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Plus grading and a Cautionary Note on Grade Premiums (a forum classic)
kranky
Posts: 8,709 ✭✭✭
Brought back to the top April 2010 as I think this is very relevant to the Plus grading now being offered. The original title of the thread was " Visual Argument against Over-Reliance on Population Reports and A Cautionary Note on Grade Premiums"
This post was originally made by Supercoin in 2002. Since it's archived now, it can't be bumped and I think this was a very interesting post and worthy of revisiting and fresh discussion. There is a lot of information in this post, it's long but worth the time to digest.
If Supercoin was still around I would have asked him to do this. If you want to read the replies to the original post, it's here, there is good info in the replies there as well.
Below this line is Supercoin's original post, verbatim.
________________________________________________
The title is a warning, it's also a long post.
I thought it might be useful to put in visual terms some of what I've been saying off-and-on over the past months. As you might have guessed by the number of photos I post, I think better in visual terms. In fact, doing this, I reached a specific conclusion that I hadn't really formed before.
I use Ikes as an example, but the same reasoning applies equally to any common-date condition-rare coin (State Quarters, 1881-S Morgans, 1945-P Mercury dimes, etc.)
_______________________________________________________
The population reports are, I feel, one of the greatest benefits of professional grading. Obviously they are key to my favorite series, Ike dollars, as virtually all Ikes are common in typical condition. It's not until you try to find high-end examples that things get tougher and more interesting.
I have always maintained that the pop report's strength is to show general trend, not specifics, since grading is in an inexact art.
The pop report is very useful, then, to show that 1972-P Ikes are tough to find in gem MS65+ grades despite their huge mintage. They also show that lower-mintage 1972-S Ikes are by the far the easiest date to find nice, readily available even in superb MS68 grades.
That's valuable information for enthusiasts of the series, dealers and collectors alike. It helps confirm an individual's experience by seeing what others' experience around the country has been. In the simplest terms, a collector knows that he can expect to pay more for a gem 1972-P than a superb 1972-S despite the much lower grade of the 72-P. A powerful and informative tool, used correctly.
However, once we start trying to use the pop report as an exact measurement, it falls apart. For example, it is not valid to assert that the three 1972-S Ikes graded PCGS MS69 are nicer than all 463 of the PCGS MS68 examples, even assuming they were all graded by the same standards.
But, that's often exactly how high-grade low-pop coins are marketed -- i.e. "finest known" is used in place of "highest-graded". But these are two very different things.
Making this distinction more important is that in today's market high-grade low-pop coins are bringing previously unheard of premiums.
So I put together some visual graphs that may help show the fallacy of those marketing claims, as well as help show what you are getting when you buy a high-grade low-pop coin.
In each graph, circles represent coins in various grades according to color. From left to right, each position represents an increase of 1/4 point in grade. The numbers along the bottom indicate the grade written on the label.
_______________________________________________________
Pop Report as Discrete Numbers
When we read a pop report, we get just the number of coins in each grade, we have no information as to whether those coins are low-end or high-end for the grade.
The above graph shows how a pop report "looks" in the manner in which it is generally discussed. It assumes the coins are all middle of the grade. Everything is neat and tidy, with significant gaps between each grade.
Each jump in grade clearly deserves a premium for those who seek condition-rarity.
_______________________________________________________
Pop Report Distributed Realistically
The above graph shows a more realistic distribution of the same populations, tapering off as the grade increases.
It assumes that PCGS grades perfectly, so all coins are still within the correct grade range.
This graph shows a very important trend -- the higher the grade level, the more likely the coin is to be on the low-end of the grade.
In this particular example, an MS66 is twice as likely to be low-end as high-end, an MS67 is four times as likely to be low-end as high-end, and of course the sole MS68 is low-end for the grade.
Looking at this graph, you could conclude that grade increases are still worth premiums, but not as significant as before. In particular, you need to be much more careful paying a premium for the top grades, as they progressively tend towards "just made it" status.
_______________________________________________________
Pop Report Distributed Realistically, Including Margin of Error
The above graph shows the same distribution of the populations, but assuming a margin of error in PCGS grading consistency, of +/- one-quarter point.
It shows the obvious and well-known fact that some coins are over- or under-graded. But more importantly, it shows that coins that are at the upper grades are more likely to be overgraded, simply because more of those coins are at the lower end of the grade and thus more vulnerable.
_______________________________________________________
So, what does that all mean? Unfortunately, exactly what you might hope it didn't:
Highest-grade, low-population coins are more likely to be overgraded than lesser grades.
Or put in financial terms, coins with the most financial risk also carry the most grade risk.
Obviously there are a whole bunch of assumptions implied and expressed here.
One obvious implied assumption is that PCGS grades all coins with equal care, when in fact you could argue that they are more careful with higher and more expensive grades.
But, on the other hand, another assumption is that PCGS can routinely grade to within a quarter-point of accuracy. That is a stunning degree of accuracy which is unattainable in the real world, and if increased to a more realistic level would of course make overgrades much more likely.
So, specifics aside, I think the general argument is valid and in line with common sense. If not, poke some gaping holes in it.
This post was originally made by Supercoin in 2002. Since it's archived now, it can't be bumped and I think this was a very interesting post and worthy of revisiting and fresh discussion. There is a lot of information in this post, it's long but worth the time to digest.
If Supercoin was still around I would have asked him to do this. If you want to read the replies to the original post, it's here, there is good info in the replies there as well.
Below this line is Supercoin's original post, verbatim.
________________________________________________
The title is a warning, it's also a long post.
I thought it might be useful to put in visual terms some of what I've been saying off-and-on over the past months. As you might have guessed by the number of photos I post, I think better in visual terms. In fact, doing this, I reached a specific conclusion that I hadn't really formed before.
I use Ikes as an example, but the same reasoning applies equally to any common-date condition-rare coin (State Quarters, 1881-S Morgans, 1945-P Mercury dimes, etc.)
_______________________________________________________
The population reports are, I feel, one of the greatest benefits of professional grading. Obviously they are key to my favorite series, Ike dollars, as virtually all Ikes are common in typical condition. It's not until you try to find high-end examples that things get tougher and more interesting.
I have always maintained that the pop report's strength is to show general trend, not specifics, since grading is in an inexact art.
The pop report is very useful, then, to show that 1972-P Ikes are tough to find in gem MS65+ grades despite their huge mintage. They also show that lower-mintage 1972-S Ikes are by the far the easiest date to find nice, readily available even in superb MS68 grades.
That's valuable information for enthusiasts of the series, dealers and collectors alike. It helps confirm an individual's experience by seeing what others' experience around the country has been. In the simplest terms, a collector knows that he can expect to pay more for a gem 1972-P than a superb 1972-S despite the much lower grade of the 72-P. A powerful and informative tool, used correctly.
However, once we start trying to use the pop report as an exact measurement, it falls apart. For example, it is not valid to assert that the three 1972-S Ikes graded PCGS MS69 are nicer than all 463 of the PCGS MS68 examples, even assuming they were all graded by the same standards.
But, that's often exactly how high-grade low-pop coins are marketed -- i.e. "finest known" is used in place of "highest-graded". But these are two very different things.
Making this distinction more important is that in today's market high-grade low-pop coins are bringing previously unheard of premiums.
So I put together some visual graphs that may help show the fallacy of those marketing claims, as well as help show what you are getting when you buy a high-grade low-pop coin.
In each graph, circles represent coins in various grades according to color. From left to right, each position represents an increase of 1/4 point in grade. The numbers along the bottom indicate the grade written on the label.
_______________________________________________________
Pop Report as Discrete Numbers
When we read a pop report, we get just the number of coins in each grade, we have no information as to whether those coins are low-end or high-end for the grade.
The above graph shows how a pop report "looks" in the manner in which it is generally discussed. It assumes the coins are all middle of the grade. Everything is neat and tidy, with significant gaps between each grade.
Each jump in grade clearly deserves a premium for those who seek condition-rarity.
_______________________________________________________
Pop Report Distributed Realistically
The above graph shows a more realistic distribution of the same populations, tapering off as the grade increases.
It assumes that PCGS grades perfectly, so all coins are still within the correct grade range.
This graph shows a very important trend -- the higher the grade level, the more likely the coin is to be on the low-end of the grade.
In this particular example, an MS66 is twice as likely to be low-end as high-end, an MS67 is four times as likely to be low-end as high-end, and of course the sole MS68 is low-end for the grade.
Looking at this graph, you could conclude that grade increases are still worth premiums, but not as significant as before. In particular, you need to be much more careful paying a premium for the top grades, as they progressively tend towards "just made it" status.
_______________________________________________________
Pop Report Distributed Realistically, Including Margin of Error
The above graph shows the same distribution of the populations, but assuming a margin of error in PCGS grading consistency, of +/- one-quarter point.
It shows the obvious and well-known fact that some coins are over- or under-graded. But more importantly, it shows that coins that are at the upper grades are more likely to be overgraded, simply because more of those coins are at the lower end of the grade and thus more vulnerable.
_______________________________________________________
So, what does that all mean? Unfortunately, exactly what you might hope it didn't:
Highest-grade, low-population coins are more likely to be overgraded than lesser grades.
Or put in financial terms, coins with the most financial risk also carry the most grade risk.
Obviously there are a whole bunch of assumptions implied and expressed here.
One obvious implied assumption is that PCGS grades all coins with equal care, when in fact you could argue that they are more careful with higher and more expensive grades.
But, on the other hand, another assumption is that PCGS can routinely grade to within a quarter-point of accuracy. That is a stunning degree of accuracy which is unattainable in the real world, and if increased to a more realistic level would of course make overgrades much more likely.
So, specifics aside, I think the general argument is valid and in line with common sense. If not, poke some gaping holes in it.
New collectors, please educate yourself before spending money on coins; there are people who believe that using numismatic knowledge to rip the naïve is what this hobby is all about.
0
Comments
Russ, NCNE
Thanks a ton for the re-visit. I do not think I read the original post, or replies, but it's worthwhile thinking about the high enders with pop 3 or fewer coins reported. Especially when you are considering forking out big bucks.
The presentation can extend to many series, where there are multiple 64's and 65's, and just a handful of 66's. In most of the dates in capped bust halves, there are many more pq 64's, and some pq 65's, and only a very infrequent 66, that some one might say is on the edge of a higher grade.
I have several MS 66's(PCGS and NGC) in this series, and off-hand, I can only come up with one 66 (1823) that is awesome for grade. But among the 64's and 65's, there are many.
The PCGS 1818 in MS 65 I own is nicer than every other MS66 in the set, besides the one mentioned above. While it may eventually upgrade, it reflects Supercoin's theories to a T. I have not viewed the pop 1 MS 66 for this date, but doubt it is nicer than the PQ 65 mentioned.
I also agree that one needs to be real careful in buying top pops, and that the coin needs to be awesome, if you are about to pay an awesome price.
Thanks again for the re-visit.
New collectors, please educate yourself before spending money on coins; there are people who believe that using numismatic knowledge to rip the naïve is what this hobby is all about.
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1) On regrades, does this mean that higher the grade a coin is in a series, that it is more likely that a coin will either increase a grade or reduce a grade (rather than stay the same grade)? If this is the case, and PCGS limits the downgrade exposure, then it seems that the odds are higher that one will get an upgrade as the population thins up. (I'm not statisically challenged, I'm just playing with numbers.)
2) On crossovers, based on a normal distribution within a grade, that unless there close to a full grade difference, then the crossover % should be higher than what the evidence suggests. The experience that many of us see is that crossovers seem to show a full grade differential...that is, only the top 25% of the grade seem to cross. I didn't explain this point very well but think about it for a moment.
keoj
I had to read this 3 times, but you said it more accurately than I did. Certainly more clear than the former Fed Chairman ever mad any point.
keoj
As Tad said in his disclaimer.......One obvious implied assumption is that PCGS grades all coins with equal care, when in fact you could argue that they are more careful with higher and more expensive grades.
and it sets us apart from practitioners and consultants. Gregor
However more information is necessary to validate the outcome. One important question: Who assigned the 1/4 point grade to the coins in the graph. Was the grading unbiased. That is how do we know that the 1/4 point grader was more onbjective than the TPG. The experiment would need to be designed to remove any bias that more coins in each range should be in the lower quartile for assigned grade.
<< <i>Great analysis Kranky. It makes grading seem more scientific than objective. It also makes good that old addage "buy the coin not the holder" >>
Everything was written by Supercoin, I just reposted it from an old thread that couldn't be bumped.
New collectors, please educate yourself before spending money on coins; there are people who believe that using numismatic knowledge to rip the naïve is what this hobby is all about.
K
Doggedly collecting coins of the Central American Republic.
Visit the Society of US Pattern Collectors at USPatterns.com.
I wound up with a very nice Registry set (#14), without paying Moon Money for it. and I'll bet my set (since sold) looked as nice or nicer than some with higher numbers that had one or two fewer insignificant marks than mine, but less fur on the Buffalos.
(edited to fix typos.)
my early American coins & currency: -- http://yankeedoodlecoins.com/
New collectors, please educate yourself before spending money on coins; there are people who believe that using numismatic knowledge to rip the naïve is what this hobby is all about.
Website-Americana Rare Coin Inc
New collectors, please educate yourself before spending money on coins; there are people who believe that using numismatic knowledge to rip the naïve is what this hobby is all about.
One flaw, and I mean not to be picky, but Don Willis said the coins in each grade formed a bell curve distribution. Meaning the majority of the coins were xx.4 xx.5 and xx.6. This shows the majority at xx.0 then xx.1, and so on.
I am a visual guy too so I wonder how the graph would look as a bell curve.
New collectors, please educate yourself before spending money on coins; there are people who believe that using numismatic knowledge to rip the naïve is what this hobby is all about.
<< <i>Very good insight. I mean this came out 4 years ago. Well done.
One flaw, and I mean not to be picky, but Don Willis said the coins in each grade formed a bell curve distribution. Meaning the majority of the coins were xx.4 xx.5 and xx.6. This shows the majority at xx.0 then xx.1, and so on.
I am a visual guy too so I wonder how the graph would look as a bell curve. >>
It sort of does, actually. Let there be three uncirculated grades, ugly (equivalent to 60-61), plussable (62-68), and übergrade (69-70). Consider an issue for which there is a statistically useful number of uncirculated specimens in the plussable grade range. You could have a few different types of grade distributions that approximate reality. If you have the right half of a normal distribution, starting at the point within the plussable grade range that is the mean, your grade distribution would look like this, assuming a variance of 3, with the data normalized such that the sum under the normal distribution curve from the mean on up is 50 (there's no good BBS markup language to show mathy stuff):
Grade Pop Split Total
mean+0 23.03878388
0.1 23.00041789
0.2 22.88570282 68.92490459
0.3 22.69578107
0.4 22.43253555
0.5 22.0985586
0.6 21.69710955 88.92398477
0.7 21.23206172
0.8 20.70784025
0.9 20.12935206 62.06925404
1 19.50190952
1.1 18.83114946
1.2 18.12294928 56.45600826
1.3 17.38334189
1.4 16.61843107
1.5 15.83430916
1.6 15.03697826 64.87306037
1.7 14.23227659
1.8 13.42581104
1.9 12.62289697 40.28098461
2 11.82850605
2.1 11.04722264
2.2 10.28320914 33.15893783
2.3 9.540180301
2.4 8.821386449
2.5 8.129605389
2.6 7.467142417 33.95831456
2.7 6.835837894
2.8 6.237081625
2.9 5.67183322 11.90891485
The first column represents the grade above the mean for that issue, the second represents the population at that grade, and the third is a sum of a grouping of 3 (low end for the next point), followed by 4 (mid-range/"solid"), followed by 3 (high-end/"+"). Every three of these sums more or less represents a bell curve which becomes more and more stingy at the high end as the grade goes up. The chart below illustrates this.
(Edited to add chart)
Keeper of the VAM Catalog • Professional Coin Imaging • Prime Number Set • World Coins in Early America • British Trade Dollars