2005 Leaf Random Inserts' Odds Revealed

[S.A.M.]

Hello Sportscard Forum!

First let me say I've been reading some of the various threads around the site and it looks like this forum is a great community.

Second, this post is the result of some calculations I did to come up with the odds of finding a card from the 2005 Leaf baseball randomly inserted sets in a single pack.

This post is pretty long so if you just want to see the odds of for the randomly inserted sets skip to the "Odds" section. For the more curious/mathematically/statistically inclined the "Methodology" section may be of more interest.

Who this article is for: 2005 Leaf baseball collectors, collectors who want to know how to calculate the real odds of the randomly inserted cards in any set, collectors who believe that card scarcity is an important factor in valuing a card.

Introduction

I recently moved and while going through storage I found the baseball cards I collected as a kid (1988-1992) and decided it was time to organize and price them. By going through my cards, my interest in collecting was reawakened and I bought a couple of boxes of 2005 Leaf. As you can imagine I was surprised to learn that there are cards that have pieces of bats and jerseys in them or are signed and/or serial numbered. So those first few game-used and auto cards where a blast to find in the packs! I also started to investigate the state of the hobby and found this site as well as Beckett's and I feel pretty caught up on everything that's changed in the last 15 years.
Out of the cards I got in the Leaf boxes, I liked the Sportscasters the best. For some reason I just think they look pretty cool. Anyway, my interest in the multiple insert sets grew as I investigated how many variations there are and the print runs for each card, etc. Long story short, my train of thought led me to the calculation of the odds of finding any of the random 2005 Leaf insert cards and this is what I came up with:

Odds

2005 Leaf Set consists of a 300 base card set and an additional 51 insert or insert/parallel sets. Here I consider insert parallels as their own set. Some of the odds were impossible to calculate accurately or their accuracy was debatable; for the reasons see the methodology section below. The odds marked as "stated" were given by Leaf, all others are the result of my calculations. All odds are in terms of packs, so 1/8 means 1 card from this set in 8 packs.

Press Proofs Red (1/8) stated
Press Proofs Blue (1/40)
Press Proofs Gold (1/120)
Base Autographs (impossible)
Red Autographs (1/30)
Blue Autographs (1/120)
Gold Autographs (1/299)
Home (1/22) stated
Rode (1/22) stated
Home Jersey (impossible)
Home Jersey Prime (1/1196)
Rode Jersey (impossible)
Rode Jersey Prime (1/1196)
Clean Up Crew (1/49) stated
Clean Up Crew Die-Cut (1/239)
Four Star Staffs (1/48) stated
Four Star Staffs Die-Cut (1/239)
Picture Perfect (1/20) stated
Picture Perfect Die-Cut (1/449)
Cornerstones (1/37) stated
Cornerstones Bats (impossible)
Cornerstones Jerseys (1/179)
Cornerstones Prime Jerseys (1/897)
Fans of the Game (1/24) stated
Fans of the Game Signatures (impossible)
Leaf Certified Materials Preview (1/21) stated
Leaf Certified Materials Mirror Red Preview (1/299)
Leaf Certified Materials Mirror Blue Preview (1/598)
Leaf Certified Materials Mirror Gold Preview (1/2392)
Gold Leaf Rookies (1/24) stated
Gold Leaf Rookies Autographs (impossible)
Mirror Gold Leaf Rookies (1/3588)
Mirror Gold Leaf Rookies Autographs (1/3588)
Gamers (1/31) stated
Quantum Gamers (1/342)
Picture Quantum Gamers Die-Cut (1/1196)
Gold Stars (1/27) stated
Mirror Gold Stars (1/1794)
Cy Young Winners (1/31) stated
Gold Cy Young Winners (1/171)
Gold Cy Young Winners Die-Cut (1/598)
Alternate Threads (1/18) stated
Holo Threads (1/239)
Holo Threads Die-Cut (1/718)
Shirt Off My Back (1/111) stated
Patch Off My Back (1/449)
Patch Off My Back Autographs (debatable)
Leaf Game Collection (1/119) stated
Leaf Game Collection Autographs (debatable)
Recollection Collection (debatable)
Sportscasters (1/4) stated
Sportscasters break down:

• Cards #d to 5 (1/1196)
• Cards #d to 10 (1/449)
• Cards #d to 15 (1/100)
• Cards #d to 20 (1/64)
• Cards #d to 25 (1/34)
• Cards #d to 30 (1/28)
• Cards #d to 35 (1/24)
• Cards #d to 40 (1/28)
• Cards #d to 45 (1/36)
• Cards #d to 50 (1/51)
• Cards #d to 55 (1/65)
• Cards #d to 60 (1/150)
• Cards #d to 65 (1/138)
• Cards #d to 70 (1/256)

Methodology

The easy part:

To calculate the odds of finding a card from a randomly inserted set four bits of information are required. The most necessary piece is the total number of cards that exist for a product, the number of cards in a pack, number of cards in a set, and the print run for the card.
Once the you have the the required information calculating the odds of finding a card for that set is a breeze. Here is the equation that I used:
Variable key:
T = total numbers of cards in production
CPP = cards per pack
CNS = cards in set
O = odds for a card (in terms of packs)
# = print run for that card

Equation:
O = 1 / ([(CNS * #) / T] * CPP)

The equation works like this. If you know the print run for a card you know how many of that card exists (CNS * #). So when you divide the number of that card in existence by the total number of cards in production you get the percentage that card makes up of the whole production run [(CNS * #) / T]. Next you multiply the percentage in the production run by the number of cards in a pack, this gives you the probability that given a pack of 2005 Leaf a card from the given insert set will be in it. Dividing this probability into 1 gives you, on average, the number of packs that would have to be opened to find that card.

The hard part:

The hard part is determining the total number of cards in production. To calculate this I needed 2 pieces of information about a single card (or set of cards). The required information is the print run for a card and the probability of finding that card. This doesn't seem like it would be hard to find information but it is. From what I could find, card companies do 1 of 2 things when describing their insert sets. The set has either stated odds and isn't serial numbered or is said to be randomly inserted and serial numbered. Never do they say what a card is serial numbered to and the odds of finding that card in a pack. Never you say? Well this is where the Sportscasters come in.
Leaf states that there is 1 Sportscaster card in every 4 packs (6 Sportscasters per box 24 packs) and it just so happens that each Sportscaster is numbered to 70 or less. This by itself isn't enough information because we need to know the exact print run for a card. To sort and price my old cards I purchased a 1 month subscription to Beckett online and luckily for us Beckett lists the print run for each card in the Sportscasters sets. At first I wasn't sure if Beckett's print runs were correct but after checking my 12 Sportscasters and another 30 or so listed online against the Beckett list they all matched up so I believe Beckett's print run numbers to be correct. So here's what I did to calculate the total number of cards in production.
I calculated the total number of Sportscasters cards by multiplying the number of sets per print by the size of the set (50 cards) and summed these values. This sum (224,250 to be exact) is the total number of Sportscasters in existence. Then using the stated odds of 1 in 4 packs I determined the total number of 2005 Leaf baseball cards to be 7,176,000. After that I just used the equation above to calculate the odds for the other insert sets.

The impossible ones:

Some of the odds where impossible to calculate because the cards in the set are randomly inserted but not serial numbered so there is a missing variable in the calculation.

The debatable ones:

Some of the odds where debatable to calculate because of their variable print runs. Because the stated print run is something like "#d to 200 or less", without the each card's print run information the odds can't be calculated exactly.

Conclusions, questions, and revelations:

Through these calculations some interesting information came to light. First, the actual rarity of certain cards is not what one would expect. For instance there are actually fewer Sportscasters #d to 70 than there are ones #d to 35, so based on scarcity Sportscasters #d to 70 should be more valuable than those #d to 35.
Second, how does Beckett get exact print run information? There are exactly 7000 (140 variations on the 50 card set) different Sportscaster cards #d to between 5 and 70. I find it hard to believe that Beckett has received information from the marketplace on all of these cards which leads me to believe that they get their information directly from Leaf. Which to me is a little weird because they are giving information to Beckett that they won't directly give to collectors.
Well thanks for reading, if anybody actually made it this far, and I hope this has been informative.
I haven't taken a look but because of Beckett-revealed information this calculation may be possible for other sets.


Have a good rest of the weekend,
S.A.M.

[spuds1961]

thanks for the informative article s.a.m. welcome back to collecting and enjoy ,some of the new inserts are mind boggling ,hope you managed to pull a few from your 2 boxes ,i would suggest a box of leaf certified materials 2004 baseball for 62.95 from dacardworld nice looking cards with an average of 4 hits per 10 pack box ,i am not a spokesman for dacardworld just know thats the best price for that product ,i also had my best pull ever from it a tom seaver autographed fabric of the game 2 color jersey numbered 3/5,take care spuds

[S.A.M.]

spuds you're welcome.
and you're right, the insert sets are too numerous to a fault. I noticed that dacardworld had good prices. I actually bought my boxes from J&J Sportscards because they sell on Amazon and I had a few Amazon gift certificates. Incidentally J&J shipped incredibly fast. I chose to have my order shipped ground but it actually came the next day.

[staregazer]

I think the reason why they have so many insert cards now in each brand they bring out is so that you have good odds of getting an insert. They also make multiple brands so that you will be more likely to buy another brand when it comes out. The card manufactures figured that if they made more brands then they could shortprint each brand more making each one more rare. Then they also figured that if they made more inserts for each brand then each insert would be even more rare instead of making fewer inserts and more of each insert.

For example, one company used to make just one brand. They would have lets say three inserts. Two of them had a good bit of each one made but one of them fewer than the other. The third one would be a lot more rare and perhaps individually numbered. Later on down the road that one company ends up producing four, five, or more brands basically dividing the prodution of one brand into multiple ones making each one more scarce. In each brand they put a lot more different selection of inserts making each one of those more scarce. This allows for better odds of getting an insert and still making each one scarce while still having the same number of cards on the market altogether. From what I have read or heard a while back the overall cards being produced is a bit less than it was about 10-15 years ago anyways so it makes it even more scarce than that.

I used to collect cards back in the early to middle 90's and see a big change in how things are being done now and reading up on how this hobby I used to have is changed. Since I heard that the 1/1 cards came out some of the other rare ones I thought it would be very nice to have one of those cards particularly of a popular player and say that I am the only one in the world to have this card. It is now the norm to get numbered and GU cards so I wonder what is going to be the "next big thing".