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Some Very Quick Rules of Thumb: 

An unsearched 5,000 count wheat bag should contain around 61 teens, 146 1920s, 394 1930s, 2286 1940s, and 2113 1950s.

Unsearched 1,000 count should have 12, 29, 79, 457, and 423 respectively.

One pound of wheats (about 150 cents) should have 2, 4, 12, 69, 63 respectively.

One roll (50 cents) should have 1, 1, 4, 23, 21 respectively.

If interested, here is the story on how I came up with these numbers...

So, just how do you know if a bag of wheat cents is truly unsearched?  It is unlikely that any large collection of wheat cents being sold commercially is truly unsearched.  There are exceptions of course, but having personally been buying and selling wheat backs for some time, I know what is like to get that 5000 count “unsearched” wheat bag only to find 1940s and 1950s with an occasional earlier date being thrown in.  It is very frustrating!  So how do you know if a bag of wheats is unsearched?  There is a way to tell. Read on…

 Being both a wheat cent collector and a college professor, I have always wondered if there was a scientific method to determine if a collection of wheat cents was unsearched.  In fact, applying basic statistics to the problem, some rules of thumb can be utilized to determine the probability that a collection of wheat cents is unsearched.

 It all starts with the mintage figures.  One could reason that a single wheat cent would have a probability of showing up in a general collection of cents as a proportion of its own mintage to the overall mintage of all wheat cents.  For instance, let’s look at the famous 1909-S VDB Lincoln.  There were 484,000 of these minted.  Overall, there were about 25.8 billion wheats minted.  484,000 divided into 25.8 billion yields around .00002 (or 2 for every 100,000). So, in theory, for every 50,000 or so wheat cents you search, one should be the 1909-S VDB.  Is that the answer -- just go out and buy ten 5,000 wheat bags on Ebay (which are readily available) and you should find the elusive -09-S VDB?  Unfortunately, the answer is no.  You would more than likely have to buy about two-hundred and eighty-six (286) 5,000 count wheat cent bags to have a decent shot at finding the 09-S VDB!  And, that’s assuming the bags are truly unsearched (which they probably are not).

 The problem, in statistics circles, is known as decay.  The fact is, coins have a life span (as published by the mint) of around 30 years.  Assuming a normal distribution of lifespans and a standard deviation (sigma) of 10 years (an educated guess), roughly 68% of all coins will be in circulation from 20-40 years (one sigma).  And, roughly 95% of all coins will have a life span from 10-50 years (two sigma).  This last figure is what we are most interested in when determining the life span of the 09-S VDB.  Wheats were no longer minted after 1958 (roughly fifty years after the 1909).  So, using the distribution data from above, roughly 2.87% of 1909-S VDB coins made it to 1958!  That’s a surviving population of 13,899!  This is known as statistical decay – the amount of coins that leave the population over time.  Of course the total population of wheat cents decayed as well, which reduces our denominator when estimating probabilities.  But, because the vast majority of these cents were minted in later years, we can expect a decay of around 4 billion cents (this is just using some rough, back of the napkin math).  So, back to the 1909-S VDB:  searching a truly random lot of wheat cents, you should come across this coin 13,899/21 billion, or .0000007 of the time. This equates to roughly 7 out of every ten-million cents you search, or 1 in 1,248,000 cents (two-hundred and eighty-six 5,000 wheat bags)!

 You can use mintage numbers and decay to calculate some rules of thumb.  For instance, in a 5,000 count wheat cent bag, how many cents should you find from the teens (including 09), 20s, 30s, 40s and 50s?  The answers are 61, 146, 394, 2286, and 2113, respectively (using a mean coin life of 30 years and a sigma of 10 years).  In a single roll of 50 cents, you can expect 1, 1, 4, 23, and 21, respectively.

 When I look to buy supposedly “unsearched” wheat cents, I will sample around 1,000 of them, although a smaller number (say 300-400) should work as well.  But the 1,000 count sample should run a ratio of 12, 29, 79, 457 and 423.  If the ratio significantly deviates (a much broader topic) either way, I pass on the collection (or renegotiate the terms).  Why would I pass (or renegotiate) on a collection that has a disproportionately large number of early dates?  Because, I reason, someone must have artificially inflated the number of earlier wheat cents.  This would mean they looked at the cents; the term “unsearched” would most likely be false.  Thus, if someone searched the lot, presumably they already removed the more valuable coins.

 Of course, the decay concept used above does not include those coins selected for numismatic value (like the 1909-S VDB).  While it is nearly impossible to compute, most certainly valuable coins have been “pulled” from the population; perhaps we can term this numismatic decay!  This would reduce the odds of finding rare wheats even more.

 Finally, if you can verify that a hoard of wheat cents hasn’t been touched since the 1920s or 1930s (perhaps through a relative’s collection), the percentages of older coins will greatly increase.  For instance, if a collector hoarded 2,000 wheat cents and stopped in 1935, that collection should have 843 teens, 754 1920s, and 403 1930-1935 cents.  No 1909-S VDB, 1914-D or 1931-S should be expected however (we’d need around 6,800 wheats collected before 1935 to get 1 VDB!).

 All of this can be calculated easily on an excel spreadsheet or with a statistical program.  I can provide an excel template if you would like.  If you have any questions, feel free to contact me!

Kiera River Coins