Circulated Nickle Find Rate Comparison

Fair warning ....... this will be a long post with some math involved ..... read on if you wish!

Background

Coppernickeldaddy (henceforth abbreviated CND since I will use it a lot in this post) and I have both been aggressively roll searching circulated nickels. We share a common objective ... keep the older coins and compile a complete circulation strike set without paying more than .... well ... a nickel per coin.

CND has completed that objective ..... I have not.

This post is an initial attempt to compare the rates of finds between CND data and my data ..... sort of a sanity check on the differences between geography (and lady luck) in contemporary nickle searching.

I will also introduce my method of measuring circulation obsolescence as a method to understand the relative scarcity of Jefferson nickels.

We both hope others will join the nickel search bandwagon and add their ... well .... 5 cents worth to this discussion.

CND has posted his awesome data set on the forum ..... and has agreed to allow me to use his data to make this comparison.

This will be fun .....

Data Set Characteristics

We started our searches at approximately the same time ...... CND initial post on his self-proclaimed "40,000 Roll Quest" was 1/27/2008. I broke open my first 10 rolls on 2/25/08. Soooo .... in both cases we are talking about current data that is .... hopefully .... representative of what is being found today at banks in circulated rolls.

I live outside Baltimore, MD. My coins come from a variety of banks in this area. Don't know where CND finds his coins ..... he can offer this if he wishes to.

CND has, of course, searched 10,000 rolls.

I have searched 1680 rolls.

There is one minor difference between our data sets ..... CND keeps coins 1958 and prior ...... while I keep coins 1959 and prior. To make the rate statistics comparable ..... I have modified my MS-Excel circulation obsolescence algorithm to eliminate my 1959 data.

That said ..... the 1959 and 1959-D coins make up a disproportionately large percentage of my finds.

Since CND is throwing these away .... and many of us are not ..... I'll also report my rates using this data as well.

As a teaser for those who choose to read through all this ...... at the very end of this post I'll tell you how many 1959 and 1959-D CND has returned (the number is staggering).

Executive Summary of the Data:

For those who only want the bottom line without the details ...... this section is for you .......

1. Our Overall Find Percentage is very close to each other ..... CND at 1.085% and me at 1.137% ....... this is the percentage of 1958 and prior coins found in rolls.
2. Combining our data sets, and translating the resulting rate into coins ..... an Overall Average is that for every box (50 rolls) .... you can expect to find 21.8 coins dated 1958 or prior.
3. My Overall Find Percentage including the 1959 coins is 1.275% ...... this might be more useful for those of you who are keeping pre-1960 coins. ALL OTHER DATA in this summary will use CND comparable ..... i.e., I eliminated the 1959 data from my data set.
4. CND is finding more 'special coins' (read below for a definition) that I am ..... he finds a 'special' every 39.5 rolls while I find a 'special' every 60 rolls.
5. CND is finding Jefferson's from the 1930's at 1.5x the rate that I am. Not sure if this is geographic influence, or just 'bad luck' on my behalf.
6. Our circulation obsolescence rates (read below for a definition) are comparable ....... suggesting some consistency in different geographic regions relative to why coins are lost from circulation.
7. Both of our data sets ... when you consider the factor of circulation obsolescence .... show that the 1950-D is the most difficult Jefferson to find in circulation today, edging out the 1939-D for the honor.

Now ..... on to the details ...

Overall Find Percentages:

We both define a 'find' as a 1958 or prior coin ...... recall that I save 1959 coins but have eliminated that data from this discussion. With that change ..... CND and I are both tracking very close to each other in this overall statistic.

For CND:

Overall Find Percentage: 1.085%
Number of Coins per 1 Find: 92.2
Rolls per 1 Find: 2.30

For Me:

Overall Find Percentage: 1.137%
Number of Coins per 1 Find: 88.0
Rolls per 1 Find: 2.20

Special Coins Found:

This requires some definition ......

"Special coins" are as follows:

1. Anything pre-Jefferson (Buffalo, Liberty-V, etc)
2. Silver war coins (1942 thru 1945)
3. Any of the nine (9) Jefferson circulation strike with annual mintage below 10 million. None of these are 'rare' as you would define perhaps a 1909-S VDB ..... but for circulated nickle hounds these 9 coins are the 'key' to our collections ...... I have 5 of the 9 so far.
4. In descending order ..... the 'key' circulation strike Jefferson are 1950, 1949-S, 1955, 1951-S, 1939-S, 1938-D, 1938-S, 1939-D and 1950-D

For CND:

Rolls per overall 'Special Coin': 39.5
Rolls per War Silver: 68.0
Rolls per Liberty 'V': 454.5
Rolls per Buffalo: 256.4
Rolls per 'key' Jefferson: 222.2

For me:

Rolls per overall 'Special Coin': 60.0
Rolls per War Silver: 120.0
Rolls per Liberty 'V': 1680
Rolls per Buffalo: 280.0
Rolls per 'key' Jefferson: 240.0

Rates By Decade:

For CND:

Rolls per 1930's: 46.3
Rolls per 1940's (excluding war silver): 5.7
Rolls per 1950's: 4.6

For Me:

Rolls per 1930's: 62.2
Rolls per 1940's (excluding war silver): 5.1
Rolls per 1950's: 4.3

Some other Unusual Observations:

1. The 1938 coin is the only 'non-key/non-silver' that I have yet to find. CND is finding this coin at a rate of 1 find per 12,500 raw coins searched. Using CND rate statistics, I should have found 5+ 1938 by now.
2. CND data set supports my own observations that something unusual is going on with the 1949-S 'key'. We should reasonably expect this coin, with a mintage of 9.7 million, to show up at rates comparable to the 1950 'key' which has a mintage of 9.8 million. It's not even close. Using our combined data sets, the 1949-S appears at a rate of 1 find per 93,440 coins searched, where the 1950 appears at a rate of 1 find per 35,940 coins searched. Makes you wonder what is going on here?
3. It appears that Lady Luck has smiled on me by having already found both the 1939-D (found at 57,200 coins) and 1939-S (found at 32,400 coins). CND is finding these at rates of 1 in 400,000 (39-D) and 1 in 133,300 (39-S).

The Concept .... and Measurement ... of Circulation Obsolescence

All of us understand this concept at the gut level .... over time a variety of reasons conspire to remove coins from circulation ..... so that the current 'circulating population' always tends towards recent date coins as opposed to older coins.

If you are in doubt about this ... well ..... do you really think that TODAY you can buy a full roll of Buffalo nickels at every bank every time you wanted to buy one?

You could have done exactly that in 1937 (admittedly with some V-nickels thrown in) ....... the difference between then and now is circulation obsolescence.

It's a simple concept to understand ..... but how do you measure it? I have found a way to do so with reasonable accuracy in the Jefferson nickel series.

This is one of the primary reasons why CND data set is of such interest to me ..... any statistical measurement tends towards improved accuracy with increasing data set size. CND data supports mine ..... and we need more data!

Before I explain ..... first I must digress a bit so you understand the reason why Jefferson's are my strawman for this circulation obsolescence research ...

IMHO .... the Jefferson series is the only currently circulating coin that we can have a reasonable expectation of collecting the entire circulation strike set out of rolls.

This is due to the fact that for a very long time the design/look of the series never changed. With the important expectation of the silver war series (discussed later) ..... the actual fact is that a 1938 coin looks very much to the average layperson as a 1993 coin.

This is not the case with any other circulating series ..... dimes, quarters, etc lost their silver in 1965 .... cents lost their wheatie in 1959 ... etc

Bottom line ..... to most laypeople out there a 1938 nickel is just another coin and the appearance does not give a clue to 'remove from circulation'

Soooo ... all the above said .....

I wanted a way to actually measure the percentage of coins that were being 'lost' over time. As my roll searches grew ..... I kept thinking about this until one day I had the idea.

Make the assumption (which will be wrong) that there is zero circulation obsolescence. If this were true ... then what I find in my roll searches would be distributed exactly according to the original mintage ratios.

For example ..... the 1940 coin with a mintage of 176.5 million should show up almost 10x as likely than the 1958 with a mintage of 18 million ........ if there was no circulation obsolescence.

To make a long story short .... and keep the math to a minimum .... I developed an Excel based algorithm to measure the 'difference' between the above scenario and what I am truly finding in my searches. This difference is the actual circulation obsolescence ....... i.e., what percentage of the original mintage has, for whatever reason, disappeared from circulation today.

Using that data, I am able to make predictions on how likely it is in fact to find a given coin today given it's original mintage and the band of obsolescence it falls into.

This works powerfully well for coins where we have sufficient 'finds' in the database. For example;

In both CND and my data set, the 1946 coin has the most overall finds. It falls into a band of circulation obsolescence where I predict that 19.3% of the original mintage has 'disappeared'. I calculate a 'Loss Adjusted Raw Coins per 1 Find" for the 1946 at 1 find per every 1684 searched. The actual, true, find rate for 1946 is 1 find per every 1626 coins searched.

As impressive as that might sound ..... ..... this method completely falls apart and is useless for those coins that we have very few finds. For example, between CND and my data, we have found 1 total 1950-D (you know who found that one!). The calculated "Loss Adjusted Raw Coins per 1 Find" for a 1950-D is 84,880.

I believe the problem here is related to small data set statistics somehow. When you have 463 or something, adding or losing a few makes little difference to the overall picture. When you have only 1 of something .... well ..... making a change of 1 in either direction is huge.

What we need is more data!

Anyways ..... for those who are interested ... here are the Circulation Obsolescence Rates for the various date groups I chose. Read this as 'What percentage of the original mintage has disappeared from circulation?'

1930's : 23.2%
Pre-War 1940's: 21.8%
Silver War: 96.8%
Post-War 1940's: 19.3%
Early 1950 (50 thru 53): 4.6%
Late 1950 (54 thru 58): (25.7%) Yes ... negative ... we can discuss this later if anyone is interested.

Finally ..... What has CND Thrown Back?

For those who have patiently waited ..... Coppernickeldaddy has thrown back 78+- 1959 and a staggering 840+- 1959-D coins!

I find 1959 at a rate of 1 per 5169 searched, and 1959-D at a rate of 1 per 840 searched.

Hey Coppernickeldaddy ..... send them to me.

That's it ..... I'm done. Hope this post is useful to someone out there. I'll respond to any comments, questions or clarifications.

Post some find data ..... I would enjoy making the database larger.

Best

David