[Mike Wagner]

Mike,

Since you know essentially nothing of my talents, how can you draw conclusions about them?

You say my conclusions about verifiable statistic are wrong, because I am not a tour pro, but you are apparently willing to accept Dave Pelz conclusions about nonverifiable statistics  (he could have made them up) even though he is not a tour pro.

You seem to believe in a discontinuity in tour pro performance, because after all they are tour pros.

We all know the modern-day ball goes farther. We all know courses have been lengthened to adjust for that. So shouldn't we see a rather smooth curve in improved scoring to account for that? What is your explanation for the discontinuity?
And, don't give the because tour pro are tour pros answer. That explains nothing.

I never said you were wrong.  What I said was I don't think you know how good tour pros really are.  I said that because it seems as though you're discrediting talent for your conclusion.


All in all, it's probably a relatively smooth curve based on the #s of golfers today (that can take it low),  and generally, once a barrier is broken, it becomes the new norm - the barrier gets broken.  Couple that with the fact that generally, with just about everything we do, there is continual improvement.  It's sort of the human condition, is it not?  Ultimately I'm saying your conclusions on equipment are a very small part of the equation.


Oh, and I never said Dave Pelz' conclusion were RIGHT either. 

[Garland Bayley]

Tour pros are very very good.

However,  ball manufacturers created a performance discontinuity with an over engineered ball.

Tour pros can hit it very long, because of that. The adjustment was to lengthen courses. Also, tour pros can hit it very straight because of that. However, I haven't seen the USGA narrow open fairways from 20 yards to 15 yards to adjust for that.

It is not just me saying the pros have gained straightness from the ball. I have seen remarks along those lines from Jack and others. Some of the old tour pros even say you couldn't hit the old ball straight, so had to play a curving shot every time.

[Rick Shefchik]

Has anyone calculated the Z score (or how many standard deviations from the mean) that Grace's score was vs Miller's?  That should give a pretty good indication of which round was more of an outlier - my intuition would tell me that Miller's was better.  Are the scores for all of the players still available for the day that Johnny shot 63?

Here's a page with the scores:


https://www.thoughtco.com/1973-us-open-63-reasons-johnny-miller-won-1564911


65 players teed it up that Sunday at Oakmont. Four of them broke 70: Miller (63), Lanny Wadkins (65), Jack Nicklaus (68) and the immortal Ralph Johnston (68.) The average score that day was 73.8.


By contrast, there were 77 players in the field on Saturday at Royal Birkdale. Forty-three -- or more than half -- broke 70. Next closest to Grace was Dustin Johnson's 64; there were five 65s. The average score was 69.0.

There is always pressure in an Open, but final-day pressure ratchets things up another notch. If Miller thinks his Sunday, tournament-winning 63 was a better round than Branden Grace's Saturday 62, he has some statistical evidence.

[Kalen Braley]

Has anyone calculated the Z score (or how many standard deviations from the mean) that Grace's score was vs Miller's?  That should give a pretty good indication of which round was more of an outlier - my intuition would tell me that Miller's was better.  Are the scores for all of the players still available for the day that Johnny shot 63?

Here's a page with the scores:


https://www.thoughtco.com/1973-us-open-63-reasons-johnny-miller-won-1564911


65 players teed it up that Sunday at Oakmont. Four of them broke 70: Miller (63), Lanny Wadkins (65), Jack Nicklaus (68) and the immortal Ralph Johnston (68.) The average score that day was 73.8.


By contrast, there were 77 players in the field on Saturday at Royal Birkdale. Forty-three -- or more than half -- broke 70. Next closest to Grace was Dustin Johnson's 64; there were five 65s. The average score was 69.0.

There is always pressure in an Open, but final-day pressure ratchets things up another notch. If Miller thinks his Sunday, tournament-winning 63 was a better round than Branden Grace's Saturday 62, he has some statistical evidence.

Rick,

As per the other thread going on about quality of players back then vs currently.....

This can be interpreted as yet another data point to claim there are far more better players now than back then.

[Rick Shefchik]

Yes, Kalen, it can. But it seems to me that Johnny Miller's detractors would use the data either way: If not many players went low, the field must have been lousy. If a lot of players had gone low, it would have been an easy day to score.   

[Kalen Braley]

Yes, Kalen, it can. But it seems to me that Johnny Miller's detractors would use the data either way: If not many players went low, the field must have been lousy. If a lot of players had gone low, it would have been an easy day to score.

Rick,


Just like Johnny's supporters would also use the data either way!! 


P.S.  The old guys vs current crop is perhaps my funnest one because its completely unwinnable! 

[Rick Shefchik]

Agree with your second point -- it's a hopelessly unwinnable argument.


But going back to the statistics from the two tournaments in question, it's hard not to conclude that Miller separated himself from the field better than Grace did. That's all you can ask a player to do.

[Kalen Braley]

Rick,


Agreed he separated better...as expected because the field was so much weaker! 

[Rick Shefchik]

Rick,


Agreed he separated better...as expected because the field was so much weaker! 

Let's agree to leave the unwinnable argument about respective fields out of this discussion. Do you think Birkdale on Saturday this year was as tough a golf course as Oakmont in 1973?

[Kalen Braley]

Rick,


Agreed he separated better...as expected because the field was so much weaker! 

Let's agree to leave the unwinnable argument about respective fields out of this discussion. Do you think Birkdale on Saturday this year was as tough a golf course as Oakmont in 1973?

Thats a really good question Rick.  I suspect Oakmont would be the tougher venue on thier respective days and respective equipment/length demands.

[Wayne_Kozun]

Miller	Grace
Score	63	62
Mean Score	73.77	69.03
Standard Deviation	3.14	2.68
Distance from Mean	-10.77	-7.03
Z score	-3.43	-2.62
Probability	0.03%	0.47%

I can't get the columns to line up properly but here is a bit of a statistical analysis.  You would have to say that Miller's feat is way more impressive.

[Matthew Essig]

Miller	Grace
Score	63	62
Mean Score	73.77	69.03
Standard Deviation	3.14	2.68
Distance from Mean	-10.77	-7.03
Z score	-3.43	-2.62
Probability	0.03%	0.47%

I can't get the columns to line up properly but here is a bit of a statistical analysis.  You would have to say that Miller's feat is way more impressive.

That z-score! Okay, Miller's was quite a bit better

[Garland Bayley]

... Do you think Birkdale on Saturday this year was as tough a golf course as Oakmont in 1973?

That's easy. At 7156 yards at sea level vs 6921 yards at near 1000 feet in elevation, clearly Birkdale is tougher. On average, Johnny would have to hit approaches 12.5 yards farther in denser air. His approaches would not have been near as close, and he couldn't have shot 65 obviously.
 

[Garland Bayley]

Miller	Grace
Score	63	62
Mean Score	73.77	69.03
Standard Deviation	3.14	2.68
Distance from Mean	-10.77	-7.03
Z score	-3.43	-2.62
Probability	0.03%	0.47%

I can't get the columns to line up properly but here is a bit of a statistical analysis.  You would have to say that Miller's feat is way more impressive.

Pretty poor analysis when you leave equipment out of the question.

[Wayne_Kozun]

Why does equipment matter?  Everyone today has better equipment and balls then they had 40 years ago.


Isn't the question - what is the best round in a major championship - Miller's or Grace's.  And Miller's round was statistically more exceptional.

[Garland Bayley]

Why does equipment matter?  Everyone today has better equipment and balls then they had 40 years ago.


Isn't the question - what is the best round in a major championship - Miller's or Grace's.  And Miller's round was statistically more exceptional.

If the equipment hasn't had an equalizing effect, then Miller's round was better, else Grace's round was better.

If the ball has not had an equalizing effect,  then why are 31 of the 35 rounds of 58 & 59 happened in professional tournaments in the last 17 years since the new ball came into being, and only 4 happened in the over 100 years of professional tournaments before that?

[Wayne_Kozun]

Why do the number of sub 60 rounds have anything to do with equalization?  I see that as improved absolute performance or, all things being equal, reducing the average score.  So a 59 today is fewer strokes below the mean, just like Grace's score was "only" 7 shots better than the average that day whereas Miller's score was about 11 strokes better than the average.  By equalization I presume you mean the dispersion of scores which statistically is measured by the variance or standard deviation.


And how do you know that the equalization of equipment is more important than the equalization of players skills?  In baseball there have been fewer equipment changes than in golf and I have been told that the variance in batting averages has come down, therefore there is an equalization of batting skill in baseball.  Perhaps the same has happened in golf and would have happened even if we were using 1970s equipment.

[Garland Bayley]

Well Wayne, it seems you haven't paid much attention to the thread, but just jump in with a meaningless statistical calculation without any consideration of controlling for variables.

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