In 2024, an independent audit firm investigated Topps and their baseball card pack odds. Allegedly, Topps provided “loaded” boxes to prominent case breakers to create excitement on social media when those influencers had big hits (or “pulls”) from those boxes. However, the independent auditor found Topps was packaging cards randomly, as advertised.
The audit – believed to be the first of its kind by the sports card industry – likely won’t be the last. As big hits and social media drive intense interest in baseball cards, companies like Topps and their parent company, Fanatics, will need to continue to provide open books to keep everyday collectors satisfied that they, too, have a chance at pulling a great card.
All of this begs several questions:
- How do baseball card pack odds really work?
- What does “random” really mean
- Do average collectors have a real chance?
Baseball Card Pack Odds
For baseball fans and collectors alike, the allure of ripping open a fresh pack of cards is undeniable. The anticipation of unearthing a hidden gem – a rookie autograph, a coveted parallel, or a legendary throwback – fuels the hobby. However, shrouded in a layer of mystery lies the question: what are the actual odds of pulling that coveted card?
Baseball Card Pack Probabilities
Manufacturers typically express baseball card pack odds in two main ways:
Ratio Notation: This format presents the odds as a ratio, for example, “1:100.” This signifies that, on average, one card of that specific type appears in every 100 packs.
Percentage Notation: Odds are expressed as a percentage chance of finding a specific card in a pack. Converting from ratio to percentage is straightforward: (1 / ratio) x 100%. For instance, 1:100 odds translate to a 1% chance per pack.
It’s crucial to remember that these odds represent averages across the entire production run. Each individual pack operates as an independent event, meaning the odds of pulling a specific card remain constant regardless of previous pack openings. In other words, opening nine packs without success does not increase your chance of success on the tenth pack.
Odds appear on the outside of each pack, or the back of every box. For newer releases, however, some odds are available only online, because they’re increasingly complex and specific to the type of pack or box.
One clarification: Odds aren’t stamped on the card itself – Those are serial numbers. They denote the print run instead of the odds. The rarest of these is the “1/1.” That card is the only one in existence; therefore the odds of receiving it are one in the entire print run of cards. These cards are exceedingly rare and typically valuable.
Understanding Probability Distribution
The concept of probability distribution plays a key role in comprehending baseball card pack odds. Most often, the distribution of desirable cards in a set follows a hypergeometric distribution. This complex mathematical model factors in the total number of cards in the set (population size), the number of packs produced (sample size), and the number of desirable cards (number of successes).
Example
Imagine you’re a kid picking jelly beans out of a giant jar. You know there are a certain number of, say, red jelly beans (let’s call them “hits,” like valuable cards) mixed in with all the other colors (let’s call them “misses”). Crucially, in this scenario you don’t put the jelly beans back in after each grab, whether hits or misses.
The hypergeometric distribution helps us understand how likely it is to pick a specific number of red jelly beans (hits) if you take a certain number of total jelly beans (total picks) out of the jar, without putting any back in.
Here’s the key difference from a regular probability scenario:
- Regular Probability: Imagine you have a coin with heads (hit) and tails (miss). Every time you flip the coin, it has a 50% chance of landing on heads, regardless of previous flips.
- Hypergeometric Distribution: With the jelly beans, the chance of getting a red one (hit) changes after each pick. If you already took out all the red ones, the next pick is guaranteed to be another color (miss). However, with baseball cards, you never know when all of the hits have been removed.
So, the hypergeometric distribution considers:
- Total number of jelly beans (population size): This is like the total number of cards in a set.
- Number of red ones (successes): This is like the number of valuable cards you’re looking for.
- Number of jelly beans you pick (sample size): This is like the number of packs you open.
Using these factors, it calculates the probability of getting a specific number of red jelly beans (valuable cards) in your picks (opened packs), considering that you don’t put any back in (no replacement).
In simpler terms: It helps us understand how likely it is to pull a certain number of desired cards from a set, knowing the total number of cards and the number of desired ones, while acknowledging you won’t get any back once you open a pack.
Reality Check: The Odds Aren’t Always in Your Favor
Let’s face it, the odds of pulling high-value cards are often stacked against collectors. Here’s a breakdown of some common pack odds scenarios:
Base Cards
These comprise the bulk of a set and typically boast odds of 1:1 or even higher, translating to a high chance of appearing in every pack. Consider that a retail pack of 2024 Topps has 14 cards with no guaranteed inserts. Therefore most – if not all – cards in the pack will be base cards.
Insert Cards
Inserts are limited-edition cards randomly placed in packs. They may be autographs, relics, parallels or special releases. Odds vary wildly, depending on the type of insert. For example, in 2024 Topps packs, the 1989 Topps inserts appear at 1:2 odds in hanger packs, while the same hanger pack has 1:96,027 for the 2023 All-Topps Team Autograph.
Expected Value vs. Reality: A Numbers Game
Expected value (EV) is a statistical concept frequently employed in card collecting. It represents the average return you can expect from buying and opening a pack, considering the cost of the pack and the value of the cards you might pull. Here’s the formula:
EV = (Probability of pulling a card) x (Value of the card) – Cost of the pack
However, it’s essential to remember that EV is just an average. The reality of pack openings can deviate significantly, with collectors experiencing both windfalls and duds. Chasing high-value cards solely based on EV can be a recipe for disappointment.
Randomization and Perceived Odds
The concept of randomization in baseball card packs is a fascinating interplay between probability and human psychology. While manufacturers employ sophisticated methods to ensure randomness, our brains can struggle to grasp the true nature of random chance. This can lead to misinterpretations of pack odds and ultimately, skewed perceptions.
Let’s delve deeper into how randomization works and how it can influence perceived odds:
Baseball Card Pack Randomization
Major card manufacturers utilize complex systems to guarantee random distribution of cards within packs. Here are some common methods:
Collating
Manufacturers arrange cards in large sheets based on rarity, before being cut and shuffled. This ensures a predetermined number of high-value cards are distributed across the print run. However, the exact placement within each pack remains random.
Auto-packers
These automated machines utilize random selection algorithms to pick cards from designated feeders and assemble packs. This method eliminates human bias and ensures each pack has an equal chance of containing any specific card.
Despite these measures, our brains struggle with the idea of true randomness. We tend to identify patterns where none exist, and this can influence how we perceive pack odds.
The Psychology of Opening Baseball Card Packs
Here’s how the interplay between randomness and perception can affect collectors:
Hot Hand Fallacy
This cognitive bias leads us to believe that streaks of good or bad luck will continue. After opening several packs without a valuable card, some collectors might mistakenly feel the next pack is “due” for a chase card, despite the odds remaining constant.
Clustering Illusion
Our brains naturally look for patterns. After seeing a particular insert card a few times in a short span, collectors might misinterpret this as an increased chance of pulling another one, when the randomization process treats each card independently.
Confirmation Bias
We tend to favor information that confirms our existing beliefs. Collectors who pull a valuable card early on might believe their pack-opening skills are superior, neglecting the inherent randomness of the process.
Understanding these cognitive biases can help collectors approach pack openings with a more realistic perspective.
Odds & Randomization: Tips for Collectors
Here are some tips to mitigate the influence of perception on your card collecting experience:
- Focus on the Averages: Remember that pack odds represent averages across the entire production run. Don’t let short-term streaks of bad luck discourage you.
- Set Realistic Expectations: Base your expectations on the actual odds, not hunches or wishful thinking. Understand that pulling high-value cards is a low-probability event.
- Enjoy the Process: Focus on the thrill of the hunt and the joy of building your collection, rather than solely fixating on the outcome of each pack opening.
By acknowledging the limitations of randomness and our own cognitive biases, we can approach card collecting with a healthier perspective, transforming pack openings into exciting forays into the world of baseball cards, not exercises in frustration.
A Strategic Approach: Beyond Just the Odds
What is an average collector to do if they want big hits? Opening packs is a key part of being a collector, and that’s a great option for having fun, getting a variety of cards and enjoying the thrill of the chase and the excitement of finding a big hit.
However, the odds are against the average collector who wants to pull a specific card of a specific player from a pack or box. If you love opening packs, of course – do it! This is the most basic joy in card collecting. You may be disappointed if you buy packs with the intent of pulling one specific, rare card of your favorite player. You’ll have more luck selling what you pull from the case and buying or trading for that card on the secondary market.
Certain packs also favor certain types of product. Popular sets like 2024 Topps have over a dozen types of packs and boxes, all with different odds and guarantees. Know what you’re getting before you purchase it; for example, if you want a guaranteed autograph, look for 2024 Topps Hobby or Hobby Jumbo boxes. By doing your homework, you can ensure that you’ll get the type of hits you want.
Conclusion
While understanding pack odds empowers collectors with knowledge, it’s crucial to maintain a realistic perspective. Chasing elusive cards solely based on statistics can lead to frustration and financial pitfalls. The true joy of card collecting lies in the thrill of the hunt, the satisfaction of building a collection, and the connection to the sport’s history and personalities.
