Tacking, laying-up and course management

[Kalen Braley]

I think Jason hit it on the head, the use of the work "lucky" is the big hang up.

If you take 25 putts from 20 feet out, and none of them are ending up near the hole and 1 hits the back of the cup and goes in? That's luck.

But if you hit same putts and they are consistently burning the edge and ending up very close, I wouldn't consider it luck if 5 of them drop on one iteration, when you typically only average 2 or 3.

For the basketball analogy,  Steph Curry's career conversion rate for 3 pointers is 43.3%.  But is it really "lucky" if he shoots 66% on any given night?

[Erik J. Barzeski]

He is, however, a guy who made almost 90% of putts inside 10' for the year, and over 50% from 9'.

That's a horrible stat. The vast majority of those putts are tap-ins. And an inside 10' stat isn't particularly relevant to 100-yard wedge shots.

• Zach averaged 17'10" from 75-100 yards (in the fairway) in 2007.
• He averaged 20' 9" from 100-125 (fairway).
• Your "from 9' stat" is actually putts from 8-9 feet ("For all holes where putting distance was determined with a laser, the percent of putts made when the ball is greater than 8 feet and less than or equal to 9 feet from the hole.") Zach was 10th at 57.5%. Small nit-pick (but be careful when you look at "putts from 4'" and stuff, because those numbers change fast).

If his average wedge shot from 50-125 yards was inside 20' already, I don't think it's some incredible statistical outlier that he had a 16 hole stretch on par 5s where he hit a couple extra wedge shots inside 10', made a couple more putts than usual when he did, and rolled one or two in from a longer distance. In fact, statistically, a sample like that is almost inevitable for a player with his statistical profile at some point over the course of a season.

If you actually do the math, you'll see how quickly the likelihood drops. Let's just look at one round and the chances he birdies just three of them after hitting a wedge from 100 yards (in the fairway). From 100 yards, he's normally going to average about 18.5 feet. Let's say he hits it to 8.5', more than halving the distance. Let's give him a 35% chance on any one shot to hit it that close seems reasonable given his average. Then let's say he's a 60% putter from that distance. So you have, for just four holes, trying to make three birdies… 0.6^3*0.35^3. That has a ~0.93% chance of happening. And that's just one round.

Obviously he's not going to hit it to those exact distances every time, but if he hits it to a farther distance (say, 15') on one hole, that shot is easier (higher odds, more likely), but then the odds of making the putt drop quite a bit.

"Lucky" that it occurred during the Masters

No, lucky that he had sustained wedge/putting performance that high above his norm for four rounds.

The odds are really small.

As usual, my take is about halfway in between, as I agree with Erik that statistically Zach probably didn't play it "right."  That doesn't mean playing it by the book always results in a win, or that gambling or playing against type guarantees a lesser result. I'm not sure how a few of you don't get that about Erik's position on stats.

Thank you. I'm not degrading his win. He still had to DO those things. But he needed some luck, too, because if you ran that simulation a thousand times, he's not winning with that strategy very often. And… he's not winning with another strategy very often, either!

Someone of Zach's level has to get lucky the way I'm using it here (I'm not talking about a ball bouncing off a tree and landing on the green, though that's luck too) AND play well during a week to win. Zach not only played well, he got very lucky.

I once played an 18-hole and then a 9-hole putting match against my teaching partner. The 9-hole match went to ten holes, and all of the putts were from outside 20'. He lost the 18-hole putting match 5 down, and lost the nine-hole putting match on the 10th hole (sudden death). He putted really well: he was 5 under on the 18-hole match and four under on the 9-hole match (he "parred" ten with a two-putt). I was 15 under (10 and 5). Now, I'm a good putter, but I was incredibly lucky to make almost 54% of my 20-30' putts.

If you take 25 putts from 20 feet out, and none of them are ending up near the hole and 1 hits the back of the cup and goes in? That's luck.

No, that's one definition of luck.

But if you hit same putts and they are consistently burning the edge and ending up very close, I wouldn't consider it luck if 5 of them drop on one iteration, when you typically only average 2 or 3.

For the basketball analogy,  Steph Curry's career conversion rate for 3 pointers is 43.3%.  But is it really "lucky" if he shoots 66% on any given night?

Yes.

[Garland Bayley]

Just because you said it, doesn't make it true. Either you have the data, or you don't. If you don't have the data, then you are just blowing smoke.

I have the data. And as Michael Felton points out, you could have done a minute of research as well and gotten a pretty good idea what the data says, too. Zach fairly sizably out-performed his typical performance from those distances.

If you actually had the data, then you would post it. Clearly you don't have the data, and are just blowing smoke.

Interesting that you reference Micheal Felton's post since 1) it (and the referenced website) doesn't give the sufficient stats to back up your claims about Zach's Masters performance, and 2) he comes to the opposite conclusion than you do on his choice of strategy.

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His going for the green stats aren't great either. He only hit the green 19% of the time when going for it. Perhaps not the end of the world on a lot of golf courses, but on 13 and 15 at Augusta, those stats are going to be going swimming with some fair regularity. On the basis of this, it appears he was playing the right strategy.
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[Garland Bayley]

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We also can't totally discount feel and feelings.  For all we know, Zach was on the range and felt that his putting was great going into the tourney, and his wedge game from 100 was also going above average, so he felt that in this particular case, it was a better play for him, that week.
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The one thing that the website Michael referenced does show is that Zach's putting was exceptional during that portion of the season. It doesn't give the Masters stat, but he gained over 1 stroke over the field in the 3 tournaments preceding the Masters, gaining 2.578 strokes in his last tournament before the Masters.

[Erik J. Barzeski]

If you actually had the data, then you would post it.

Nice try, but no. The data is proprietary, and not only does it make for bad business to just share it nilly willy, it may even violate the terms of the contract(s).

Do you have contradictory data? No, you don't, because it doesn't exist: the odds of Zach doing what he did that week were miniscule. Not zero, but darn close. About the same as the odds of you contributing to a discussion in a meaningful way.

Interesting that you reference Micheal Felton's post since 1) it (and the referenced website) doesn't give the sufficient stats to back up your claims about Zach's Masters performance, and 2) he comes to the opposite conclusion than you do on his choice of strategy.

No it doesn't. You can't conclude that Zach employed the optimal strategy from a low sample size, particularly when it's such an outlier. And I think Michael would agree with that, too.

The one thing that the website Michael referenced does show is that Zach's putting was exceptional during that portion of the season. It doesn't give the Masters stat, but he gained over 1 stroke over the field in the 3 tournaments preceding the Masters, gaining 2.578 strokes in his last tournament before the Masters.

🤦🏼‍♂️

[Rob Marshall]

I don’t see getting hot or getting in the zone as luck. I think you made 54% of your putts because you had a great day putting. Your speed was on and you were hitting your lines. Curry hitting 66% of his threes isn’t luck. He was hot and in the zone. When he makes 20% he’s not unlucky he just had a bad shooting day.

[Garland Bayley]

As usual, my take is about halfway in between, as I agree with Erik that statistically Zach probably didn't play it "right."  That doesn't mean playing it by the book always results in a win, or that gambling or playing against type guarantees a lesser result. I'm not sure how a few of you don't get that about Erik's position on stats.
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It seems to me that "playing it by the book" is for someone who's averages tend to correlate highly with the book. Zach's don't! Therefore, only Zach specific stats should determine his book.

[Garland Bayley]

If you actually had the data, then you would post it.

Nice try, but no. The data is proprietary, and not only does it make for bad business to just share it nilly willy, it may even violate the terms of the contract(s).
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More BS from the BS king.

[Jason Thurman]

If you actually do the math, you'll see how quickly the likelihood drops. Let's just look at one round and the chances he birdies just three of them after hitting a wedge from 100 yards (in the fairway). From 100 yards, he's normally going to average about 18.5 feet. Let's say he hits it to 8.5', more than halving the distance. Let's give him a 35% chance on any one shot to hit it that close seems reasonable given his average. Then let's say he's a 60% putter from that distance. So you have, for just four holes, trying to make three birdies… 0.6^3*0.35^3. That has a ~0.93% chance of happening. And that's just one round.

The thing about showing your work is that other people can then see your work. You didn't calculate what you claim you calculated, but instead calculated that on any consecutive 3 holes where he hit a ~100 yard wedge shot, he had about a 1% chance of hitting 3 consecutive approaches to 8'6" and then making the putt (ignoring that you used a made-up percentage for frequency of approaches to exactly 8'6").


His odds of pulling off EXACTLY that feat three times in four holes are better by definition.


And your math doesn't account for the fact that he's still capable of making birdies on a hole where he doesn't hit it to exactly 8'6" after a 100 yard wedge shot.


But whatever. You've beaten the horse to death. Must be an unlucky quiet week on the lesson tee.

[Kalen Braley]

Erik,

You are correct in that luck can be used in several contexts and has no specific boundaries or bench marks.

It can certainly raise conundrums like, If I typically hit 7 fairways in a round, and I get 3 "lucky" bounces in one round that unexpectedly kick my ball in the fairway, to bring my total for the day to 7.  Did I shoot my average and incur "no luck"?  Or was I just "lucky" to get those great bounces to shoot my average?

The way you're applying luck in this instance, every player on tour incurs some amount of luck over 72 holes to win, whether it was their own good luck, or the bad luck of fellow contender(s). Hell for that matter, every round of golf every golfer ever plays they are almost certain to incur at least one "lucky" good or bad break.

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.

[Erik J. Barzeski]

I don’t see getting hot or getting in the zone as luck. I think you made 54% of your putts because you had a great day putting. Your speed was on and you were hitting your lines. Curry hitting 66% of his threes isn’t luck. He was hot and in the zone. When he makes 20% he’s not unlucky he just had a bad shooting day.

I do.

• Flipping a coin and getting heads ten times in a row is luck.
• A golfer making two holes in one in one round is luck.
• Winning the lottery is luck.

All have low chances of happening, so when they occur, they're luck.

More BS from the BS king.

You've got that title for life, buddy. Again I'll ask: do you have any contradictory data? No, of course you don't.

The thing about showing your work is that other people can then see your work. You didn't calculate what you claim you calculated, but instead calculated that on any consecutive 3 holes where he hit a ~100 yard wedge shot, he had about a 1% chance of hitting 3 consecutive approaches to 8'6" and then making the putt (ignoring that you used a made-up percentage for frequency of approaches to exactly 8'6").

I know what I demonstrated. Of course Zach didn't hit it to 8.5' every time. It's not an exact re-telling of his round, it's meant to illustrate how quickly the odds get very, very small.

And your math doesn't account for the fact that he's still capable of making birdies on a hole where he doesn't hit it to exactly 8'6" after a 100 yard wedge shot.

I know…:

Obviously he's not going to hit it to those exact distances every time, but if he hits it to a farther distance (say, 15') on one hole, that shot is easier (higher odds, more likely), but then the odds of making the putt drop quite a bit.

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

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…

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.

"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.

[Jeff Schley]

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

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…

Erik I don't believe you gave your stance on if Tiger's victory at Hoylake was a great example of course management? If you search for any commentary of his victory that week you hear the following from names much more respected than me or you on the subject. But also that even for Tiger's shot making ability, it was a week he himself said: "I only missed 3 shots the entire week."

What matters now is how he plans to manage his game -- rust and all -- at a place where Haney contends he had the single best ball-striking tournament of his career.https://www.espn.co.uk/golf/theopen14/story/_/id/11204462/tiger-woods-history-resurfaces-hoylake-open-championship-royal-liverpool-golfHe was so good he had even Nick Faldo gushing with compliments:  "This has been a master class of tactitional golf. It's really been fantastic to watch." 
Later, Faldo described Woods' ball-striking as "sheer perfection."


-- Paul Azinger also liked Woods' conservative game plan. "Who knows, maybe Tiger Woods will change his strategy from now until the rest of time and rein it in a little bit." Hmm. Have you watched Woods play in recent years? Azinger was onto something.

https://www.golfdigest.com/story/british-open-hoylake-tiger-woods-2006
BTW you can watch his entire final round here: https://www.youtube.com/watch?v=Ky6Icq0K8hc

Zach Johnson I watched the final round coverage and noted that it was hard to even see all his shots in the coverage as Tiger dominates the screen time.  I couldn't see 2 on the broadcast (he birdied), but on hole 8 he chips in from just off the front of the green from about 30 feet for birdie.

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.

Hole 15 he had 230 to the front and choose to lay up  from about 85 yards and didn't hit a good approach to about 20 feet and 2 putts for par.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.
For Tiger at Hoylake, no one else made the decisions Tiger did and by all accounts he had the best ball striking week (which is saying something for him) of his career with approaches from well over 200 yards on many that required running the ball into hole locations on a links course which requires luck in and of itself.So Tiger not hitting in a single fairway bunker all week and happening to have his best ball striking week I wouldn't call either Zach or Tiger lucky, but peak performance for their skill sets. To call Zach lucky (super-hot in your words), but not Tiger I think is incongruent. 

Also what about Phil Mickelson on 18 at Winged Foot to blow his 2 shot lead?  Yet JVDV is unlucky with a 3 shot lead and making 2 bad decisions in a row. I see both as terrible examples of course management myself and not unlucky. I also don't think David Toms was lucky to win by laying up on 18 for his major on the par 4. 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. Not common, but possible and when they can conjure up that performance on the biggest stage they should be lauded, not lucky.

Edit: formatting attempt

[Erik J. Barzeski]

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

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?

Your quotes are all also looking back with hindsight. People before-hand were a little skeptical, 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  ). 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.

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.

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.

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.

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?

https://www.youtube.com/watch?v=ZhKDQTDoEwE (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.

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.

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

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

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

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?

Yet JVDV is unlucky with a 3 shot lead and making 2 bad decisions in a row.

JVDV didn't really make two bad decisions. Unless maybe you're talking about after he hit his second shot.

He drove it off the tee, and he kept it right because OB is left. He got a little lucky that his ball went over the burn, but had he gone in the burn, he could have dropped, hit his third up short of the green if he wanted, chipped on (or wedged on), two-putted for a six, and won.

The only place he couldn't go there was OB. Left.

Then for his second shot, the only place he couldn't go was left again (OB), so he hit it up near the green, where just about anyone on the Tour can get down in three, and had the terribly bad luck of having his round ball hit a round pole at just the right angle to end up where it ended up.

If you're talking about later decisions, and standing in the burn for way too long, etc. then sure, maybe, but none of us know exactly what the lies were like, etc.

I also don't think David Toms was lucky to win by laying up on 18 for his major on the par 4.

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.

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).

[Ben Hollerbach]

Should you judge a PGA tour course management strategy based on how it affects average score?

Finishing 25th every week is nice, at the end of the year you’ll earn a lot of money and will probably finish with a pretty low scoring average, but you won’t really matter in the overall impact of the season. In professional golf, a player's value is significantly measured by their wins.

Who on the PGA tour today would rather finish in the top 10 at the Masters 10 years in a row over winning once and missing 9 straight cuts?

Tiger Woods is about the only person in the last 30 years who has been good enough to win while being "average". For everyone else, in order to win they need to play well beyond their average. If the goal is to win, it doesn't make any sense to play for averages, you should instead build a strategy that gives you the highest probability to WIN.

In mathematics there is a concept called Jensen's Inequality. In its simplest form, it states that for many things the function of an average does not equal the average of the function. Golf tournament wins are one of those things.
 
Last year, if a player shot 2 strokes better than the field average every round, they would have won the scoring title for the season (best average). But they would have never come close to winning an event (the output of the function).

The best scoring average would have tied for the worst win total, with a big fat zero. 

For everyone not named Tiger, winning is a tail event, it is an outlier, and It doesn't happen often.  Therefore to maximize wins, you have to try and maximize the probability of a positive tail event, not maximize the average.

Relating this to Zach Johnson’s Masters win in 2007.  If he felt his wedge game and putting was hot that week, then the right strategy for him TO WIN was to play into that strength as much as he could. You can't let a potential hot streak go to waste and you have to take advantage of it if it's real.

Now would this make sense if you're trying to maximize your year long average score.  LIkely not. But in golf, winners aren't average. They are exceptional that week, and you can't let the potential for an exceptional week go to waste.

If your goal is to have a low scoring average, then by all means, judge a strategy on how well it lowers a scoring average. This probably makes sense for amateurs not in competition.  But if the goal is to win, then judge a course management strategy on how it maximizes the players chance of WINNING.

[Tim Gavrich]

For everyone not named Tiger, winning is a tail event, it is an outlier, and It doesn't happen often.  Therefore to maximize wins, you have to try and maximize the probability of a positive tail event, not maximize the average.

Relating this to Zach Johnson’s Masters win in 2007.  If he felt his wedge game and putting was hot that week, then the right strategy for him TO WIN was to play into that strength as much as he could. You can't let a potential hot streak go to waste and you have to take advantage of it if it's real.

Now would this make sense if you're trying to maximize your year long average score.  LIkely not. But in golf, winners aren't average. They are exceptional that week, and you can't let the potential for an exceptional week go to waste.

If your goal is to have a low scoring average, then by all means, judge a strategy on how well it lowers a scoring average. This probably makes sense for amateurs not in competition.  But if the goal is to win, then judge a course management strategy on how it maximizes the players chance of WINNING.

This is terrific, and gives mathematical backing to something that seems to be overlooked in the always-interesting but ultimately reductive Big Data view of things.


Separate from whatever advantage Johnson may (or may not) have tapped into by playing the par 5s the way he did in '07, I think he gave himself an extra boost simply by formulating an affirmative game plan and executing it to the hilt. I think by knowing from the outset that he was going to approach that 16-hole portion of the golf tournament in that specific way, he freed himself up to simply let his plan unfold, rather than "make" it unfold. Especially with the course playing so differently from usual (it's been said that Johnson's performance was an outlier; so was the course's!) that year, I think he had a bead on the place that gave him an extra advantage over players who may have been trying to play those holes closer to the way they would normally play them.


How many extra shots did this combination of confidence and strategic preparation give ZJ off the top? It's unquantifiable (sorry, Big Data golfers!), but I reckon it was greater than we would initially think because of the way supreme confidence tends to super-charge the talents of the best athletes.

[Erik J. Barzeski]

Ben, your point is understood, but you're agreeing with me more than you seem to realize: in running the tournament a hundred times, or a thousand times, you're not eliminating strategy, you're eliminating the effects of the coin landing on heads a bunch of times in a row. You're eliminating luck.

About a decade or so ago the Browns were 11-point (IIRC?) underdogs at New England and they won the game outright. Play that game 100 times and the Patriots are going win the vast majority. That one win didn't mean the Browns had a better "strategy" or played better that day, the small number of times they "win" in the simulation, it just means they got a couple of good bounces or calls (or the Patriots got some bad ones, or a combination, etc.).

Players are always striving to raise their baseline, because then when they have good or bad luck, that bell curve is centered around a better average score.

For all any of us knows, Zach could have shot what he shot and still won with a bit less luck ("randomness that went in his favor") by employing a "better" strategy, or shot lower if he got the same amount of "beneficial randomness"? Nobody here can say much definitively at all because the sample size is so small. It was one tournament.

The pop song "Everybody's Free to Wear Sunscreen" contains these lyrics:

Whatever you do, don't congratulate yourself too much
Or berate yourself either
Your choices are half chance, so are everybody else's

My main point in all of this is that what many here want to chalk up to "a great strategy" or "hot play" is likely more a matter of… the way the coin lands sometimes. I wasn't appreciably any better or worse of a putter when I made > 50% of my 20-30 footers over 28 holes. The coin just landed on the "tails" (I always pick tails) side a lot more frequently for a short span of time than you'd normally expect. Blackjack players "get hot" too — their skill doesn't improve (not talking about card counters), they just get a bit more "beneficial randomness."

Separate from whatever advantage Johnson may (or may not) have tapped into by playing the par 5s the way he did in '07, I think he gave himself an extra boost simply by formulating an affirmative game plan and executing it to the hilt. I think by knowing from the outset that he was going to approach that 16-hole portion of the golf tournament in that specific way, he freed himself up to simply let his plan unfold, rather than "make" it unfold. Especially with the course playing so differently from usual (it's been said that Johnson's performance was an outlier; so was the course's!) that year, I think he had a bead on the place that gave him an extra advantage over players who may have been trying to play those holes closer to the way they would normally play them.

I agree with that.

For my college players, last year at our conference championship, we mapped out a gameplan for every par four and five with options. They laid up on this one dangerous (but drivable) par four. I stressed to them that even if their opponents hit the green, they're laying up and leaving a simple pitch on, because as a team, we'll come out way ahead (and we did). Psychologically, removing the burden of having to make that decision paid dividends and simplified so much for them, a few times per round (one of my longer hitters teed off with a hybrid on a par five because of the incredible trouble near his 3W and driver landing zones, etc.).

But again, Zach employed the same strategy after that victory, and only once again finished inside the top 30.

[Jason Thurman]

Ben and Tim touch on something I find pretty compelling in modern discussion of strategy - the balance between the "right play in a big sample" and the "right play in a small sample."


It's obvious that some of the big-sample gurus are far less aware of the peculiarities of how small samples often bear out. Something like "3 straight 100ish yard approaches hit to 8.5' followed by a made putt" may only have a 1% chance of happening for a given player, but it's VERY likely that he pulls it off at some point during the season over 500 or so holes. Large sample data doesn't do much to predict when those inevitable hot streaks will occur, but an intuitive player might just be able to do it and ride it to a W.

[Rob Marshall]

“About a decade or so ago the Browns were 11-point (IIRC?) underdogs at New England and they won the game outright. Play that game 100 times and the Patriots are going win the vast majority. That one win didn't mean the Browns had a better "strategy" or played better that day, the small number of times they "win" in the simulation, it just means they got a couple of good bounces or calls (or the Patriots got some bad ones, or a combination, etc.).”

Bounces or calls? Isn’t it possible that the Browns just out played them that day? A scratch player at my club beat a +4 in the Club Championship. Interesting in that the +4 made bogey on 3 of the last 4 holes while the scratch player made 4 solid pars.  Looked to me like the better player just got beat that day. Happens. Sometimes the better player or team doesn’t win and it’s not always because of a bounce or bad call. That’s why they play the game.  IMO

[Erik J. Barzeski]

It's obvious that some of the big-sample gurus are far less aware of the peculiarities of how small samples often bear out. Something like "3 straight 100ish yard approaches hit to 8.5' followed by a made putt" may only have a 1% chance of happening for a given player, but it's VERY likely that he pulls it off at some point during the season over 500 or so holes. Large sample data doesn't do much to predict when those inevitable hot streaks will occur, but an intuitive player might just be able to do it and ride it to a W.

I've cited examples like that specifically: the odds of flipping heads more often or x times in a row, making > 50% of your putts from 20-30 feet, etc. When those things happen it's not an example of "good strategy." It's an example of luck. "Good randomness." Of "right place, right time."

Bounces or calls? Isn’t it possible that the Browns just out played them that day? A scratch player at my club beat a +4 in the Club Championship.

The Browns are not going to win 0 of the 100 games. Or 0 of 1000. The games they win, because they're the less talented team, are going to be a result of a lot of things. Their bell curves overlap. That the bell curves overlapped that day is luck. Even if the Browns performed to the peak of their levels, they needed some amount of "luck" (chance, randomness, whatever) for the Pats to not play at something near THEIR peak level, too.

[Michael Felton]

Should you judge a PGA tour course management strategy based on how it affects average score?

Finishing 25th every week is nice, at the end of the year you’ll earn a lot of money and will probably finish with a pretty low scoring average, but you won’t really matter in the overall impact of the season. In professional golf, a player's value is significantly measured by their wins.

Who on the PGA tour today would rather finish in the top 10 at the Masters 10 years in a row over winning once and missing 9 straight cuts?

Tiger Woods is about the only person in the last 30 years who has been good enough to win while being "average". For everyone else, in order to win they need to play well beyond their average. If the goal is to win, it doesn't make any sense to play for averages, you should instead build a strategy that gives you the highest probability to WIN.

In mathematics there is a concept called Jensen's Inequality. In its simplest form, it states that for many things the function of an average does not equal the average of the function. Golf tournament wins are one of those things.
 
Last year, if a player shot 2 strokes better than the field average every round, they would have won the scoring title for the season (best average). But they would have never come close to winning an event (the output of the function).

The best scoring average would have tied for the worst win total, with a big fat zero. 

For everyone not named Tiger, winning is a tail event, it is an outlier, and It doesn't happen often.  Therefore to maximize wins, you have to try and maximize the probability of a positive tail event, not maximize the average.

Relating this to Zach Johnson’s Masters win in 2007.  If he felt his wedge game and putting was hot that week, then the right strategy for him TO WIN was to play into that strength as much as he could. You can't let a potential hot streak go to waste and you have to take advantage of it if it's real.

Now would this make sense if you're trying to maximize your year long average score.  LIkely not. But in golf, winners aren't average. They are exceptional that week, and you can't let the potential for an exceptional week go to waste.

If your goal is to have a low scoring average, then by all means, judge a strategy on how well it lowers a scoring average. This probably makes sense for amateurs not in competition.  But if the goal is to win, then judge a course management strategy on how it maximizes the players chance of WINNING.

Typical variance means that you'll never shoot your average score every round. Simple fact of the matter is if your scoring average is two shots better than the average, you have a far better chance of winning tournaments than someone whose scoring average is the average. Playing optimally strategically doesn't mean you won't make birdies or that you won't have much chance to win.


For example, in the final round of the 2019 Masters, Tiger Woods's ball landed on the fat side of the green on 15 out of 17 approach shots (the 5th hole the pin was right in the middle). Best player ever whose strength is his iron play and he's pretty much certainly not aiming at flags. What's that tell you?

[Ben Hollerbach]

Michael,

If your scoring average is two shots better than the field average you only have a better chance of winning IF your scoring distribution is equal or larger than that of the fields.

Lets say that the field average is 50% for a given week and to win a golf tournament you must play above the 80% range for the week. If you're average is 65% +/- 15% you'll will only ever kiss the win threshold on the furthest of outliers, just one week out of the year. But someone who is average at 50% and has a distribution of +/- 40% will clear that 80% threshold more often, giving themselves a lot more chances to win the golf tournament.

They will of course miss a very high number of cuts in the process, but if the goal is to win, they are the better bet.


Tiger is one of the best putters who has ever played....

[Erik J. Barzeski]

Michael,

If your scoring average is two shots better than the field average you only have a better chance of winning IF your scoring distribution is equal or larger than that of the fields.

Lets say that the field average is 50% for a given week and to win a golf tournament you must play above the 80% range for the week. If you're average is 65% +/- 15% you'll will only ever kiss the win threshold on the furthest of outliers, just one week out of the year. But someone who is average at 50% and has a distribution of +/- 40% will clear that 80% threshold more often, giving themselves a lot more chances to win the golf tournament.

They will of course miss a very high number of cuts in the process, but if the goal is to win, they are the better bet.

That's so bad… and I don't think you know why.

I agree that playing a game that has higher highs and lower lows is likely a great way to have "success" on the PGA Tour given how disproportionate the reward for winning/finishing top three is in PGA Tour events (and majors).

[Kalen Braley]

Erik,

Another perspective to consider for Zach's win at the Masters 2007. 

In poker its often asked, when someone wins a decent-sized event is it due to luck or skill?  And the simple answer is both.  When you're playing against 50 other skilled players, no way in hell you win without a few lucky hole cards, draws, and suck-outs, even if you have all the experience in the world.  To me the question is what percentage of one's success can be attributed to luck or skill.   For very good players in big events, I'd put the ratio at perhaps 67% skill and 33% luck.

When you look at Zach, and ask same question, of course there was a component of luck to his win, same as almost any winner.  To assign a value on the ratio in this case, I saw your stats on his approach shots that year, and agreed they were pedestrian.  But did you look at his putting stats?

2007
Category                  Tour Rank
One putt %                -  31
Putts/Round               -  22
Putt. from 5-15 feet  -  38
3 putt avoidance       -   8
Stroke Gained -putt   -  5
Total Putting               -  14

He was great with the flat-stick all year, perhaps borderline elite, so I'm inclined to think his performance in the Masters was far more attributable to skill than luck.

P.S.  Congrats on the win with your college team, but do you think they could use that same strategy and win the vast majority of the time on the same course against the same team?  Too bad all we have is one data point.

[Tim Gavrich]

But again, Zach employed the same strategy after that victory, and only once again finished inside the top 30.

I find it hard to believe that Zach Johnson has laid up on every single par 5 at Augusta since 2007. Is that really true? If so, that would be really strange as, from what I understand, ZJ's decision in '07 was driven by the cold and firm conditions. Obviously the course has played differently in many ways in the years since.

[Tim Martin]

Erik runs a glue factory as a side hustle when the lesson book is light. Apparently there aren’t any horses quite dead enough.