A New Way to Compare Sets?

tradedollarnut

Recently I remarked to Keoj that I felt there should be some way to mathematically differentiate between Registry Sets that were all top pop, but in different series. After all, we intuitively know that it's much tougher to be top pop in Bust Dollars vs some recent Modern sets - but how to show it? He came up with a fantastic idea: Condition Census Weighting. Take the average grade for the 10 coin condition census and use it to weight the Registry Set's coins. Using this method, an all top pop set of easily acquired coins weights out by definition at 1.000 but a much tougher set weights out much higher.

Here are a few results of condition census weighting on some outstanding sets [I only did a few shorter sets - the number crunching was making me giddy]:

Bruce Scher 3 cent nickel Circ strike: 1.009
DRG SBA Circ Strikes: 1.005
Illinois Collection #1 Buffalo nickels: 1.003
Alergar Saccie Proofs: 1.000


But the Granddaddy of all that I looked at is:

Cardinal Collection Bust Dollars: 1.026 [note: assumed 1794 was MS63 and combined pops of varieties]

In my opinion, anything of 1.002 points or more is an amazing accomplishment - which goes to show exactly how outstanding the Cardinal Collection truly is! It'd be extremely useful if PCGS would add this measurement to the front page of each set.


Note: The above numbers are a straight up average. Doing a weighted average might do an even better job of showing the best sets.

Russ

Pretty cool idea. Now, I know you must have crunched the numbers for The Legend Collection. Cough them up.

Russ, NCNE

tjkillian

I don't quite get how the math works, could you please elaborate? How could the Cardinal collection of Bust dollars be only 25% better than a set of "Saccies"?

Tom

tradedollarnut

It's not "only 25% better". Don't compare the numbers that way. Just recognize that the higher the number, the more difficult it was to complete the set. Perhaps it would help if you think about how outstanding Bruce Scher's set is and look at the difference between that and the stunning buffalo nickel set. Then look at the difference between Cardinal and Scher and shake your head in amazement like I did!

BTW - I crunched the weighted numbers on Cardinal and the set came out to an amazing 1.038!

roadrunner

This has some real merit. Does the Cardinal 25% sort of imply that
he holds 25% of the pop tops or some average thereof? In the more common sets where say 20 coins might be pop top I would expect a weight of say 1.00. But in sets where one guy has a bunch of pop tops, or exceeds the 2nd place coin by multple points, large premiums should be accorded.

What is the theoretical top of the heap? 2.000? Or is it unlimited?


roadrunner

tradedollarnut

I would say in theory that there is no theoretical maximum. In reality, however, I simply can't think of a real life set of coins that would exceed even 1.1

Perhaps the small numbers are causing some confusion here. One way to make it numerically more impressive would be to simply subtract 60 from the grades. That way, on a set that averages 65, the differences are divided by 5 instead of 65 and thus the census weight differences would be 13 times greater.

ColonialCoinUnion

Neat idea - I like it.

I think the theoretical maximum might be much higher in colonials where the pop top coin may be a 64 and the next best an XF45.

Windycity

Working your math, could you tell me how the 1892 Columbian Expo Proof Set would score???

prooflike

You could do some logrithmic or geometric multiplication of your 1.00 to 1.xx numbers. The 1.00 would stay a 1 and any fraction above one would be worth considerably more.

DRG

I am just impressed that Tradedollarnut ever noticed my humble little set. I am in awe of his.

That said my set does contain 2 POP #1 coins, a POP #2, a Pop #3, a POP #6, a POP #7, & a POP #9 coin. That is 7 very low POP coins out of a set of only 12 coins. It is kind of a cool accomplishment even if it is only a ugly modern dollar.

I like the overall idea. It might be very interesting if PCGS used the idea to ultimately have a "weighted" listed of all the best registry sets. It would be a ranking of the "All Time Best Sets" without regard to series.

Now that would be an interesting competition and a complex bit of math.

tradedollarnut

Please note that I had dropped a decimal place in the first post which made it impossible for others to get the same numbers .... I've corrected all the census weight averages. The relative strengths of all the sets remained the same.

Russ - the Trade Dollar set is significantly below Cardinal's average.

cardinal

TDN,

Not to sound self-serving, but I do think the census weighting approach has real merit! This approach factors in the "degree of difficulty" of one set versus another, that is not considered in the current PCGS weightings (scale of 1-10 for EVERY set).

Thanks for noting the corrected scores! Now I've been able to replicate your figures.

As ColonialCoinUnion points out, sets that include low population varieties (with low average grades for condition census specimens) may display much higher scores. So, with my set as an example, the basic date set scores out as 1.026, whereas the full variety set scores 1.115 based on the current online Pop Report.

Now, this really highlights the effects of re-submissions dilluting the rarities of varieties in the Pop Report. For the key 1794 dollar in my set, the online Pop Report reflects an average grade of the top 10 coins as 61.4. However, in reality, the reported population is in error.

The reported population is: 3 in MS66, 1 in MS65, 1 in MS64, 1 in MS63, 1 in MS61, 2 in AU55, 1 in AU53, 1 in XF45, and 9 in XF40, with the top 10 ranging from MS66 to AU53. From my research in 1794 dollars, I know that the MS65 and MS64 specimens are duplications of other listings (both now MS66), the MS63 listing represents an old certification of my coin, and the two AU55's have since been crossed over to NGC (and upgraded). When you adjust the Pop Report, the top ten range from MS66 to XF40, and the average grade becomes 51.4.

Using the 51.4 condition census average for the 1794 dollar, my basic date set would score 1.042 and the full variety set would be 1.120.

I'm sure other sets are affected in this way also, so the relative rankings from condition census weighting should still be reasonably accurate.

STEWARTBLAYNUMIS

Bruce

You must be REALLY bored.


Stewart

Lakesammman

Bruce - you must be really bored - Stewart


So, what does the Blay Lincoln set look like after you crunch the numbers?

FrattLaw

Ah, the math ....... please make it stop........ ah, my head hurts!

Really cool theory and it works well. I just wish I understood it. I guess that's why I went to law school -- no math.

Michael