Questions about Odds and Rarity

[dcs6f4]

So I'm new any kind of sports card collecting outside of being a kid in the 90s.

I get the idea behind all the inserts and parallels in modern sets--my main question is about the relative rarity of inserts.

For example, in 2017 Donruss Optic Football there is a base set which is more common than an insert from "The Rookies" or Gridiron Kings or something. I'm curious to see if there is any info about the odds of pulling a standard insert like these (not the numbered parallel) in a pack.

To be very specific... How much rarer is a Mahomes "the rookies" card than the Mahomes rated rookie?

[jplcom]

This is a fun exercise! Here are some variables to consider to help answer your question.

How big is the base set?
How many base cards come in a box of hobby?
How many base cards come in a box of retail?
How many different insert sets exist?
How big is the "The Rookies" insert set?
How big are the other insert sets?
What are the odds of pulling any one "The Rookies" card?


Let's take a look at the set. 200 cards make up the entire set, the first 100 are base cards, the next 50 are rookie cards, and the last 50 are Rated Rookies. If all base cards are equal in print run, it's 100/200 (veterans), 50/200 (rookies), and 50/200 (Rated Rookies). Expressing that as a percentage, 50% of the set are veterans, 25% are rookies, and 25% are Rated Rookies. However we can't be certain that Rated Rookies aren't short printed. We'll get into that later.

A Hobby box has the following breakdown: 4 cards per pack, 20 packs per box. That's 80 cards in a box. Panini says that on average you will pull 1 autograph card, 10 holo parallels, 10 Rated Rookies, 10 Rookies, and 4 inserts. We'll subtract out the inserts and parallels, 80-1-10-4 = 65 base cards. Of those 65, 10 are Rated Rookies and 10 are regular rookies, the last 45 are regular base. We agree that if there is no short printing going on, 50% of the base cards would be vets and 25% each rookies and Rated Rookies. With the 65 base cards, you would expect 32.5 to be veterans, 16.25 rookies, and 16.25 Rated Rookies. However we are only getting 10 rookies/Rated Rookies, not 16.25. You can then argue that rookies are short printed in a Hobby box. By how much? I would argue that instead of getting the estimated 16.25 rookies/Rated Rookies, you are only getting 10. Divide 10 by 16.25 and you get .615, or only 61.5% of what you would expect. That means they are about 38.5% (100% - 61.5%) more rare than expected. So according to Hobby box odds, we know that rookies and Rated Rookies are short printed compared to the base set. This doesn't actually go towards your question of rarity of a Mahomes "The Rookies" insert vs a Rated Rookies base card. But it does tell you the scarcity of base cards in general.

Now, we know there are 50 Rated Rookies and that in a Hobby box you can pull 10 Rated Rookies. That means you have 10:50 chance, or 1:5 (20%) chance of pulling a Mahomes in any one Hobby box. We also know that in a Hobby box you can be expected to pull 4 insert cards. How many insert sets are there? 1981 Tribute (35 cards), AKA (30 cards), Fans of the Game (4 cards), Gridiron Kings (57 cards), Illusions (30 cards), Inducted (4 cards), The Rookies (40 cards). I'm assuming the jersey cards are not considered part of the 4 inserts. All told there are 200 different insert cards you can pull across all the different insert sets. Panini doesn't list odds for any one particular set anymore so it's reasonable to think that they are all of equal odds. This means that you have a 4:200 chance of pulling a Mahomes "The Rookies", or 1:50 (2%).

If you have a 20% chance of pulling a Mahomes Rated Rookie and a 2% chance of pulling a Mahomes "The Rookies", that means there should be 10 times the amount of Rated Rookies printed vs "The Rookies", or 1/10th the amount of "The Rookies" as compared to Rated Rookies. I wouldn't make the argument that "The Rookies" is 10x more valuable than a Rated Rookies, since if one cards has 1,000,000 copies printed and another has 100,000 copies printed, is there really a shortage of either card?

I'm curious to see if there is any info about the odds of pulling a standard insert like these (not the numbered parallel) in a pack.

In a Hobby box of cards you will pull 4 inserts per box. There are 200 total non-parallel, non-autographed, non-memorabilia insert cards, meaning in any given box you will pull 4 of the 200 inserts. To pull any one SPECIFIC insert, you have odds of 1:50 boxes.

To be very specific... How much rarer is a Mahomes "the rookies" card than the Mahomes rated rookie?

The odds to pull any one SPECIFIC Rated Rookie, you have odds of 10:50 boxes, or 1:5 boxes. To pull a SPECIFIC insert, you have odds of 1:50 boxes.

[dcs6f4]

This is a fun exercise! Here are some variables to consider to help answer your question.

How big is the base set?
How many base cards come in a box of hobby?
How many base cards come in a box of retail?
How many different insert sets exist?
How big is the "The Rookies" insert set?
How big are the other insert sets?
What are the odds of pulling any one "The Rookies" card?


Let's take a look at the set. 200 cards make up the entire set, the first 100 are base cards, the next 50 are rookie cards, and the last 50 are Rated Rookies. If all base cards are equal in print run, it's 100/200 (veterans), 50/200 (rookies), and 50/200 (Rated Rookies). Expressing that as a percentage, 50% of the set are veterans, 25% are rookies, and 25% are Rated Rookies. However we can't be certain that Rated Rookies aren't short printed. We'll get into that later.

A Hobby box has the following breakdown: 4 cards per pack, 20 packs per box. That's 80 cards in a box. Panini says that on average you will pull 1 autograph card, 10 holo parallels, 10 Rated Rookies, 10 Rookies, and 4 inserts. We'll subtract out the inserts and parallels, 80-1-10-4 = 65 base cards. Of those 65, 10 are Rated Rookies and 10 are regular rookies, the last 45 are regular base. We agree that if there is no short printing going on, 50% of the base cards would be vets and 25% each rookies and Rated Rookies. With the 65 base cards, you would expect 32.5 to be veterans, 16.25 rookies, and 16.25 Rated Rookies. However we are only getting 10 rookies/Rated Rookies, not 16.25. You can then argue that rookies are short printed in a Hobby box. By how much? I would argue that instead of getting the estimated 16.25 rookies/Rated Rookies, you are only getting 10. Divide 10 by 16.25 and you get .615, or only 61.5% of what you would expect. That means they are about 38.5% (100% - 61.5%) more rare than expected. So according to Hobby box odds, we know that rookies and Rated Rookies are short printed compared to the base set. This doesn't actually go towards your question of rarity of a Mahomes "The Rookies" insert vs a Rated Rookies base card. But it does tell you the scarcity of base cards in general.

Now, we know there are 50 Rated Rookies and that in a Hobby box you can pull 10 Rated Rookies. That means you have 10:50 chance, or 1:5 (20%) chance of pulling a Mahomes in any one Hobby box. We also know that in a Hobby box you can be expected to pull 4 insert cards. How many insert sets are there? 1981 Tribute (35 cards), AKA (30 cards), Fans of the Game (4 cards), Gridiron Kings (57 cards), Illusions (30 cards), Inducted (4 cards), The Rookies (40 cards). I'm assuming the jersey cards are not considered part of the 4 inserts. All told there are 200 different insert cards you can pull across all the different insert sets. Panini doesn't list odds for any one particular set anymore so it's reasonable to think that they are all of equal odds. This means that you have a 4:200 chance of pulling a Mahomes "The Rookies", or 1:50 (2%).

If you have a 20% chance of pulling a Mahomes Rated Rookie and a 2% chance of pulling a Mahomes "The Rookies", that means there should be 10 times the amount of Rated Rookies printed vs "The Rookies", or 1/10th the amount of "The Rookies" as compared to Rated Rookies. I wouldn't make the argument that "The Rookies" is 10x more valuable than a Rated Rookies, since if one cards has 1,000,000 copies printed and another has 100,000 copies printed, is there really a shortage of either card?





In a Hobby box of cards you will pull 4 inserts per box. There are 200 total non-parallel, non-autographed, non-memorabilia insert cards, meaning in any given box you will pull 4 of the 200 inserts. To pull any one SPECIFIC insert, you have odds of 1:50 boxes.



The odds to pull any one SPECIFIC Rated Rookie, you have odds of 10:50 boxes, or 1:5 boxes. To pull a SPECIFIC insert, you have odds of 1:50 boxes.

Amazing. Thanks so much for the breakdown... I'll be able to do that on my own in the future---much appreciated