a lot more wedges closer and/or made a lot more putts than he normally would, and thus it's chalked up to his "strategy" that week. But again, what of his "strategy" the weeks he MCed at the Masters? In those weeks (and all the rounds he's played at Augusta National) you're starting to get a larger sample size, an average expected score.

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To call Zach lucky (super-hot in your words), but not Tiger I think is incongruent.

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Tiger was otherworldly with his irons. In a class by himself. His results were not nearly as unlikely as Zach's were.

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Also what about Phil Mickelson on 18 at Winged Foot to blow his 2 shot lead?

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What about it? You wanna talk about a small sample size? What I remember having watched that tournament was that it was surprising Phil was still in the lead on 18 given his play the rest of the day. He drove the ball poorly most of the day, IIRC. So one tournament isn't a small enough sample size, you want to reduce it to one hole now?

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I think all are just thinking using the term LUCK so cavalierly for professionals when they win is diminishing their skills and peak performance is possible.

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It doesn't diminish their skills in my eyes. If you charted a PGA Tour player's actual performance (regardless of result) on a bell curve, then added "luck" to it, luck would flatten and widen that bell curve. Skill + luck => Results. Zach needed not only a highly skilled period that week to win, but a good bit of luck, too. He needed to have a shot from the right side of his Shot Zone come out when the hole was a little right of where he might have been aiming (or a shot from the center of his Shot Zone come out when he was aiming at the flagstick, or whatever).

[From some earlier posts…]

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The way you're applying luck in this instance, every player on tour incurs some amount of luck over 72 holes to win

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Yeah, and…? We covered this on the first page: Zach was "more lucky" than Tiger was in winning at Hoylake because Zach's performance was so much less likely than Tiger's was.

If you flip a coin a bunch of times, you can figure out the odds that you'll flip heads up 10 times in a row. Or 25. Or 100. The higher the number, the longer the odds. The more "luck" you need to do it. Tiger winning at Hoylake was like flipping heads three times in a row. Unlikely, but not super out there. Zach's was like flipping heads 15 times in a row. It'll happen if you flip coins long enough…

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So in this context, you are probably right that some amount of luck was involved for Zach.  But I just don't see how that is interesting or notable in any way given it happens every week on tour for the winner, and several other guys in contention who were "unlucky" to lose.

P.S.  I think a better word to use here is randomness...and whether it helped or hurt, cause that happens all the time to everyone.

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"Randomness" is fine, but randomness implies both good and bad sides. So, Zach, in winning, got much more of the "good" randomness than the "bad."

And… it's notable and/or interesting because the topic is whether he employed the right strategy. Over a small sample size, you simply can't tell. Simulate the tournament 100 times where he lays up every time, and simulate it another 100 times where he goes for it every time he's reasonably within range, and he might score lower going for it more often. Small sample sizes or outlier "lucky" (or "unlucky") performances lead to bad conclusions when really, you shouldn't try to draw any.

For example, how did Zach perform after winning the Masters in 2007, as one would think he has come to understand how great his strategy is… right? Well, he finished T20 in 2008, missed the cut in 2009, 42nd in 2010, MCed in 2011… and then in his next ten Masters, finished in the top ten once, finished outside the top 30 five other times… not counting his four other times.

You may not find it interesting (in which case… why post?), but I find it interesting because it directly affects how golfers play, how they feel about how they played, how they make decisions, etc. These are all things that I spend a good chunk of my week discussing with my players: expectation management, Decision Mapping/GamePlanning, etc.

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[Bold again added by me here at TST.]

The last bold part is why I am interested in this stuff. Because golfers really, really need to understand their Shot Zones. They need to understand probabilities, and odds, and chances. I coach a lot of good players, and I hate when they:

• Hit a wedge from 120 yards out to 15' and are pissed at themselves for not sticking it to 3'.
• Two-putt for birdie from 20' after reaching a par five in two and walk off the green disappointed in themselves.
• Call a 550-yard par five a "birdie hole," get into a little trouble off the tee and proceed to employ a strategy that would result in a higher chance of birdie but which also results in a significantly higher score on average… and then they make a 7. (Basically, because they think of the hole as a "birdie hole" they are too aggressive in getting out of trouble and make a mess of the hole, when they probably could have made a par pretty easily.)
• Hit a shot from 180 yards out on a par three to 40' on the green and are ticked.
• Flag hunt from that same par three to a pin way front left, pull it 30 yards, and it hits the cart path and bounces OB.
• Etc. The list goes on and on.

How you FEEL about your shots affects how you play future shots. It affects how you feel about how you played. Managing your expectations allows you to not get too high or too low and to accurately process how you played.

I'm a very good putter. There are days when I don't make much of anything, and days when I make a lot of putts. My skill level doesn't change much day to day, but my "luck" does.

[Darkfrog]

  On 10/29/2021 at 4:49 PM, iacas said:

Call a 550-yard par five a "birdie hole," get into a little trouble off the tee and proceed to employ a strategy that would result in a higher chance of birdie but which also results in a significantly higher score on average… and then they make a 7. (Basically, because they think of the hole as a "birdie hole" they are too aggressive in getting out of trouble and make a mess of the hole, when they probably could have made a par pretty easily.)

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I fall for this one all the time. There is a 505-yard par-5 at my home course, but usually middle tees are setup 450-475 yards. In my opinion, it is easiest hole on the course, so I walk up to the tee expecting par or better. A well struck drive, regardless of dispersion, always leaves less than 200 yards to the green, and when I find myself in a difficult spot for my 2nd shot, without fail I attempt a riskier approach to get on/near the green to attempt to salvage an "easy" hole, rather than play a smart recovery shot that advances the ball as far as possible while avoiding greater harm. I've probably birdie this hole more than any other hole on the course, but I also have my share of stupid double-bogey or worse scores too.

I think there is a lesson in this for me.

[Pretzel]

Managing expectations is such a big one.

When I played the most golf of my life I was a better player than I am currently, and I could hit shots then that I can't now. Getting heavily back into golf again after college I was trying to hit the same shots, or expecting the same results from easier shots, and playing absolutely awful compared to how well I was still hitting the ball. I even had an entire club (looking at you, 3-iron) that was unreliable enough I just stopped hitting it altogether.

I was playing as though my Shot Zones hadn't changed, when in reality they were quite different. Once I took the time to actually set and maintain realistic expectations, my scores immediately dropped by 5 shots because I was no longer playing "stupid" golf.

[KMP]

  On 10/29/2021 at 4:49 PM, iacas said:

How you FEEL about your shots affects how you play future shots.

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But isn't this the essence of golf or the "zen of golf" to be able to inhibit that "FEEL"? To be able to accept and forget the past, and evaluate the current shot to determine the highest probability of success is a key to my improvement.

[GolfLug]

This is such a solid OP. 

  On 11/6/2021 at 7:47 AM, KMP said:

But isn't this the essence of golf or the "zen of golf" to be able to inhibit that "FEEL"? To be able to accept and forget the past, and evaluate the current shot to determine the highest probability of success is a key to my improvement.

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Speaking for myself here but knowing my shot zones has helped me from living and dying with each shot. I also realized I was a bit cherry picky about the shots that populate my shot zones. For example, it took me a while to accept that my driver shot zone was 3 fairways wide. I would get on a hot run (in the shot zone) and think it tightened up for a couple of rounds but I don't fall for it anymore and don't find myself sulking for too long for 2-3 OBs (my home course has 14 holes with OB) that 'ruined' the round. 

Accepting the fact that I get out of sequence few times a round and pump out the ball off the planet (part of work on myself), keeps me from psychologically throwing away unnecessary shots. 

Edited November 6, 2021 by GolfLug
Typo

[ChetlovesMer]

That was quite the read.

After he won The Masters, Zach Johnson himself said that nobody would ever win The Masters that way again. He said it was a perfect storm of conditions and others making critical mistakes at the right time for him to win using the strategy he used. He himself said that strategy of never going for a par 5 in 2 would be terribly flawed and would likely never work again. 

So, I think even Zach Johnson would pretty much agree with you. 

[iacas]

  On 11/6/2021 at 11:57 PM, ChetlovesMer said:

That was quite the read.

After he won The Masters, Zach Johnson himself said that nobody would ever win The Masters that way again. He said it was a perfect storm of conditions and others making critical mistakes at the right time for him to win using the strategy he used. He himself said that strategy of never going for a par 5 in 2 would be terribly flawed and would likely never work again. 

So, I think even Zach Johnson would pretty much agree with you. 

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Do you have links to these types of quotes? They'd be pretty helpful in the other conversation… 😉

[ChetlovesMer]

  On 11/7/2021 at 12:11 AM, iacas said:

Do you have links to these types of quotes? They'd be pretty helpful in the other conversation… 😉

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He talked about it in a Golf or Golf Digest article I read. He also said pretty much the same thing when I saw him in person at an event at what used to be my home course. I'll see what I can find. 

[iacas]

  On 11/8/2021 at 2:46 PM, ChetlovesMer said:

He talked about it in a Golf or Golf Digest article I read. He also said pretty much the same thing when I saw him in person at an event at what used to be my home course. I'll see what I can find. 

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Thank you. I'd appreciate it.

[ChetlovesMer]

How a statistical miracle propelled Zach Johnson to one of the most unlikely Masters wins ever | For The Win

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10 years on, we relive one of the most unlikely Masters wins ever.

It's always funny to me how people remember what they want to remember. 
Everyone remembers that Zach Johnson didn't go for any of the par-5's in two.
But few remember:

The final round of the 2007 Masters Zach Johnson went 1 under and won the tournament. It was his FIRST time EVER playing a Masters round under par in 10 tries. 

To me that's a far more amazing stat. 

[saevel25]

I think the luckiest thing was the weather, and it flattened the curve a bit for him to succeed with the game plan he had. Outside of that, having an amazing wedge game, to go that under par on Par-5's is more about his skill that day than luck.