Tuesday, March 2, 2010

Preserving The Past

Although I have in the past chided coin statisticians, half-mockingly because I feel their time could be more productively spent, the data they provide can occasionally prove useful to conjecture. In order to speculate on the scarcity of the oldest Lincoln cents, which will be today's topic, it's necessary to refer to the meticulous record-keeping of individuals who take the time to painstakingly assemble such numbers. So today I doff my hat, and offer my thanks. I couldn't fashion the following guesstimates without your assistance.

On Realcent, the coin collecting/gathering/hoarding forum on which I participate, member Uthminsta has established a thread in which members post their most recent findings in their search for pre-1940's cents from their penny sorting. They often provide the percentages of copper cents - those pre-1982 pennies that were 95% copper - encountered amidst the mix of copper and zinc cents, as well as further specifying how many "wheaties" they discovered. The wheaties designation refers to the Lincoln cents that were produced up until 1958. In 1959 the reverse of the coin was changed to feature the Lincoln Memorial.

If you've ever dropped by my blogsite, you'll notice I haven't been writing as much lately as I once did. Why? Because I've been sorting more cents myself. While enjoyable, it can prove a very time-consuming activity. I decided, after writing a number of columns touting the value of sorting and saving the copper Lincoln cents - for their more than double face value metal content of the copper from which they are comprised - to jump on the bandwagon and practice what I was preaching. I don't want to get up from my keyboard someday only to discover they're all gone.

So I've been doing a lot of sorting myself. I utilize a Ryedale coin sorting machine, which allows me to at least triple the speed at which I could hand sort. The machine processes the pennies for you, separating the zincs from the copper cents. What it cannot do, is to keep all the copper cents from falling into the wrong pile. Prior to 1945, there was a very small percentage of tin in the Lincoln cents, and the Ryedale does not differentiate these from zinc cents. Consequently, the 1944 and earlier cents wind up in the zinc pile. If you don't search your zincs, these older cents will inadvertently get returned to the bank.

From some earlier calculations, I deemed that - for simplification - only about one percent of the pennies you find will be wheaties. And of those, I calculated, four out of five will be from the Forties and Fifties. It turns out that I was too generous in assuming a that twenty percent likelihood would represent the percentage of pre-1940's wheaties that you would discover. After examining a number of wheaties that I had accumulated in my handsorting days, prior to my purchase of a Ryedale, I determined I had made an error.

The likelihood of one finding a pre-1940 wheatie differs from the result you would expect if you merely analyze the original mintage figures. Those numbers would suggest that since about twenty three percent all wheaties had been minted prior to 1940, one could surmise that roughly the same percentage would be encountered in searches. But I forgot to factor in extinction. A simple definition of extinction would be that, regardless of original mintage, cents do not survive, for one reason or another.

Given any particular starting point, the following year only 99% or those cents might remain. The next year only 99% of that remainder would survive. And so on. I can't provide a reliable extinction rate for any given year, only strongly postulate that the principle undoubtedly holds true. Spend enough time with a calculator and you might be able to hypothesize what the extinction rate would need to be in order to arrive at these numbers. My sample size was not huge, yet I feel it was large enough to form the basis for this premise.

When I counted the wheaties I had sorted, I found that of 505 total, only 34 were pre-1940's. So my likelihood of finding one had not matched my expectations, but had fallen far short. The reality was that only 6.7%, not 23%, were of older dates which preceded 1940. An extinction theory could account for the attrition that would minimize their presence in circulation. A Realcent member whom is a great statistician, cwgii, posted that in the past year of searching he had found nearly 30 (29.95) wheaties per 10,000 cents searched.

If you combined his findings with mine, it forms the basis of an equation whose solution would imply that your chances of finding a pre-1940 wheatie is only one in 5,000. For every $50 face value you search, you could expect to find only one. Learning this, as I've been sorting, lately I've been wondering,"what are the odds that I'll find any pre-1920's cents in the zinc pile?" If the extinction premise holds true here as well, then one cannot assume, again, that merely reviewing mintage figures would provide an accurate clue.

In order to determine the likelihood of encountering a cent from the teens (including the issues of 1909) you would need to know both the original mintages and an extinction rate. During the Teen's there were 2,125,713,683 cents minted. The Twenties produced 1,664,218,000. And the Thirties added the count of 2,214,324,143 to their number. So 6,004,255,826 pennies were produced in total. If we proceeded simply on that basis, then you might expect to find that 35.4% were Teen's, 27.7% Twenties, and 36.9% Thirties. But this doesn't account for extinction.

Extinction will cause the oldest decades to produce fewer cents remaining in circulation due to their greater exposure to years of whatever factors contributed to their attrition. Thus there would be a commensurate distribution of cents found to mintages produced that was skewed towards the most recent years. You will, therefore, find fewer of the earliest decade Lincoln cents, despite their original mintages, simply because they've had a greater opportunity to disappear from our change.

It's impossible with sure accuracy to predict what the odds would be of encountering - in boxes of rolled pennies obtained from banks - any particular cent minted during the first decade of their production. Only a guess can be derived from analysis of data, but an idea of what odds you have is better than none at all. So here's my guess. From my own purposeless and demented scrutiny of these numbers, I would venture to say that of the pre-1940 cents that you'll discover, only about ten to fifteen percent will be 1919 and older.

Perhaps only fifteen to twenty-five percent will be from the Twenties. And the remainder, the bulk of them, will be common date Thirties pennies. When my initial musings led me to believe I might find one pre-1940 per 5000, I wasn't factoring in extinction. My expectations were that about 76-77% of the wheaties would be of more recent vintage. But it turns out, based on my own experience, that greater than 90% of the wheaties will be Forties and Fifties. If you do find a wheatie reverse laying in your zinc pile, chances are it will be from the Thirties, or one of those tin-bearing early Forties coins.

The chance of finding a first decade cent is much less than what is suggested by simple scrutiny of mintages, when extinction is factored in. You might have to search 100,000 or even 150,000 cents to find a single pre-1920 cent. I'm writing this to offer consolation, and to prepare you for what to expect, after I learned myself by sorting nearly a million cents. Finding a scarce key date coin, particularly one in good condition, is next to impossible. Certainly you could buy one, but if you're in the search for the thrill of the hunt be aware that, in most cases, the fox will vanish, outrunning the hounds. Remember, though, it's not always the capture as much as the quest, that provides the adventure of the chase. So as Realcent member PreservingThePast would remind: enjoy your coin searches, everyone.


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3 comments:

  1. For statisticians, educators, students and researchers: I have put one of the most comprehensive link lists for hundreds of thousands of statistical sources and indicators (economics, demographics, health etc.) on my blog: Statistics Reference List. And what I find most fascinating is how data can be visualised nowadays with the graphical computing power of modern PCs, as in many of the dozens of examples in these Data Visualisation References. If you miss anything that I might be able to find for you or if you yourself want to share a resource, please leave a comment.

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  2. Thanks for the mention, and for really thinking this out. I had been thinking about 1909... Consider that there were 6 main varieties of coins minted that year. How do you think your chances of finding each one would match up with the comparative mintages within that one year:

    Lincoln: 72,702,618
    VDB Lincoln: 27,995,000
    Indian: 14,370,645
    S-Lincoln: 1,825,000
    S-VDB Lincoln: 484,000
    S-Indian: 309,000

    This makes me think that perhaps a factor of your "extinction" theory would be that an "obsolete" (like Indians) or "peculiar" (like '43 steelies) design would move toward extinction at a much accelerated rate.

    Just thinking...
    uthminsta

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  3. I really like your work figuring out the odds of getting pre-1940 wheats. Nice work.
    Copper Penny

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