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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[Sleepy Holow]

I just looked to see how much of a difference it makes for me personally.

Note that my "As Minted" and "Using Circulation Constant" values don't subtract the number of proofs and just use the base mintages.

Mint	As Minted	Using Circulation Constant	My finds
Denver	56.2%	58.2%	72.3%
Philadelphia	39.5%	38.4%	24.4%
San Francisco	4.4%	3.4%	3.2%

For me there is a clear difference based on the mint it was produced at with a significantly higher percentage from Denver and lower percentage from Philadelphia.

Wow, that really seems to make a significant difference. Before we brought in any data to support or deny the "Geography Factor" I honestly could see it going either way. I mean, it makes sense that your hunting grounds in relation to the mints would make a difference, but at the same time I wasn't sure how much time needed to pass before that kinda stuff didn't matter. Apparently, it does matter. I guess dimes might not be as fluid as one might think; however, this is just one sample so far. I'll go through my roosies tonight and see if I get something similar.

One more thing...Your data is based on FDR's only and not Mercs, right? I'm assuming those would probably need to be two separate calculations.

 

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[Sleepy Holow]

Sorry Sleepy I hate math and the math makes my head hurt!I do know that I get on avg about 1 dime per box and got 4 dime in 160.00 CRW last week.
HH Cooper

Nice score on those CWRs last week, Cooper! Are you currently trying to collect the FDR set? Your average is looking better than mine so far. Good luck to you.

 

[GMan00001]

One more thing...Your data is based on FDR's only and not Mercs, right? I'm assuming those would probably need to be two separate calculations.

Yes, only FDR's. I already had the FDR mintages in a spreadsheet as I had done some "How many silver dimes are remaining?" calculations 5 or 6 years ago, so I spent an hour and whipped together the calculations as they applied to me.

My sample size for Mercs is lower, so I started with FDR's. Maybe if I am feeling up to it, I'll try that tonight as I may have entered the Merc mintages in as well, have to go look at my old spreadsheets.

As a separate note, I ignored the mintages for everything after 1964 in my calculations because I don't think they really matter if using the find rate of the data. Unless I am wrong once you know what the find rate of silver is (X silver dimes/$$$ searched), how many silver dimes you would have to find to complete a set (on average), and what the adjusted mintages of each coin are, you can just apply your find find rate to those numbers to figure out how many boxes it would take to find a particular coin.

If nothing else, it simplifies the data entry.

 

[sjlund]

Nice sjlund! If you've got all those, then you must be pretty close to completing the whole set then, huh?

I'm honestly not sure, I've never thought of roosies as anything other than 90% bullion. I might have to grab an album one of these days.

 

[Sleepy Holow]

Hey GMan, you said you've got 908 roosies...how much volume have you done? I'm putting in the geographical factor and I'm noticing a huge effect on the odds so far. The only thing is my sample size is far smaller than yours I'm sure. I feel like we're getting into uncharted territory here. Pretty exciting stuff.

 

[mark1982]

i need to start searching dimes more. My averages is 2.1 per box for 2013. However I have only searched about 18k worth this year. did a box tonight and got 1939,1957,1960d

 

[GMan00001]

Hey GMan, you said you've got 908 roosies...how much volume have you done? I'm putting in the geographical factor and I'm noticing a huge effect on the odds so far. The only thing is my sample size is far smaller than yours I'm sure. I feel like we're getting into uncharted territory here. Pretty exciting stuff.

No, I have found 1150 silver Rosies from $207,389.2 searched (actually probably a bit more searched as I search the teller trays when at the bank with a glance, but I don't add those in).


The 908 is the average number of silver Rosies I should have to find to complete a set based on the results of the calculations using my geographic factor.

Since I have found more than law of averages would say I should need to find (based on the current calculations), either there are other factors at play, I am just unlucky, or a little of both. I suspect both at this point.



Also, I did have the Mercury dime mintages already typed in so I spent a few minutes doing my calcs for the mercs and here was what I found

Mint	As Minted	Using Circulation Constant	My finds
Denver	17.8%	18.1%	32.3%
Philadelphia	65.8%	65.7%	52.3%
San Francisco	16.4%	16.2%	15.4%

So even for Mercury dimes which have been in circulation for a lot longer, I still see a significant geographic factor.

From having read the posts going back a few years, I noticed that those out west seem to find a higher percentage of older S-mint wheat cents whereas those in the east rarely found them, so these results don't really surprise me. I'm just glad that I now have a way to quantify it and apply it to show how it impacts me.

And my results were from the same amount searched with 65 mercury dimes found.

My probability calculations show that I should be able to complete the set after finding a mere 10,390 mercury dimes which at my mercury find rate should take approximately 132,602 boxes.... Guess I better get a move on if I want to complete it in my lifetime as that is over 18 boxes a day (including sundays) for 20 years.

 

[Sleepy Holow]

i need to start searching dimes more. My averages is 2.1 per box for 2013. However I have only searched about 18k worth this year. did a box tonight and got 1939,1957,1960d

2.1 per box! Wow! That's a stellar average, Mark! Sounds like you've got some good boxes in your area.

 

[Sleepy Holow]

So GMan, I ran your numbers on my spreadsheet using 1150 FDRs (832 D's, 281 P's, and 37 S's) on $207,389.20 searched. With the Geographical Factor added, I show that you should have finished your collection after encountering 928 FDRs/ 670 Boxes/$167,500. I feel like this number could be pretty close to accurate. I mean, it is just on average and like you said, maybe you're just on the wrong side of that average. What do you think?

 

[GMan00001]

So GMan, I ran your numbers on my spreadsheet using 1150 FDRs (832 D's, 281 P's, and 37 S's) on $207,389.20 searched. With the Geographical Factor added, I show that you should have finished your collection after encountering 928 FDRs/ 670 Boxes/$167,500. I feel like this number could be pretty close to accurate. I mean, it is just on average and like you said, maybe you're just on the wrong side of that average. What do you think?

My number came to 908 instead of 928, but again I didn't subtract the proofs from the mintages, so that may account for the difference.

I still suspect there is probably an additional "Collectability Factor" for key/semi-key dates in sets such as Mercury Dime (1916-D), Jefferson Nickel (1950-D), and Wheat Cent (1909-S VDB, 1909-S, 1914-D, 1931-S, etc), but for Rosies with the lack of any true key dates, I would say we are probably pretty close especially with the ability to adjust for geographic differences which is something I had never accounted for before.

I think I am probably just a bit unlucky with regards to the randomness of my silver Rosies.

 

[GMan00001]

And after all I might be 250 over the predicted average, but I am also only 2 short so it seems reasonable.

 

[Sleepy Holow]

And after all I might be 250 over the predicted average, but I am also only 2 short so it seems reasonable.

I was also thinking that the 908-928 number is only valid if you never search the same coin twice. So maybe you're a little over due to the fact that you've inevitably searched though some of the same coins.

 

[GMan00001]

I was also thinking that the 908-928 number is only valid if you never search the same coin twice. So maybe you're a little over due to the fact that you've inevitably searched though some of the same coins.

Searching the same coin twice would have only impact the 908 number if I was turning in the silver coins I found and then finding them again as 908 is how many silver Rosies I have to find to complete the set, and that number is independent of my find rate. If I found 1 silver Rosie every 10 coins or 1 silver Rosie every 10000 coins, I would still need to find (on average) 908 silver Rosies to complete the set if the coins come up at the calculated distribution. The find rate only affects how many coins I have to search through to get to 908 silver Rosies.


Separately, although it is technically possible that I searched through some of the same coins, but I'll bet it's a really low percentage for me personally.

With the exception of the occasional box, I typically only buy bags of coins off of coin machines at a couple of local banks.

When dumping, I always dump at branches of a couple of other banks and those are carted off by the armored carrier to be wrapped, rolled, and recirculated.

But because I am pretty much only buy bags, I will only get the same coins if they find their way to my pickup bank through circulation and since there are more people in the Twin Cities metro area than dimes I have searched to date in my lifetime.... I would bet that I haven't searched the same coin twice very many times at least not with dimes.

Halves... that might be a different story as they just don't circulate much.

 

[sjlund]

Nice sjlund! If you've got all those, then you must be pretty close to completing the whole set then, huh?

I finally took the time to look - I'm missing 55p, 50s, 49p, and 48s.

 

[SilverForBrains]

I love my spreadsheets too. unfortunately I keep changing the format every few months so none of it is compatible with each other!