Is Buying a Player From a Case Break Worth It?

I’ve recently gotten into baseball cards, and am focused on specifically collecting 1 player’s (Kyle Manzardo: Guardians #2 prospect) Topps cards. This is a minor league player, so they only way to collect them is through Bowman cards and Topps pro debut cards. One way to collect these cards is to buy them off of eBay, but another that I’ve recently discovered is buying this player’s cards from case breaks.

When you buy this player’s card from a case break, you are playing a probability game: does the probability of this pulling player’s rare card * their price equal the price of buying buying into the case break? This article is my exploration into this topic.

Unfortunately, this isn’t exactly something that I can do broadly. Instead, I will focus specifically on Kyle Manzardo’s 2022 Pro Debut cards but use 2023 odds, since we already have values for the 2022 cards but the odds have magically disappeared (thanks Topps). However, hopefully the conclusions taken can be used for your own card of choice.

Methodology

The first place to start is the price to buy in. Based on looking at completed eBay auctions, it looks like you can easily buy into a case break for a less-popular prospect for less than $10, but more promising prospects may set you back $25. Given that Kyle Manzardo is less popular, I’ll set $10 as the break-even point.

The second decision we need to make is which case to buy into. There are two options: Hobby cases and Jumbo cases. There are multiple factors we need to consider here. Each case has a different amount of cards and different odds. Lets start with calculating the number of cards per case.

Hobby Card Count = 12 boxes per case * 24 packs per box * 8 Cards per Pack = 2304 cards
Jumbo Card Count = 8 boxes per case * 6 packs per box * 24 cards per pack = 1152 cards

Based on these calculations, we can expect to get 11.5 cards of our specific player if we buy into a hobby case break and get 5.75 cards if we buy into a jumbo case break. However, most of these cards will be base cards. We need to do some calculations to identify how many non-base cards we will get.

Probabilities

Luckily for you, I’ve done exactly that in a giant spreadsheet:

2023 Topps Pro Debut Odds (No Inserts)

The two columns that have color are the expected variants per case per player that we can expect. The first is for hobby cases and the second is for jumbo cases. For example, we can expect to get 0.72 chrome Kyle Manzardo cards if we buy into a hobby case break, and 1.36 chrome Kyle Manzardo cards if we buy into a jumbo case break.

At the bottom of these columns, you can see the sum of all variants per case per player.

For hobby cases, this comes out to 1.12, meaning we can expect to receive about 1 variant and 10 base cards if we buy into a hobby case break.

For jumbo cases, this comes out to 1.78, meaning we expect to receive about 2 variants and 4 base cards if we buy into a jumbo case break.

However, it is most likely that we will only get a chrome variant. For hobby cases, we will only get 0.4 non-chrome variant cards on average. For jumbos, we will only get 0.425 non-chrome variant cards on average (interesting how similar those numbers are).

Expected Value

In order to calculate the expected value of a case break, we will need to multiply each of these odds per case with the value of that specific card. Luckily for you, I’ve done that below (only for cards with a greater of .1% chance of getting).

As you can see in the 4th and 6th column, the expected value for Kyle Manzardo from a hobby case break from variant cards is $5.63 and from a jumbo case break is $5.25.

It is very interesting that, although you are expected to get more variants from the jumbo case break, you are expected to get a higher expected value from variants from the hobby case break. I believe this is primarily attributed to the much higher odds for autographs in hobby case breaks, which outweigh the higher odds for chrome in jumbo breaks.

Now that we have the expected value from variants, we also need the expected value from the base cards. The Kyle Manzardo cards has had some crazy fluctuation (from $0.25 to $2), so I’ll take the low end of the spectrum at $0.25 per base card.

Now, we can calculate the expected value for both of these types of breaks:

Hobby Case Break Expected Value = $5.63 + (10 * $0.25) = $8.13

Jumbo Case Break Expected Value = $5.25 + (4 * $0.25) = $6.25

Summary

Based upon the above expected values, it doesn’t appear to be worthwhile unless you can buy in at below those expected values. However, there are many factors that can change these calculations:

• Base Card Price: If the base card price is higher, it quickly becomes very worthwhile to buy into hobby case breaks as you are expected to get 10 base cards per hobby case break, compared with only 4 base cards per jumbo case break.
• Value of Auto vs Chrome: Jumbo cases will give more chrome (1.36 vs 0.72) and Hobby cases will give more autos (0.18 vs 0.08). Based on the relative value of these cards, it might be more worthwhile to buy into hobby case or jumbo case.
• Tolerance for Risk: Since hobby cases provide more base cards but fewer variant, they are the “safe” approach: buy in, get ~10 base cards, sell them, profit. Jumbo cases have fewer base cards, but have higher expected values for more valuable variants (see spreadsheets above), so they are the “risky” approach.

Regardless of which type of case you provide, it seems to me that there could be positive expected value in buying into case breaks, especially if the base card prices increase at the same rate that Kyle Manzardo 2022 base card increased ($0.25 -> $2 over a year). Given their low buy-in price (<$10), these seem like a pretty good investment, especially if you are very bullish on a particular prospect, such as I am with Manzardo.