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mathematically speaking...

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For one thing, machine vision systems have improved by light years over those that were available back then. I remember my engineers trying to build them from scratch back when the PCGS computerized grading came on line. Everything was custom design back then. Now you can buy many of the system modules off the shelf.

 

Desktop computers have the power (or more) of large mainframes in that era and the speed to go with them. The computers along with integrated circuits for vision interpretation and control are available now that could most likely build a very good vision inspection (grading) system. tongue.gif

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TDN: a few years ago I tried charting pricing and populations. I also experimented with using Regression Analysis to predict pricing for coins. There are too many variables, so I did not get very far.

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Alright GDJMSP, TDN and others! I've agreed to work with Arch on this one. A model prototype will happen between now and mid-January, as I'll have to do this in my "spare" time. After the prototype development, it'll be up to Arch or someone with large database skills to get the wheels crankin'. This will be fun (I hope) blush.gifsmile.gif! It's a project that could have some nice long-term implications. (Last full-scale Bayesian model I worked on took me and a team of 4 statisticians, a panel of 10 experts (for the input), and a panel of 6 reviewers 2 1/2 years to complete! Thankfully, this is not that complex!)

 

p.s. Don't hold your breath! tongue.gif I'll try to keep you apprised, at least with model form.

 

Hoot

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Several factors come into play here.

 

First the major driving force that determines the value of a coin is demand. If very few collectors want an item, it does not matter how rare it is, the prices are going be low. One need only look at the value of tokens versus coins. I own some Civil War Tokens that are as rare as an 1804 silver dollar, yet they are worth 1/1,000 of the price of an 1804. I own a rare die variety of 1800 silver dollar (B-20) that is tied for the finest known and is the plate coin from Bolender's book. Bolender said that it is as rare an 1804 dollar, yet it's worth only a few thousand as opposed to many thousands of dollars for the 1804. Once it is established that something has a following of buyer who will make a market, THEN supply comes into play.

 

Second, as has been pointed out earlier, some coin prices escalate rapidly as the grade gets higher. Others are fairly flat. Given this it is statistically impossible to (1) predict prices in a all grades from ONE data point and (2) apply a mathematical function that can predict prices for all U.S. coin series. At best one could build functions for one series, but even that would be flawed.

 

Years ago Dr. William Sheldon invented the grading numbers that we now use as a pricing system for early large cent die varieties. He theorized (or perhaps his case set in stone) the idea that an MS-60 coin was worth 60 times the value of a heavily worn but undamaged and attributable large cent. A Fine was worth 12 or 15 times as much. VF, which was the widest range, was worth from 20 to 35 times as much.

 

Today Sheldon's evaluation system is totally discredited. It is useless because markets are dynamic and the demand functions are different for each collectable. Even if you devised the perfect system for a point in time, which would be a huge accomplishment, within a brief period it would be invalid.

 

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Wow! That's enthusiasm! grin.gif

 

Hoot and I haven't really fully discussed the end-goal that I'm shooting for, so I'll amend Hoot's statement by saying that the approach he and I have been talking about is still just one avenue that's being investigated to get done what I'm trying to get done. How far we go with it is really a matter of how practical things look after Mark and I chat a little more.

 

BUT, it is a pretty cool little project we're kicking around. I'd like to see it pan out. We'll see how it goes.

 

Thanks to Mark for all his noodling power on this thus far and as things go forward! smile.gif

 

Arch

 

P.S. A team of twenty for 2.5 years?! What are you getting me into, Mark!?!? (laughing)

 

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There seems to be few mathematicians around us...

 

Pretty much everything that Hoot said is correct. This ``project'' is a simple exercise for statisticians and mathematicians. Its accuracy is only as good as its two inputs: one price point, and the census data.

 

The census data represent the shape of the curve, and that one price point determines the level of the curve. You can have your panel of experts try to determine the curve, and then you build what I would call a Taylor series centered around the price point. (Hoot, yes, I know that a Taylor series is centered at the origin!)

 

If the market prices for a specific coin in a specific grade differs from the Arch-Hoot model, then that's how we determine what's overrated and what's underrated.

 

EVP

 

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I worry that a Bayesian analysis is going to yield low probabilities for each coin's price. Because of the dynamics of coin pricing, wouldn't it be easier to use one price point and a formula for the other points of that coin's slope? That way you could easily calculate the price of any grade.

 

Bill: You are correct. There is a direct relationship between price/demand. Without one, you do have the other.

 

 

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EVP - I'll bet that in the end a reasonable Taylor approximation could be used for any given series. It may be a computationally less intense procedure and is appealing that way. And we can make the origin wherever we want! smile.gif

 

Charlie - I don't think we'll run into the issue of singularly low probabilities of price across grades, but it may rear its head in series that have high populations and essentially identical price structures (including range) from grade to grade. For the most part, however, it's more a matter of trying to come up with "most likely" price for any given grade (or vice-versa). There is probably enough distinction in most series between prices for grades that this will yield plausible results. But you, Bill, EVP and others are right that the model will have its underlying flaws no matter how it is formulated. tongue.gif Yet, just because it is flawed does not mean it is useless.

 

Hoot

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Ok, it might be obvious or previously stated, but I have to ask why? How would this model be used?

 

Second, I don't see how it can work. I am looking at prices for a MS 67 Buffalo Nickel on teletrade and they are $207, $231, $352 and $495. How can a statistical model predict price when they vary so much for the "same" coin in the "same" grade. Three of these coins were NGC and one was PCGS (the high).

 

I am not a stat expert so maybe it can be done, but to a lay person, it seems almost impossible.

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