Probability Statistics for Us Dime Nerds

[Sleepy Holow]

So I was crunching some numbers concerning the probability of me filling another hole in my FDR folder. So I calculated the probability of a silver FDR find being a certain date and mint. I love taking data and making spreadsheets. All of my data is based on known mintage numbers. The odds of an random silver FDR find being a 1964D are 4:1 while the odds of the same unknown coin being a 1955 are a staggering 529:1.

Some known sources of error include people hoarding key dates, 1964 dimes having had the least amount of time to disappear in the 1946-1964 set, and not actually knowing how many of each date/mint are still in existence.

If you add up the probabilities of finding each hole left on the Most Wanted List, it comes out to about a 10.83% chance of finding one of them each time I come across a silver FDR. Not too bad...8:1 odds. So all I've got to do is find 9 dimes and I should be able to fill a hole! Or at least that's what was supposed to happen. I haven't been able to fill a hole for about a month now. That's no new FDR finds in the last 45 Silver FDRs. Well, if we take into account that there's an 89.17% chance that the found FDR is a duplicate, then the probability of this occurring 45 times in a row is 0.8917^45, or 173:1 odds. By my calculations, that's crazy unlucky! Hmmm..173:1 is good enough to break into the Top 15 toughest silver FDRs odds. Do I have a Top 15 Dime coming this week? Maybe, maybe not, BUT MAYBE! You never know what the next box will bring my friends...HH


For Your Viewing Pleasure: Silver FDR Dime Probability Chart

 

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[boristhespider88]

So I was crunching some numbers concerning the probability of me filling another hole in my FDR folder. So I calculated the probability of a silver FDR find being a certain date and mint. I love taking data and making spreadsheets. All of my data is based on known mintage numbers. The odds of an random silver FDR find being a 1964D are 4:1 while the odds of the same unknown coin being a 1955 are a staggering 529:1.

Some known sources of error include people hoarding key dates, 1964 dimes having had the least amount of time to disappear in the 1946-1964 set, and not actually knowing how many of each date/mint are still in existence.

If you add up the probabilities of finding each hole left on the Most Wanted List, it comes out to about a 10.83% chance of finding one of them each time I come across a silver FDR. Not too bad...8:1 odds. So all I've got to do is find 9 dimes and I should be able to fill a hole! Or at least that's what was supposed to happen. I haven't been able to fill a hole for about a month now. That's no new FDR finds in the last 45 Silver FDRs. Well, if we take into account that there's an 89.17% chance that the found FDR is a duplicate, then the probability of this occurring 45 times in a row is 0.8917^45, or 173:1 odds. By my calculations, that's crazy unlucky! Hmmm..173:1 is good enough to break into the Top 15 toughest silver FDRs odds. Do I have a Top 15 Dime coming this week? Maybe, maybe not, BUT MAYBE! You never know what the next box will bring my friends...HH

View attachment 839850
For Your Viewing Pleasure: Silver FDR Dime Probability Chart

Hopefully you will beat the odds and get something new and rare!

- DS

 

[hokiemojo]

As I'm sure you know, the odds just don't really hold up in CRH. People that may pull a 64 will stick it in a paper roll with other 64's. People that pull a key date might stick it in a 2x2 coin flip. those 64's might get dumped someday when someone is cleaning out their grandparent's home, but the 2x2 is far less likely for that to happen. I know I'm explaining what we all know, but I often find myself running through the quirks that factor into the odds.

For example, War Nickels are the most easily identified silver coinage. They are the only US coin (aside from bullion) that has a marking intended just to signify that it has silver. Yet, it is the least known source so almost no one pulls them. I can find as many war nicks in box as I can find in a dime box, yet they were only made for 4 years. Anyway, sorry for rambling. I like to think about this stuff like you do (but I don't enjoy the spreadsheets as much - haha).

 

[Sleepy Holow]

those 64's might get dumped someday when someone is cleaning out their grandparent's home, but the 2x2 is far less likely for that to happen.

Really good point, hokiemojo. This make the 64's all the more likely and just pushes those 529:1 odds of a CRH'd silver FDR being a 1955 even higher.

 

[boristhespider88]

Really good point, hokiemojo. This make the 64's all the more likely and just pushes those 529:1 odds of a CRH'd silver FDR being a 1955 even higher.

Also, which this is statistically impossible, is figuring up and totaling the amount of dimes that have been melted down, damaged, lost, etc. So that will skew the numbers too.

Still though, from a practical standpoint, this is a a good reference guide!

- DS

 

[Sleepy Holow]

Also, which this is statistically impossible, is figuring up and totaling the amount of dimes that have been melted down, damaged, lost, etc. So that will skew the numbers too.

Yeah, I was thinking...let's say instead of there being an 89.17% chance of finding a duplicate it's closer to 95%, just to account for the factors you guys have mentioned. Even that would be roughly 9:1 odds of me going through 45 silver FDR finds and not getting a hole filled. I'm still going to call it unlucky! Although, having found 5 MERCs (4 of them filling holes in my MERC book) during this unlucky FDR streak, you don't have to feel too bad for me.

 

[boristhespider88]

Yeah, I was thinking...let's say instead of there being an 89.17% chance of finding a duplicate it's closer to 95%, just to account for the factors you guys have mentioned. Even that would be roughly 9:1 odds of me going through 45 silver FDR finds and not getting a hole filled. I'm still going to call it unlucky! Although, having found 5 MERCs (4 of them filling holes in my MERC book) during this unlucky FDR streak, you don't have to feel too bad for me.

What do you think your odds are of finding a Merc (even a 1916-D?), Barber, Seated, or anything before that vs. a FDR? What about silver proofs?? These are the questions going through my mind, haha.

 

[sjlund]

What do you think your odds are of finding a Merc (even a 1916-D?), Barber, Seated, or anything before that vs. a FDR? What about silver proofs?? These are the questions going through my mind, haha.

Last year I found 17.25 roosies for every 1 merc. So far this year I've found 32.83 roosies for every 1 merc.

 

[boristhespider88]

Last year I found 17.25 roosies for every 1 merc. So far this year I've found 32.83 roosies for every 1 merc.

Found anything before Mercs (Barber, Seated, etc.)?

 

[sjlund]

Nope, my oldest is a 1919 merc. Last year I searched $64,283 in dimes, and so far this year I've searched $45,881.

 

[boristhespider88]

Nope, my oldest is a 1919 merc. Last year I searched $64,283 in dimes, and so far this year I've searched $45,881.

Wow. I would figure with that many searched you'd get something older than that.

 

[Sleepy Holow]

Last year I found 17.25 roosies for every 1 merc. So far this year I've found 32.83 roosies for every 1 merc.

Nope, my oldest is a 1919 merc. Last year I searched $64,283 in dimes, and so far this year I've searched $45,881.

I just ran my numbers and it looks like in my hometown this year from Feb-May I was getting 1 Merc per 11 FDR's found. This summer in the big city, I'm looking at 1 Merc per 13.43 FDR's found. Combined total for 2013 so far is one Merc per 12.31 FDRs with over $55K in dimes searched. My ratio appears to be a little better at first glance; however, I think this means one of two things. Either you're finding a ton of FDR's or you're not finding many Mercs.

 

[boristhespider88]

I just ran my numbers and it looks like in my hometown this year from Feb-May I was getting 1 Merc per 11 FDR's found. This summer in the big city, I'm looking at 1 Merc per 13.43 FDR's found. Combined total for 2013 so far is one Merc per 12.31 FDRs with over $55K in dimes searched. My ratio appears to be a little better at first glance; however, I think this means one of two things. Either you're finding a ton of FDR's or you're not finding many Mercs.

I don't hunt dimes much, but mine are 1 Merc for every 7 or 8 FDRs.

Lol, I've only found 1 Merc and the FDRs but I've been wanting to start up dimes again

 

[sjlund]

2 boxes gave up 5 roosies today.

I find 1 roosie in $229.61, 1 merc in $7,730.23, 1 80% canadian in $4,638.14, and 1 50% canadian in $7,730.23. I search a mix of boxes and coin counter bags.

 

[boristhespider88]

Sleepy:

Do you have this a spread sheet that figures the numbers each time you change a variable in your number of finds?

 

[Sleepy Holow]

Do you have this a spread sheet that figures the numbers each time you change a variable in your number of finds?

Right now I have it set up to where the "duplicate streak" value is a variable. Each time I update that value, the odds for the "Unlucky Streak" change. I have a formula off to the right (in column I) that calculates the percent chance of finding a New FDR. Not as modular as it can possibly get, but hey...

 

[GMan00001]

I have done some of this type of number crunching in the past to see how many dimes I would have to find to complete the silver Roosevelt set from 1946-1964.

Only I tried to take into account a couple of other factors.

Factor #1
I assumed that there were a number of coin collectors back in the day and those collectors pulled a fixed number of each date and mintmark from the number minted which disproportionately will lower the availability of the tougher dates making them tougher yet. So subtract some number off of each mintage total. Maybe 5,000,000 or maybe 8,000,000? The number has to be lower than the lowest mintage however.

Factor #2
A percentage of the coins minted each year were removed/lost and that with each passing year a percentage is also removed/lost which repeats each year after the coin is minted. So a coin from 1964 had X% removed/lost and 1963 had 2X% removed/lost and 1962 had 3X% removed/lost and so on. Essentially this is trying to represent making coins harder as they get older. What is the percentage 1%? 0.01%?

Factor #3
Location in the country. People out west will find a higher percentage of D and S mints, whereas people out east will find a higher percentage of coins from Philadelphia. Although I haven't tried, you could probably weight the mintages based on how far west or east you are. For example, I find Denver minted coins at a higher than predicted rate for almost all dates from 1946 through 1964 due to my location, but San Fran and Philly minted coins are both at lower than predicted rates for most dates.


As was mentioned above melting also occurred, but since there are no real true key dates in the Roosevelt set, I think the melting probably occurred at close to the same percentage for all dates/mintmarks and thus can be ignored unless you wanted to subtract factor #2 first before using a common percentage which would melt slightly more of the more recent dates (which is probably true anyway).

I tried to use those factors and my dime finds to date to determine how many coins I would have to find to complete the set or to try to determine the values for factors #1 and #2 so I could try to get more realistic odds to replace the ideal 529:1 that you stated above. With Factor #1 at 8,000,000 removed and Factor #2 a 1% removed/lost rate, I get a 1687:1 or so and if factor #1 goes to 9,000,000 its more like 2347:1. Note that I didn't remove the proofs from my mintage totals, as for rough averages it was close enough.

As I am well getting close to 1200 dimes and still missing two dimes, I suspect that the factors I mention play a role, but my guess is as good as your as to what a good estimate of their values are, and my data is somewhat skewed at the moment due to a recent 61 dime find that was almost all 40's to mid 50's and only two after 1959. In a normal batch of finds, about 59% should be 1960 or later, so it will take some time for my finds to statistically match again.

And in my searches I have found a couple of seated's and a couple of barber's and typically I find 1 merc for every 14 or so Roosevelts. And don't forget there were about 2.5 times as many roosevelts minted as there were mercs to begin with so even in an ideal world where all the coins are still in circulation the Roosevelt to merc rate should be 2.5:1.


Anywho, thought I would share my two cents on the subject. Hope you found it interesting.

 

[Sleepy Holow]

With Factor #1 at 8,000,000 removed and Factor #2 a 1% removed/lost rate, I get a 1687:1 or so and if factor #1 goes to 9,000,000 its more like 2347:1.

Dang GMan...If there's one thing you made me realize, it's that it's going to be darn near impossible to complete my FDR set any time soon by doing mainly boxes and MWRs. CWRs and bags are incredibly tough to get in my area. It would be easy to keep chugging along at my current pace, but sometimes you gotta put in the extra effort to get the results you wanna see. I get back to my hometown here in a couple weeks...I'll really have to think about ways to find these tougher dates.

 

[GMan00001]

Dang GMan...If there's one thing you made me realize, it's that it's going to be darn near impossible to complete my FDR set any time soon by doing mainly boxes and MWRs. CWRs and bags are incredibly tough to get in my area. It would be easy to keep chugging along at my current pace, but sometimes you gotta put in the extra effort to get the results you wanna see. I get back to my hometown here in a couple weeks...I'll really have to think about ways to find these tougher dates.

I was just adding some things to think about if trying to figure out statistics. All that being said, maybe you happen upon a collection turned in and find the five toughest dates all at one time. Who knows. Just because the statistics say it's tough doesn't mean it's tough for everyone and statistically some people will find the toughest dates first.

And because it takes longer, you are more likely to stack on the duplicates which isn't all bad either.

Good luck.

 

[jamesandsons]

Factor #2
A percentage of the coins minted each year were removed/lost and that with each passing year a percentage is also removed/lost which repeats each year after the coin is minted. So a coin from 1964 had X% removed/lost and 1963 had 2X% removed/lost and 1962 had 3X% removed/lost and so on. Essentially this is trying to represent making coins harder as they get older. What is the percentage 1%? 0.01%?

I don't know what the correct percentage should be, but I have a couple thoughts. First, it's probably not likely to be a constant % over time, year by year. All I could really feel comfortable saying is that it probably does increase every year.

Second, even though the number of each given silver dime in circulation is likely decreasing year after year, I have to think that an important factor is dimes coming back in to circulation that had been out of circulation for some time. Personally I think the likelihood is that almost any silver dime you find today in CRH was probably part of a hoard/collection at one point, and for whatever reason (death, accidental dump, theft, etc.) was dumped at a bank or spent, probably sometime fairly recently. It would be cool if there was a way to know how long a given coin had been in circulation.

Anyway, my point is that if X number of a given dime are taken out of circulation each year, that is offset by Y number of that same dime that find their way back in to circulation. Y is almost certainly less than X.