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mathematically speaking...

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Ok - silly internal discussion that DevNull and I were having: Do you think it would be possible to predict the price of a given coin in a given grade when provided with:

 

1) the population report

 

2) A single price of one grade for that coin, so for instance, for that given coin, you know that an MS66 is $1000.

 

We were kicking this around, and trying to determine whether some kind of consistent relationship between the curve of the popualtion numbers and the curve of pricing could be identified. Thus far, we feel that, without extensive statistical analysis of all the data involved, no reliable pattern can be predicted.

 

I'm relatively certain, at the very least, that no consistent pattern can be show across all coins. Can it be done on a more specialized basis? Like creating a formula that works on all buffalo nickels? It could never be perfect, of course, but can it be approximated?

 

 

Arch

Pursuing annoying mathematical puzzles because I'm apparently a masochist

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"variables like historic demand, current demand, key date premiums, MS65 and up premium and varying grade rarity premiums"

 

Well, theoretically, many of these things you list would correspond with differences in population, or would be provided by giving the single initial price.

 

So if I know what the price is for an MS65 in a certain coin, then I know something about current demand and key date premiums for that coin.

 

Grade rarity then is somewhat related to population?

 

Arch

 

 

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And how do you predict human behavior, economy and other related factors that will affect price? For example, how do you predict a down economy will affect a price or a collector that just falls in love with a coin or a bidding war between two or more buyers?

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"a collector that just falls in love with a coin or a bidding war between two or more buyers"

 

Well, it would just be a generic guide, not a crystal ball for each sale out there.

 

"For example, how do you predict a down economy will affect a price"

 

That would be handled by the seed-price. The MS-65. If the seed-price changed due to general economy issues, then you'd have to update it in the system.

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I think a range could be predicted at the wholesale level (lack of emotion buying) and a range could be predicted for certain venues, ebay, teletrade, heritage, local auctions, big auctions, conventions, etc.

 

I think the venue is a big factor based on my personal observations. I have been looking at to get a MS 67 1937 buf nickel. On ebay they are going for approximately $275, but a dealer is offering one for $539. Will he get that price? Who knows, but it will be more than the $275 on ebay for sure because in part, the coin itself, but also because of the venue in which it is being sold.

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Arch,

 

Take Lincoln cents. The populations of the 1909-S VDB are not really low, the coins are easy to find, and there are dozens available for sale at any time, but because the coin is a key date, the selling price of these pieces do not correspond to the populations.

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Some coins (i.e. gold Saints) have a pricing structure that is highly correlated to the particular grade population. Many common Saints have sharply higher prices when they reach the rare in grade threshold. You would have to have more than 1 grade pricing of any denomination to do regression analysis on the coins in this series.

 

Your theory may correlate much higher to modern coins that have more predictable prices as grades change. You would have to have a formula for each coin as well as one price point on the curve.tongue.gif

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Arch - I agree that the accuracy of the prediction will improve with certain series, e.g. buffalo nickels or Saints. However, can you make a prediction? Sure! Can that prediction have some validity? Sure. Here's how:

 

Bayesian statistics is highly devoted to making predictions with little or no data. You would need to form a prior distribution of the price structure based on (1) prior information, e.g. the distribution of prices for the coin in question in other grades; (2) expert opinion, e.g. the approximate value of the coin in question based on the opinion of experts who collect or deal in the market in question. Also, you would need to know or guess at the probability of a given grade (e.g. by way of population reports). Thus, the formulation of the Bayesian probability is:

 

P(price|grade)=[P(grade|price)P(price)]/P(grade)

 

The probability calculated (left hand side of the equation - a conditional probability or likelihood function) is the conditional probability of price given the grade. The probabilities listed on the right side of the equation are the prior likelihood of the observed grade given the price (the first term of the numerator), the prior probability of the price (the second term of the numerator), and the prior probability of the grade (the term of the denominator).

 

One can see that once information has actually been provided, e.g. an observation on a given price or a given grade (e.g. from a population report), then this formula can be readily updated and utilized to predict price and the likelihood thereof.

 

Hoot

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Where the #'s are fairly large to show the trend, the pops are accurate enough to come up with a price for a coin even if there is no current price data to go by.

While it varies from series to series and type to type, it is not difficult to get into the ball park just on one data point. Sometimes you have to come up with a price using a totally different (but similar) type coin for comparison. While current fads, interests, PQness or Doggydoness, etc all play a role in the final price, you have to land in the park first to derive a price. You have no choice but do this when you make the first pop of any coin. The guy that made the first PCGS MS68 Washington had to do this and so will the guy (Wondercoin?) who make the first

MS69. It just may be that your pop1 1945 coin in say MS67 grade has the same pop1 as a 1937 coin in MS66. The prices should be roughly equal.

 

roadrunner

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It would never be accurate. The man hours to keep up on a moving coin market would make the system to costly. You would have to re-run the number every 3 months. The numbers in the formula are dynamic.

 

 

 

 

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The formula that I provided above can be updated automatically with even a single data point. Not only does the formula track what you are after, it provides a method for updating each distribution based on every new piece of information. This is a simple dynamic that has been applied in very complex situations and could be automated in a database that tracks price, grades and populations.

 

By the way, using a probabilistic approach as shown above allows a person to explicitly describe "accuracy," and the advantage of Bayesian updating is that it can improve precision. This makes all contentions quantifiable regarding "how close" a prediction would be.

 

Hoot

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cool beans mhooten. couldn't your method be used to calculate prices for 65.1 (low end), 65.5 (average) and 65.9 (PQ) specimens on the distribution curve? would it be too much to ask that you run us through the steps of the computation? any coin from CU price guide (or numismedia) would be great. I'm developing a "just-in-time" inventory system for my "coinshop" db and this would be very helpful. the idea being, the system will stock/purchase items automatically. thanks in advance.

 

Crito

 

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Price is determined by supply and demand. To the degree to which it is possible to know the supply and a price of a coin then it would be possible to make some extrapolations to other grades. People do have the the disconcerting tendency to behave in some very unpredictable ways and cause demand which is uneven. They collect dates for type sets or birth year sets or pretty colors. By the same token coins are not produced uniformly throughout even a single year much less an entire series. This isn't to say such a mathmatical system can't work so much as that for most series it would be quite inaccurate. It would, however, highlight some interesting anomalies, some of the causes of which could be discerned.

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I still stick to my guns - it cannot be done simply from the pops and a single price. Why? Because there are other factors than population and date demand involved. It is well known that the MS65 grade is deemed the minimum "acceptable" grade for investment (ha!) - this causes jumps in the price for many coins at the MS65 grade that won't show up off a pop. If I give you that coin's price at MS63, how in the world can you get the price at MS65 if there is a squiggle in the demand for the coin at that grade?

 

I also like Greg's comment - the pops are rarely correct. Take the 1878-CC trade dollar for instance. The pops are around 20 in MS64, yet I've only ever seen 1 coin at that grade. Rumor is that a single coin was resubmitted a dozen times back in the late 1980's until it got the MS65 grade.

 

Many coins have completely different demand curves. The 1950-D nickel has a different price structure than another coin with similar populations. It's extraordinarily flat, whereas another might be very steep. I think the series also matters - especially the type of collector involved and the prices of that series. A Morgan dollar attracts a different type of collector than a trime or Sac dollar - a different mentality leads to a different price structure. A high grade low pop Morgan is going to command some silly prices compared to other series. And if you have a grade rarity in a low value series, it's going to command some stupid premiums that just can't be predicted by a program. 5000% doesn't seem so much when the starting point is $50! wink.gif

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It's almost hilarious how worked up we get about this topic. All of what has been said about the "unpredictability" of any price in a single grade is simply described as variability in statistics. And is there one "correct" answer that can be derived? No! There are many answers and each will have a cumulative probability tied to it based on the distribution P(price|grade) [the probability of the price given the grade, which can be manipulated to provide price estimates based on grade]. That distribution is updated with every piece of information that is included - both the accurate info and the inaccurate info. So, the output will be as good as (1) the quality of the input, and (2) the descriptive power (if you will) of the distributions. (This latter quantity is a matter of the entropic nature of the distributions).

 

Keep in mind that some exquisitly difficult problems are faced every day with Bayesian methods. The better the information in formulating the problem, the better the answers (greater predictive qualities). Also, and to be redundant, the answer you will arrive at will look something like X +/- f(sigma). In other words, there will be a prediction and some upper and lower bounds associated with the calculation that represent a percentile of the distribution (your choice). It will be as good as your input (how well you chose the distributions and the quality of your input).

 

By the way, the method I showed is not based on a trajectory (although there are such Bayesian methods), e.g., THIS coin sold for $XXX in MS63, thus it will sell at $YYY in MS65. It is rather based on a specification of the value in MS65 - a single data point, expert opinion (if no data), many data points (better), etc., and the family of distributions from which such data arise.

 

crito (and others) - I invite you to look up Bayesian methods in a standard probability statictics text (e.g. Probability by Jim Pitman). There are also many texts on the subject in depth (e.g. Bayesian Inference by Anthony O'Hagan [Kendall's Advanced Theory of Statistics]). Its implementation will depend on your comfort with the math, the coin(s) you are interested in and your use of existing input and/or your retrieval of such input. The methods are somewhat complex, but programmable in many computer languages.

 

As for me, I'm just sticking with the argument that it can be done and done with rigor. Done well? That depends....... laugh.gif

 

Hoot

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On an interesting semi-unrelated footnote. Bayesian methods are being used in the email program on the newest http://www.mozilla.org release. The Bayesian methods are used to "learn" what types of email are spam, and then automatically filter them out.

 

Arch

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Cool Arch! Aren't Bayesian methods GRRRRRREAT! grin.gif

 

So, are you going to begin building a database of price information based on said methods? Might be a little over the top in support of the registries! laugh.gif Still, if you then publish a price guide that discloses the methods and distributional inputs, and provides prices with percentile variability, I'll be the first to buy it!

 

Hoot

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I invite you to look up Bayesian methods in a standard probability statictics text (e.g. Probability by Jim Pitman).

 

Jim Pitman was not a name I was expecting to see in this or any other forum. He was my first Statistics professor about a million years ago, and is directly responsible for everything that has happened to me since... wink.gif

 

I would agree that the kind of project you're talking about can be done, but how well is a very good question. It may be something I try to tackle in a small way at some point. Dealing with outliers such as the finest known graded coin of the date would be the big pitfall.

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How many of you have started from scratch and built a value chart for your series? I have done just that for the trade dollar series. And I used the pop reports as one factor in building those values. BUT...there are too many variables that go into each date and grade to be ground down into a simple equation. The most basic equation out there is a simple double of value per grade and a lot of dates follow that very closely for the series. But if you used the pop report and a single price to determine values, you'd think that an 1878-S in MS66 (combined pop of 23, value in MS63 = $900) would be much cheaper than an 1877-S (combined pop of 6, value in MS63 = $900) - but it's the same price. You'd also think that an 1875 in MS66 (pop 2 with an MS60 price of $2,000) would be more expensive than an 1876-S in MS66 (pop 1 with an MS60 price of $250) - but it's worth less than half the value. Or the 1875 with its $2000 value in MS60 vs the 1874 with its $400 value in MS60 compared at the MS65 level (pop 8 vs pop 7) - both valued the same in MS65.

 

Or even better, how about I give you the AU50 value for the 1873CC ($1,000) vs the 1878CC ($4,000) and ask you to predict that they are equally valued in MS63 (pop 33 vs pop 10)???? How can that be predicted by an equation?

 

There is no common equation but EXPERIENCE for these!

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TDN - You're getting all worked into a froth over nada. laugh.gif The fact of the matter is that a single equation can be very complex and the the one provided is getting on the complex side. One would have to apply that equation to each grade for each coin!!! All that you speak of is taken care of by the selection of inputs to the equation. In the end, each coin, each grade would have its own resultant distribution. These kinds of statistics are used to measure and predict human behavior of all sorts! Coin are not an exception to that! Indeed, this is not nearly as complex of an application as such statistics are commonly employed in, and marketing research is one of the most common fields.

 

How many of you have started from scratch and built a value chart for your series?

 

I have, and I'm sure that many others have as well. Prices can be wild, grade to grade, date to date, and over time. A real Bayesian statistician would apply this method in time series! blush.gifgrin.gif

 

There is no common equation but EXPERIENCE for these!

 

Bayesian methods rely heavily on the EXPERIENCE of experts. cool.gif

 

swhuck - You must have had a blast! I'd have loved to have had Pitman as an instructor. His was a very clearly written book.

 

This is too much fun. Hoot

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we'd have computerized grading, too

 

Funny you should say that because I've wondered why we don't. A computer probably couldn't measure eye appeal, etc., but I would think it could measure strike, count the number of marks, the depth and length of the marks, etc. to determine a grade.

 

Anyway, it is interesting to think about.

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I just don't think that anyone bothered to do this before! laugh.gif Afterall, it's a lot of work for a little reward! laugh.giflaugh.giflaugh.gifcrazy.gif

 

Arch - See the "lot of work" comment. smirk.gif Afterall, that's why they pay you the big bucks, right? wink.gif

 

Hoot

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Awwwwww c'mon Hoot - and here I was gonna suggest that you build this for us. My hopes have been dashed frown.gif

 

As for the computer grading system - it was tried - failed miserably. But then that was quite some time ago and there have been many computer advances since then. Perhaps it should be attempted again.

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