07-12-2018, 01:59 PM
(This post was last modified: 07-12-2018, 04:12 PM by jplarson.)
Let's do some math and calculate serial numbers!
Let's do some math and calculate serial numbers!
The industry for years has been getting away from specifying specific odds for inserts and hits, preferring to go with "1 autograph per box on average" or "odds of pulling any insert are on average 1 per pack" without showing whether different insert sets are more scarce than others. However in 2013, Topps Finest listed printed odds for all Refractors, including the serial numbered ones. Knowing this, we can figure how many packs are out there and determine the following:
1. How many Xfractors and Refractors were printed
2. What the serial number would be for Xfractors and Refractors
3. How many packs were manufactured
4. How many hobby boxes were created
Some calculations of odds and serial numbers are easy to see. For example, it's easy to say an Xfractor is exactly twice as rare as a regular Refractor, as the odds of finding a Refractor are 1:3 (or 2:6) with an Xfractor 1:6. A Prism Refractor print run is 25 with odds of 1:14 and a Red Refractor print run is 50 with odds of 1:7. Makes sense that 50/1:7 is twice as common as 25/1:14. Finally, a Superfractor is a true 1/1 print run where as any individual printing plate is technically 1/1, there are four plates in all. Thus if we look at a Super 1/1:340 and divide the 340 by 4, the result is 85 or the expected 1:85 for any color printing plate.
The question today is this, if Refractors or Xfractors were serial numbered, what would the print runs be? This assumes that the odds per pack aren't rounded for the cards and doesn't take into account cards held back by Topps for potential damage replacements that were subsequently released to market.
Below is a table of each Refractor level, the odds expressed as a percentage (1:3 becomes 1/3 or .33%), count is the individual serial number of any given card, and total quantity is the serial number multiplied by 150, the size of the base set.
To acquire 1 Superfractor it would take 340 packs. Thus to acquire 150 Superfractors it would be 150 x 340 = 51,000 packs. This is an easy cross multiply and divide scenario:
340 x 150 / 1 = X, or X = 51,000. Who says math wouldn't be useful in adult life?! Knowing this formula, one would expect this to hold true for all the printed odds:
This holds true for the Superfractor, any Printing Plate, Camo, and Pink Refractors. Easy enough to understand as the serial numbers go up, the odds increase at the same ratio. The odds break down after going beyond a print run of /10. Using the Prism /25 as an example, one would that with a print run of 25, or 25 times that of a Superfractor, the odds would be 25 times easier to find a Prism Refractor.
Let's use a Superfractor, any Printing Plate, and Prism Refractor as our examples. Any Printing Plate is /4 and dividing the odds of the Superfractor (1:340) by 4 does yield 1:84. By this logic, we should divide 1:340 by 25 to arrive at our true odds for a Prism refractor. 340 / 25 = 13.6. So now we know that some rounding takes place in the odds. Let's now assume that the true printed pack run is 51,000 packs and calculate Total Quantity / Total Packs:
To translate these Odds % back into 1:X odds, divide the Total Quantity by the Odds, then divide that result by Total Quantity. Thus the Superfractor would be (0.00294 / 150) / 150 = 340 which matches the stated odds of 1:340.
Prism winds up being slightly more favorable, Gold and Blue even more favorable, and Red slightly less favorable in terms of odds per pack. Now that the exact odds are truly known and we are operating with the assumption of 51,000 packs, let's calculate how many Xfractors and Refractors there are and what the serial numbers would be. If the Total Packs are multiplied by the odds, the print run should reveal itself. Take the Gold Refractor for example. 51,000 x .22059 = 11250.09, allowing for imprecise rounding that is 11,250 which is the Total Quantity shown above. Using Excel will ensure precise calculations. Furthermore, dividing the Total Quantity by 150 will provide what the serial number would be for any individual card. Finally using the formula to calculate the true odds per pack will also yield the true odds per pack for Xfractors and Refractors:
The odds perfectly slot in for the stated print run which leads to stated print runs for Xfractors of 56.7 and 113.3. Since you can't make 30% or 70% of a card, the Xfractor can be rounded up to #/57 and the Refractor down to #/113. With that rounding, the odds would change slightly for Xfractors from 1:6 to 1:5.96 and Refractors from 1:3 to 1:3.01.
Not to forget the last question, how many boxes were manufactured, it would be 51,000 packs divided by packs per box (12) which leads to 4,250 boxes (or 8,500 mini-boxes). Since we know that retails got special 2-pack blasters, it's likely not all 4,250 were sold and thus some opened up to be resold through retailers.
In summary:
1. How many Xfractors and Refractors were printed = 8,500 and 17,000 respectively
2. What the serial number would be for Xfractors and Refractors = /57 and /113 respectively
3. How many packs were manufactured = 51,000
4. How many hobby boxes were created = 4,250
5. Bonus finding = Yes the odds are rounded to a certain extent
1. How many Xfractors and Refractors were printed
2. What the serial number would be for Xfractors and Refractors
3. How many packs were manufactured
4. How many hobby boxes were created
Odds of finding a parallel version:
Refractor 1:3, Xfractor 1:6, Blue Refractor 1:4, Gold Refractor 1:5, Red Refractor 1:7, Prism Refractor 1:14, BCA Pink Refractor 1:34, Military Camo Refractor 1:34, SuperFractor 1:340, Printing Plate 1:85
Refractor 1:3, Xfractor 1:6, Blue Refractor 1:4, Gold Refractor 1:5, Red Refractor 1:7, Prism Refractor 1:14, BCA Pink Refractor 1:34, Military Camo Refractor 1:34, SuperFractor 1:340, Printing Plate 1:85
Some calculations of odds and serial numbers are easy to see. For example, it's easy to say an Xfractor is exactly twice as rare as a regular Refractor, as the odds of finding a Refractor are 1:3 (or 2:6) with an Xfractor 1:6. A Prism Refractor print run is 25 with odds of 1:14 and a Red Refractor print run is 50 with odds of 1:7. Makes sense that 50/1:7 is twice as common as 25/1:14. Finally, a Superfractor is a true 1/1 print run where as any individual printing plate is technically 1/1, there are four plates in all. Thus if we look at a Super 1/1:340 and divide the 340 by 4, the result is 85 or the expected 1:85 for any color printing plate.
The question today is this, if Refractors or Xfractors were serial numbered, what would the print runs be? This assumes that the odds per pack aren't rounded for the cards and doesn't take into account cards held back by Topps for potential damage replacements that were subsequently released to market.
Below is a table of each Refractor level, the odds expressed as a percentage (1:3 becomes 1/3 or .33%), count is the individual serial number of any given card, and total quantity is the serial number multiplied by 150, the size of the base set.
To acquire 1 Superfractor it would take 340 packs. Thus to acquire 150 Superfractors it would be 150 x 340 = 51,000 packs. This is an easy cross multiply and divide scenario:
340 x 150 / 1 = X, or X = 51,000. Who says math wouldn't be useful in adult life?! Knowing this formula, one would expect this to hold true for all the printed odds:
This holds true for the Superfractor, any Printing Plate, Camo, and Pink Refractors. Easy enough to understand as the serial numbers go up, the odds increase at the same ratio. The odds break down after going beyond a print run of /10. Using the Prism /25 as an example, one would that with a print run of 25, or 25 times that of a Superfractor, the odds would be 25 times easier to find a Prism Refractor.
Let's use a Superfractor, any Printing Plate, and Prism Refractor as our examples. Any Printing Plate is /4 and dividing the odds of the Superfractor (1:340) by 4 does yield 1:84. By this logic, we should divide 1:340 by 25 to arrive at our true odds for a Prism refractor. 340 / 25 = 13.6. So now we know that some rounding takes place in the odds. Let's now assume that the true printed pack run is 51,000 packs and calculate Total Quantity / Total Packs:
To translate these Odds % back into 1:X odds, divide the Total Quantity by the Odds, then divide that result by Total Quantity. Thus the Superfractor would be (0.00294 / 150) / 150 = 340 which matches the stated odds of 1:340.
Prism winds up being slightly more favorable, Gold and Blue even more favorable, and Red slightly less favorable in terms of odds per pack. Now that the exact odds are truly known and we are operating with the assumption of 51,000 packs, let's calculate how many Xfractors and Refractors there are and what the serial numbers would be. If the Total Packs are multiplied by the odds, the print run should reveal itself. Take the Gold Refractor for example. 51,000 x .22059 = 11250.09, allowing for imprecise rounding that is 11,250 which is the Total Quantity shown above. Using Excel will ensure precise calculations. Furthermore, dividing the Total Quantity by 150 will provide what the serial number would be for any individual card. Finally using the formula to calculate the true odds per pack will also yield the true odds per pack for Xfractors and Refractors:
The odds perfectly slot in for the stated print run which leads to stated print runs for Xfractors of 56.7 and 113.3. Since you can't make 30% or 70% of a card, the Xfractor can be rounded up to #/57 and the Refractor down to #/113. With that rounding, the odds would change slightly for Xfractors from 1:6 to 1:5.96 and Refractors from 1:3 to 1:3.01.
Not to forget the last question, how many boxes were manufactured, it would be 51,000 packs divided by packs per box (12) which leads to 4,250 boxes (or 8,500 mini-boxes). Since we know that retails got special 2-pack blasters, it's likely not all 4,250 were sold and thus some opened up to be resold through retailers.
In summary:
1. How many Xfractors and Refractors were printed = 8,500 and 17,000 respectively
2. What the serial number would be for Xfractors and Refractors = /57 and /113 respectively
3. How many packs were manufactured = 51,000
4. How many hobby boxes were created = 4,250
5. Bonus finding = Yes the odds are rounded to a certain extent