The long odds of nobody shooting 62 in a major

[Aguirre]

I believe Phil Mickelson was the 29th player to shoot 63 in a Major Championship on Thursday (if not, the 28th), and this brings up a question that is more mathematical than golf related, but of course related nonetheless. How is is possible that so many have shot 63, but not 62? 

I did (an admittedly limited) google search for an article or a paper (you can often find statistical papers in PDF form online that somebody wrote for a graduate project) addressing this subject, but found none. Now, we all know that any individual golfer's scores will be something of a bell curve. If you play your home course 100 times, keeping a handicap relatively the same over that period, the scores will bunch in the middle. If you're a 10 handicap, you'll have a lot of 85s, with the occasional 97 and 76.  But what if you had 29 80s, and zero 79s? 

Golf, I believe, is the most mental of what qualify as sports. The only other actions I can think of in sports that plague a golfer in contention for a title--or for shooting a 62 in a major--are basketball players on the free thrown line and kickers lining up a winning field goal. These are scenarios in which you have time to think. There are some baseball scenarios that are close, I suppose, and other situations that are in the ballpark, but none compare, in my opinion. Sure, your team may be down two points with a few seconds remaining on the clock, and the bball is sent into your hands behind the three point line, and you shoot a potential game winner/loser. This is considered a "clutch moment" if you hit the shot, and if you brick, a "choke." But you don't have a lot of time to process the consequences. In golf, you have WAY too much time to process the consequences.

I don't know about you, but I still get a bit of first tee jitters even when I'm not betting and nobody is watching but my playing partners. Golf is very unique this way.

So, I'm interested in your opinions. Is the fact that 29 golfers have shot 63, and zero 62s in majors a bizarre statistical anomaly, or something more related to the mental side of golf?

EDIT--Penalty kicks in soccer are probably another good comparison of "time to think."

Edited July 16, 2016 by Aguirre

[Scotsclaff]

Nobody has decided to do it yet.

[ChrisP]

I figured someone would do it St. Andrews. Rory missed a 3-footer on the Road Hole or else he would have. It's one of the strangest records in all of sports because of how many guys have come one shot from it and also because just how close guys have come to it. At least 3 guys had the ball down in the hole and something kept it from going in for a 62. As if there's a real Ghost of 62 or something.

[Hardspoon]

This answer is going to be kind of lame, but here goes: I think that rather than a statistical anomaly, it's a statistical feature (I voted "other").

If you think about all the rounds that have been played in majors (it's probably over 100,000), there have been very few 63's. You're on the tail end of the distribution, and you can only shoot a whole number.

So, you'd expect to see very few scores that are one above the "zero point" of 62.

There seem to be a lot of 64's...seems like someone does that every year.

[Chris223]

Someday it will happen.  And it wont come down to needing a birdie putt on the 18th.  When it happens the birdies will have to have been made I think before the 18th leaving a 2-putt par to seal it.

[b101]

4 hours ago, Hardspoon said:

If you think about all the rounds that have been played in majors (it's probably over 100,000), there have been very few 63's. You're on the tail end of the distribution, and you can only shoot a whole number.

You also tend to be very hot with the putter and approaches to be doing it, so there's always going to be at least one 'left out there'. It'll happen - Phil had no right to make that putt and had he missed it by a few feet we wouldn't be talking about any sort of curse...

[Aguirre]

12 hours ago, Hardspoon said:

This answer is going to be kind of lame, but here goes: I think that rather than a statistical anomaly, it's a statistical feature (I voted "other").

If you think about all the rounds that have been played in majors (it's probably over 100,000), there have been very few 63's. You're on the tail end of the distribution, and you can only shoot a whole number.

So, you'd expect to see very few scores that are one above the "zero point" of 62.

There seem to be a lot of 64's...seems like someone does that every year.

That answer isn't lame at all. It's good.

[Piz]

There have been 172 majors since Johnny Miller shot a final round 63, at Oakmont, in 1973.  For simplicity let us assume that 160 players started each and that the cut was exactly half the field.  That is 320 + 160 or 480 rounds per major.  480 x 172 is 82,560.  Use 150/75 and you get 77,400.  29 for 80,000 ?  Perhaps 63's are anomalies.  Does anyone know how steep the 63, 64, 65, 66 curve is?

 

 

[Piz]

Back again with some numbers.  I counted all the rounds in the 60's...and came up with this: 69/20, 68/17, 67/8, 66/3, 65/1, 64/0, and 63/1.  A total of 50 sub-70 scores of which just 2 were sub-66.  As it stands now; 63 is one for 390.  

[Hardspoon]

Well, throw in another 63.

[natureboy]

On 7/16/2016 at 9:22 AM, Hardspoon said:

This answer is going to be kind of lame, but here goes: I think that rather than a statistical anomaly, it's a statistical feature (I voted "other").

If you think about all the rounds that have been played in majors (it's probably over 100,000), there have been very few 63's. You're on the tail end of the distribution, and you can only shoot a whole number.

So, you'd expect to see very few scores that are one above the "zero point" of 62.

There seem to be a lot of 64's...seems like someone does that every year.

I tend to agree.

I think we may be seeing two factors. One is the tail end of the distribution effect and since there are only 4 Majors in a year there have only been about 30,000 rounds played in Majors since 1950. One season on tour has ~ 15,000 rounds played so scores at the low end for Majors will be less numerous as you say.

The other factor is possibly the 'Major test' difference. Troon's Standard Scratch Score which is fairly equivalent to the USGA Course Rating is 75.  The average CR on tour is in the vicinity of 76. In 2015 on the tour, a score of 12 under the CR (63 on CR of 75) happened about 1% of the time, 13 under about 0.5%, and 11 under about 2%. There were no 16 under standard CR rounds in 2015. It seems likely to me that the Major setup shifts the 'standard' CR by a shot or two so a 63 may be equivalent to a 62 or 61 on a standard tour setup.

Either way, we clearly saw some historic quality golf.

Edited July 18, 2016 by natureboy

[boogielicious]

Golf is hard. Majors are harder. Courses are set up more challenging.

[newtogolf]

Courses that host Majors are typically set up to play tough, this years Open was very kind to the leaders but typically the winds and weather don't cooperate. 

[Groucho Valentine]

62 is a tough score to shoot regardless of the tournament..lol

But both tiger and phil have lipped out for 62's in majors. So i don't think its impossible. As many have said, the majors are just usually set up to play tougher. I kind of feel like its just an anomaly, though.  

[JxQx]

I feel like it is a mix of the mental aspect of shooting the lowest round ever in a major and the fact that the courses are set up to be extremely difficult.

[Hardspoon]

6 hours ago, boogielicious said:

Golf is hard. Majors are harder. Courses are set up more challenging.

 

3 hours ago, JxQx said:

and the fact that the courses are set up to be extremely difficult.

The difficulty of the courses explains why scores are higher overall (63 versus 59), but it doesn't explain why 63/62 seems to be an artificial "wall" (as I described above, my contention is that it actually isn't).

3 hours ago, JxQx said:

I feel like it is a mix of the mental aspect of shooting the lowest round ever in a major

This could hypothetically cause a similar effect, but I think that for PGA players it is a non-factor.  Also, rounds like Stenson's 63 on Sunday were "ruined" before the 18th hole, so it's not like it has to do with pressure on a final putt or final approach shot.

I think someone is going to get a 62 eventually; it's just a matter of time.

[JxQx]

14 minutes ago, Hardspoon said:

 

The difficulty of the courses explains why scores are higher overall (63 versus 59), but it doesn't explain why 63/62 seems to be an artificial "wall" (as I described above, my contention is that it actually isn't).

This could hypothetically cause a similar effect, but I think that for PGA players it is a non-factor.  Also, rounds like Stenson's 63 on Sunday were "ruined" before the 18th hole, so it's not like it has to do with pressure on a final putt or final approach shot.

I think someone is going to get a 62 eventually; it's just a matter of time.

I agree that it will happen at some point. I think the "wall" is just mental construct. Though they play at the highest level the idea of setting a milestone like that or shooting 57, 58, 59 etc will add pressure making it more difficulty and I'm sure the idea sets in when they are going on a tear.

[No Mulligans]

A statistical anomaly in my opinion.

All those 63's are made up of seven times 9 under, eight times 8 under, and fifteen times 7 under.  If just one of the fifteen 7 under rounds had been one or two strokes better, presumable as good as those other 15 rounds that were either 8 under or 9 under, if that happened the 63 barrier would have been broken.

For Phil it was just a spike mark moving that last putt off line.  Just luck, or in that case bad luck.