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Strength and Depth of Field in Jack's Day and Tiger's Day


Phil McGleno

Strength and Depth of Field  

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  1. 1. Loosely Related Question (consider the thread topic-please dont just repeat the GOAT thread): Which is the more impressive feat?

    • Winning 20 majors in the 60s-80s.
      12
    • Winning 17 majors in the 90s-10s.
      150


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10 hours ago, ghalfaire said:

A few have tried to address that question with various statistics but until there is consensus on the definition, the question isn't answerable.

I know, people hate engineers for injecting this sort of thought into "over a beer discussions".

Your second statement here is disingenuous. You are claiming a degree of rigour and implying that others are shooting the breeze. I would venture that Iacas' statistics - and he has never claimed that they are anything other than educated and researched opinions - are about as close as you are going to get to an objective truth. But you have to go back to the "I don't want to argue with people that don't agree with me" standpoint. I don't really understand why.

My perspective:

FIELD IN JACKS DAY - A = Jack ....B = 10 name players .....C = 100 also rans which includes guys who did very well at times, but 60 you'd never heard of

FIELD IN TIGER'S DAY - A = Tiger plus 110 players. Of those 110 players there would be 80 that are household names to most golf fans. In tournaments where Tiger was absent, there would be 80 or 90 guys who, had they won, would have supporters who said they saw it coming. In other words, probably 80% of players who have either won or have come close to winning. Maybe 15% making up the numbers - players in decline, invitees or youngsters on the up.

Put Tiger against Jack's opposition and he's beating 90% of them 90% of the time - or something

Put Jack against Tiger's opposition and he's beating 60% of them 60% of the time Β - or something.

You don't have to be a Tiger fanatic to see that Tiger would dominate even more against a field that had a high percentage of players who were never really, really, good.Β 

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13 hours ago, Shorty said:

Your second statement here is disingenuous. You are claiming a degree of rigour (rigor) and implying that others are shooting the breeze. I would venture that Iacas' statistics - and he has never claimed that they are anything other than educated and researched opinions - are about as close as you are going to get to an objective truth. But you have to go back to the "I don't want to argue with people that don't agree with me" standpoint. I don't really understand why.

Β 

Well I think the word "disingenuous" means saying something that isn't true and knowing it isn't true, i.e. a lie.Β  I intended the remark to be β€œself-depreciating” in reference to a commonly held stereotype of engineers. However, if you or IACAS took offense it wasn't intended on my part.Β  So, I apologize if that is the case.

When the OP posted to begin this Thread, he said this was not a Jack Vs Tiger discussion, but rather a discussion of the "depth of field" in the Jack and Tiger eras.Β  However, he did also post that he felt the results would show Tiger played against more skilled competition and was better than Jack. But I would have thought such a post begs the question, what is depth/strength of field and how do you measure it?Β 

First, I’d like to say, again, I certainly think Tiger would much more often beat Jack in a head to head set of matches than Jack would beat Tiger.Β  But, in my mind, that has little to do with whether Jack’s 18 (20 if you prefer) was a more significant achievement, or not, than Tiger’s 14/17 major wins.Β  As I said earlier you can only beat the guys that show up and or lose to them as the case might be.Β  For lot of reason that have been stated several times, today’s professional golfers are just better than professional golfers in the mid/late 20th century.Β  Just so I am consistent with my own principal, to me better means today’s #10 would beat the #10 from the 60’s more times than not. It doesn’t mean that being #10 today is a more or less difficult achievement than in the 60’s.Β 

Whatever depth of field means it has to somehow address how difficult was/it is to win a given tournament.Β  That’s a discussion of how skilled the Tournament’s competitors were relative to each other, not how skilled they are relative to any other era’s golfers.

My intent with my original post was not to demean or belittle anyone’s efforts.Β  Just the opposite in fact as I believe defining β€œdepth/strength of field” is a difficult task, at least if you wish to obtain a consensus.Β  But also believe it is a necessary task to answering the OP’s question.

If I were King of TheSandTrap.com, I’m not IACAS is, I would define depth of field as follows:

1.Β Β Β Β Β  Obtain/calculate the probability of win for each competitor in a given tournament

2.Β Β Β Β Β  How many of the most probable to win competitors do I have to count to achieve a minimum cumulative probability of (pick a number) of 20% of the winner coming from this group.

3.Β Β Β Β Β  Either this number is the analog of the depth of field or maybe the percentage of field this number represents.

As I said, not an easy task and there are certainly other possible definitions that address depth of field.Β  But I like this one as it seems to address the question of how many players does the winner really have to beat to win the tournament.

Butch

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2 hours ago, ghalfaire said:

If I were King of TheSandTrap.com, I’m not IACAS is,

3 things

1 - yes, Erik rocks (buy the book) but

2 - mvmac isn't chopped spinach sirΒ  πŸ˜‰, Glen used to play pro, etc etc

3 - everyone knows that GIR is the true king

Bill -Β 

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2 hours ago, ghalfaire said:

Just so I am consistent with my own principal, to me better means today’s #10 would beat the #10 from the 60’s more times than not. It doesn’t mean that being #10 today is a more or less difficult achievement than in the 60’s.Β 

Sure it is,

Todays 50-150 are FAR superior to any golfers who would rank in the 50-150 back in Jack's time. Those 50-150 have a much higher chance of getting hot for a 4 day stretch, and really challenge the top 10.Β Β 

2 hours ago, ghalfaire said:

Whatever depth of field means it has to somehow address how difficult was/it is to win a given tournament.Β  That’s a discussion of how skilled the Tournament’s competitors were relative to each other, not how skilled they are relative to any other era’s golfers.

Depth of field is what it is. How competent the entire field is at the sport they are playing. No, it's a discussion on how skilled they actually are.

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Even though it's not an easy thing to quantify, I think you can only fairly compare the fields to what they could have at the time.Β  I would take the 100th ranked golfer today over the 10th ranked back in Jack's time just because of how much knowledge and training goes into today's game compared to back then, so the 10th best vs. 10th best comparison doesn't really do it for me.Β  But in the respective times everyone knew as much as they could about the game at the level.

So with professionals deciding to skip majors, skip tournaments, etc. in Jack's day, I would say those fields aren't as good as they should have been at the time, where nowadays Tiger beat everyone coming to every major and tournament more often so the fields were made up of more consistently the best golfers the world has to offer.Β  I think that alone means that the strength of the relative field is going to be tougher in Tiger's era compared to Jack's making Tiger's feats all the more impressive, especially considering Tiger's win % in general vs. the field.

On @saevel25's point and tying my view into it, the 100 people that showed up for tournaments in Jack's era probably had more non-top 100 golfers in the field compared to today in a similar circumstance.Β  So the relative skill isn't there either.

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2 hours ago, ghalfaire said:

ο»ΏWhen the OP posted to begin this Thread, he said this was not a Jack Vs Tiger discussion, but rather a discussion of the "depth of fieldο»Ώ" in the Jack and Tiger eras.Β  However, he did also post that he felt the results would show Tiger played against more skilled competition and was better than Jack. But I would have thought such a post begs the question, what iο»Ώs depth/strength of field and how do you measure it?ο»Ώ

There's not really a super objective way to measure it, because over the years too many things have changed. EvenΒ the weather changes at a tournament course from year to year.

That doesn't mean that there aren't objective measures. The field strength in the 1959 British Open was considerably weaker than it is these days.

Also, a much larger percentage of golfers were PGA Tour regulars back then, and a comparatively much smaller percentage are now.

2 hours ago, ghalfaire said:

But, in my mind, that has little to do with whether Jack’s 18 (20 if you prefer) was a more significant achievement, or not, than Tiger’s 14/17 major wins.Β As I said earlier you can only beat the guys that show up and or lose to them as the case might be.

I still don't feel as though you've read my posts. I feel like I addressed this.

The weaker fields BEAT Jack far more often than he beat them, and givenΒ the dozens of majors in which both have played, we can use their wins and losses to evaluate players.

Again, if Jack played against a bunch of ten year olds, and won 18 times, but lost 62 other times, you'd have to conclude that he was likely much worse of a golfer than a guy who beat grown adult men 10 times but lost 70, wouldn't you?

2 hours ago, ghalfaire said:

For lot of reason that have been stated several times, today’s professional golfers are just better than professional golfers in the mid/late 20th century.Β Just so I am consistent with my own principal, to me better means today’s #10 would beat the #10 from the 60’s more times than not. It doesn’t mean that being #10 today is a more or less difficult achievement than in the 60s.

I believe that it does.

It was easier to be in the top 125, the top 50, the top 10, and the top 1 back then.

I think you're saying that because both were #1 for a long stretch of time, it's tough to gauge how far apart from #2 they were… but yet that fails for two reasons, one of which I've talked about several times now:

  • They didn't always win. This isn't a case of trying to figure out how great Secretariat was. Jack lost a lot of golf tournaments. He lost to the ten-year-olds a lot (just an example). This isn't a case of Jack going 80-0 against really really weak fields of ten-year-olds and us not being able to put that into any context. Jack lost to the ten-year-olds often. Far more often than "he could only beat the field who was there." He lost to the field that was there a lot.
  • Tiger's separation from #2 could be measured… using the OWGR. Heck, at one point, Tiger could have split his points among two people and been #1 and #2 in the OWGR. Now, I'm not saying the OWGR is perfect… but it is a form of measurement, and I imagine someone could keep going back in history and figure out the OWGR for Jack all those years if they wanted to. (Then again, there were many, many years when Jack wasn't the #1 player that year, so those who support Jack as GOAT may not wish to do that.)

At any rate, you can't keep going with the "they could only beat who showed up" because they LOST quite often to those same guys.

So again, if you go 18-62 against aΒ field that averages 290 grade points, are you better or worse than a guy who goes 14-66 against a field that averages 500 grade points. I'd argue that you're worse. That 14x > 18y.

2 hours ago, ghalfaire said:

Whatever depth of field means it has to somehow address how difficult was/it is to win a given tournament.

Again, the flaws here are that any percentage is going to add up to 100%, and if Jack plays against weaker fields, he's going to be a higher percentage, yet while a BETTER player against STRONGER fields might be a lower percentage.

In other words, let's say that Jack has a 15% chance to win against a field of ten-year-olds, but Tiger has a 10% chance to win against a field of grown men. Which one is the better golfer? I think the answer here is obvious.

But, again, winning is just ONE position, and there's only one tournament to win.

strength_and_depth.jpg

This sums up my general idea re: strengthΒ andΒ depth of field.

People have ranges of abilities. Some weeks and months Jack didn't play well, and other months he played better than his average. He was still always an "A" player. But he had far fewer "A" players against which to play, and a lot of "C" or "D" players. Those increase his chances of winning.

#125Β in the field right now might have about the same chance of winning as #125 back in Jack's day (roughly 0%, though back in Jack's day it wasΒ actuallyΒ 0%, and today it's probably more like 0.3%)… but yet #125 today would kick the snot out of #125 back then, because #125 back then was probably not even a full-time professionalΒ golfer. #125 in the field back then may have been @Phil McGleno.

2 hours ago, ghalfaire said:

If I were King of TheSandTrap.com, I’m not IACAS is, I would define depth of field as follows:

Did you miss the post where I put forward a definition of bothΒ depth and strength?

2 hours ago, ghalfaire said:

1.Β Β Β Β Β  Obtain/calculate the probability of win for each competitor in a given tournament

I spoke to this. It's a dumb way to go because there's only one event, so they're always going to add up to 100%, and yet given the example above re: Jack at 15% and Tiger at 10% playing against vastly different fields… it just doesn't work.

The percentage stuff doesn't cut it. It doesn't work. Because it's based only on the fields at the time - it doesn't compare at all the fields from 1970Β against the fields from 2000 or whatever.

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On 6/3/2018 at 7:17 PM, parman said:

Wow, there is an internet? Who would have thunk? And the information is as good as the word of God. LOL Second hand knowledge from an article or some old youtube video and everyone is an expert regardless of subject or age. I saw Jack play in Las Vegas in 1969 in person. When did YOU see him play IN PERSON? Oh, I forgot you are an internet expert so no need to actually see something live. 😎

When did you see TigerΒ play?Β  Or Ben?Β  Or Byron?Β  Or Sam?Β  Or Harry, or Walter, or Bobby?

And do you seriously think that seeing a player one time in person is enough to put him on the top of the whole world golf heap?

I'll wait while you chase those kids off your lawn.

On 6/3/2018 at 10:34 PM, fishgolf said:

I find this thread and the other Jack vs. Tiger threads entertaining.Β  It's also clear that the TW fans are continually trying to make the case - which is certainly understandable.Β  I wonder if there was similar banter between the Bobby Jones and Jack Nicklaus fans?Β 

Β 

Where would that banter ever have taken place?Β Β 

On 6/4/2018 at 8:57 AM, ghalfaire said:

Β 

I know, people hate engineers for injecting this sort of thought into "over a beer discussions".

Nah, it is probably because they think everything is quantifiable, which is pretty crazy.Β  So they come off like the English professor at the end of Dead Poet's Society who is teaching that the quality of a poem can be computed mathematically.Β  And I say this as a retired math guy.

But then again, what the hell do I know?

Rich - in name only

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1 hour ago, turtleback said:

Where would that banter ever have taken place?Β Β 

At the old fashion internet; local cafes, pubs, and work coffee break areas.Β  No doubt the Bobby Jones fans rooted against Jack surpassing his records.Β  I see this depth of field discussion as an attempt by TW fans to take the sting out of those 18 majors winsΒ and 19 2nd place finishes. That is amazing.Β  Moreover, he accomplished this amongst a very strong pool of talent who, accounting for changes in equipment, would be posting wins in todays field of players.

Just wanted to add that I have nothing againstΒ Tiger. He is a phenomenal golf talent and without the life woes andΒ medical breaks may very well have surpassed Jack's records.Β  My beef is with the media who, for me, ruined him by oversaturationΒ and uncontrolled drooling.Β 

Edited by fishgolf
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50 minutes ago, fishgolf said:

I see this depth of field discussion as an attempt by TW fans to take the sting out of those 18 majors winsΒ and 19 2nd place finishes. That is amazing.

Ha ha ha. No.

We discuss it because it’s a very real thing.

50 minutes ago, fishgolf said:

Moreover, he accomplished this amongst a very strong pool of talent who, accounting for changes in equipment, would be posting wins in todays field of players.

No. They were not nearly as amazing as more modern players, and their win totals would have been significantly affected.

You do realize that better equipment artificiallyΒ narrows the gap, right? Right???

50 minutes ago, fishgolf said:

My beef is with the media who, for me, ruined him by oversaturationΒ and uncontrolled drooling.

Gee, that’s relevant… not.

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Well after reading some of the responses to my last post and re-reading @iacas, thick though I am, I see the problem. You (all) seem to be saying that because today's professionals are as a group better than professionals of the 60s, that the depth of field is greater. If that is the definition, then you're right as I agree they today's pros are better than the pros of the 60s.

I was trying to address which of the two golfer, Tiger or Jack, had the more difficult task of winning a major.Β  As a few you pointed out Jack was beaten several time by the other good players (and some not so good players) of his era.Β  Also note worthy is that Tiger won several of his major by large margins whereas Jack, not so much, most of his wins were by a few strokes.Β  To me that meant the field he played against had skills close to Jack whereas Tiger was clearly the best golfer on the course when ever he stepped on the course.Β  In other words Jack couldn't win with his B game and Tiger did several time.Β  When you win major tournaments by more than 10 strokesΒ  I would conclude that the field Tiger played against was no where near his equal in skills.Β  To me that would mean that Jack had a tougher time because the field was more nearly his equal than Tiger's field was Tiger's equal.Β  Because of that I would personally think Jack's achievement was more difficult and therefore more significant.Β  But that's just me.Β Β  Just a last comment here,Β  I believe Tiger was the most skilled Professional golfer of my life time, and I'm over 70, and by a significant margin.Β  The reason he didn't win more majors had nothing to do with competition or depth of field, only Tiger stopped Tiger, because there wasn't anyone else that could have.

I'm now done.

Butch

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4 minutes ago, ghalfaire said:

To me that would mean that Jack had a tougher time because the field was more nearly his equal than Tiger's field was Tiger's equal.Β  Because of that I would personally think Jack's achievement was more difficult and therefore more significant.Β 

That is a ass backward way of thinking.Β 

You are saying, because Jack was not as good his achievements are better? Seriously?

Yea, that logic doesn't fly at all.Β 

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2 hours ago, iacas said:

You do realize that better equipment artificiallyΒ narrows the gap, right? Right???

So you're saying todays players continue to produce their current stats using equipment from Jacks era?Β  It works both ways.

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3 hours ago, saevel25 said:

That is a ass backward way of thinking.Β 

You are saying, because Jack was not as good his achievements are better? Seriously?

Yea, that logic doesn't fly at all.Β 

Well, he IS an engineer.Β  He doesn't get that the spread of global golf and the increase in money vastly increased the universe ofΒ golfers from which the very best are winnowed down to the 200 or so who play at a world class level.Β  Β Β Β 

3 hours ago, fishgolf said:

So you're saying todays players continue to produce their current stats using equipment from Jacks era?Β  It works both ways.

i don't have a clue of what you are saying here, but that is only because it is incoherent.

But then again, what the hell do I know?

Rich - in name only

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7 hours ago, saevel25 said:

That is a ass backward way of thinking.Β 

You are saying, because Jack was not as good his achievements are better? Seriously?

Yea, that logic doesn't fly at all.Β 

It's not that ass-backward even if it isn't entirely on-topic. Did you read the rest of his post? The part where he acknowledges that Tiger was the best golferΒ by a wide margin?

I don't know that what's he saying is true and even if so, I wouldn't agree Jack's achievements were better. But I think he's saying that Tiger was so good that he destroyed even the better competition. While Jack, against lesser competition, had to grind to pull out the victories.

3 hours ago, turtleback said:

Wο»Ώell, he IS an engineer.Β  He doesn't get that the spread of global golf and the increase in money vastly increased the universe ofΒ golfers from which the very best are winnowed down to the 200 or so who play at a world class level.Β  Β Β Β 

i don't have a clue of what you are saying here, but that is only because it is incoherent.

I know this is an emotional subject for you @turtlebackΒ and that it gets really old when not everyone agrees, but do you really have to reply like this?

Jon

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1 hour ago, JonMA1 said:

It's not that ass-backward even if it isn't entirely on-topic. Did you read the rest of his post? The part where he acknowledges that Tiger was the best golferΒ by a wide margin?like this?

Not part of this thread. This thread is about the strength of competition, not if Tiger is the best or not.

To try to shift the definition of depth to be based around the strongest person of that time doesn't make sense at all.

Now we have to say, "What if we dump Tiger into Jacks Era". By his argument then, the depth of field suddenly would disappear all together because now we must compare it to Tiger. This means the depth of field is just how good the best player is. We ask, what changed, well we added Tiger. So, actual ability of the field didn't change. This means, the depth of field didn't change at all. The strength of competition is not relative to the best player, it's what their actual playing ability is.

Yes he got it backwards.

9 hours ago, fishgolf said:

So you're saying todays players continue to produce their current stats using equipment from Jacks era?Β  It works both ways.

No one said that at all.

Let's say the best golfers in the world hit the sweet spot 98% of the time. Lets say the rest of the field hit it 90% of the time. Who is going to benefit more from equipment that is designed to help out those who do not hit the sweet spot more often?

Not only are the bottom half of the PGA Tour really good, they are also closing the gap even more because equipment helps them get away with some of the misses that the best golfers don't produce as often.

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9 hours ago, ghalfaire said:

Well after reading some of the responses to my last post and re-reading @iacas, thick though I am, I see the problem. You (all) seem to be saying that because today's professionals are as a group better than professionals of the 60s, that the depth of field is greater. If that is the definition, then you're right as I agree they today's pros are better than the pros of the 60s.

That's not what anyone has said. There are proofs of this; it's not just the opinions that "today's professionals are as a group better than professionals of the 60s…". It's a mathematical certainty.

@turtlebackΒ said it pretty succinctly:

5 hours ago, turtleback said:

Heο»Ώο»Ώ doesn't get that the spread of global golf and the increase in money vastly increased the universe ofΒ golfers from which the very best are winnowed down to the 200 or so who play at a world class levelο»Ώ.ο»Ώ

THAT is (primarily) what has increased the strength and depth of field.

Again, Jack played against fields that were literally 1/3Β local club pros. The PGA Tour back then would recruit local club pros in part because they had to (they were still part of the PGA, or had just recently split from the PGA), and in part to draw interest from the areas in which they were hosting the events.

As this graph illustrates:

strengths.png

And as the graph that I made above illustrates - the one that includes "club pros" inΒ the Nicklaus graph (because they were in the fields), and which doesΒ notΒ include "club pros" in the Tiger graph because they wereΒ notΒ in the field.

9 hours ago, ghalfaire said:

If that is the definition, then you're right as I agree they today's pros are better than the pros of the 60s.

PGA Tour players are better than the players who played in the 60s, absolutely. IMO it's not even really by a little bit. Even Jack NicklausΒ said this in 1996, while simultaneously talking about how there would never be another dominant player because the strength and depth of the field has gotten so high… D'oh!

9 hours ago, ghalfaire said:

I was trying to address which of the two golfer, Tiger or Jack, had the more difficult task of winning a major.

Uh, so have we. Tiger did, by far.

9 hours ago, ghalfaire said:

Also note worthy is that Tiger won several of his major by large margins whereas Jack, not so much, most of his wins were by a few strokes. To me that meant the field he played against had skills close to Jack whereas Tiger was clearly the best golfer on the course when ever he stepped on the course.Β  In other words Jack couldn't win with his B game and Tiger did several time.Β  When you win major tournaments by more than 10 strokesΒ  I would conclude that the field Tiger played against was no where near his equal in skills.Β  To me that would mean that Jack had a tougher time because the field was more nearly his equal than Tiger's field was Tiger's equal.

Yeah, like others said, you've got it backward.

Jack didn't have a tougher time. It was easier to win a major in Jack's era, because fewer people were capable of actually winning it. If those people had an off week, you could win. Tiger needs to have a great week or have about 100 people with an off week.

From your perspective, Jack had a "tougher" time winning majorsΒ because he wasn't as good as Tiger.

That's a horrible way to define either the strength or depth of field, the definitions for which I proposed a few posts up, which I'm still not sure you saw.

9 hours ago, fishgolf said:

So you're saying todays players continue to produce their current stats using equipment from Jacks era?Β  It works both ways.

No, it doesn't.

I said that improvements to equipment narrows the gap between, say,Β Tiger and the others.

Tiger and Jack could have played with anything and done very well. It's when equipment turned average ball strikers (PGA Tour level average) or slightly below average ball strikers into good ball strikers that the gap betweenΒ the best and the rest narrowed.


@ghalfaire, what possible proof or explanation do you have to support the idea that the strength and/or depth of fields was better in the 60s and 70s than during Tiger's time?

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8 hours ago, JonMA1 said:

It's not that ass-backward even if it isn't entirely on-topic. Did you read the rest of his post? The part where he acknowledges that Tiger was the best golferΒ by a wide margin?

I don't know that what's he saying is true and even if so, I wouldn't agree Jack's achievements were better. But I think he's saying that Tiger was so good that he destroyed even the better competition. While Jack, against lesser competition, had to grind to pull out the victories.

I know this is an emotional subject for you @turtlebackΒ and that it gets really old when not everyone agrees, but do you really have to reply like this?

Like what?Β  Pointing out the absurdity of deciding who was best by who you saw in person?Β 

Or pointing out that theΒ guy criticizing others for not quantifying strength/depth of field and putting a number on it is ignoring the 800 pound elephant in the room that the increase in strength/depth is due to the increase on the pool of players?Β  There is a flip side to the engineering argument that if you can't put a number on itΒ you don't really know anything about it.Β  Just because you put a number on something doesn't mean you know anything about it.Β  Too often putting numbers on things only serves as a fallacious way of giving a patina of objectivity to something that is inherently subjective.Β 

And it is not an emotional subject to me it is a rational subject to me, to which I make rational arguments.Β  The strength of field issue is about a lot more than Tiger/Jack, so saying that he admits Tiger was better doesn't justify ignoring factors and using bad logic.Β  The strength of field issue is, IMO, more important to things like Phil's, Ernie's and Vijay's place in the pantheon.Β 

Because even if we stipulate that Tiger and Jack faced the same strength/depth of field,Β (which, of course they didn't - but stipulated for the sake ofΒ argument)Β Β Tigers overall career still puts him far ahead of Jack.Β  That is why I rarely even bring it up in the Tiger/Jack thread.Β  I don't need it to make my case.Β  Β The strengthΒ of field argument is just icing on the cake, in that context.Β Β 

But then again, what the hell do I know?

Rich - in name only

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1 hour ago, turtleback said:

Pointing out the absurdity of deciding who was best by who you saw in person?Β 

That wasn't the quote in question. Look at whoΒ @saevel25Β was quoting and what that person was saying in that particular post.Β 

Either way, if you want to insult people on a golf forumΒ for looking at things differently about - of all things - depth of field in different eras,Β have at it.

Jon

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