Grand Cards: The Value of Cards (Part V)

Tuesday, February 3, 2009

The Value of Cards (Part V)

There were a lot of things that I wanted to have done before today. The 2008 Ultimate Checklists were supposed to be done, complete with a “best of 2008” summary post. Value of Cards Part V was supposed to be posted and subsequently ignored by the majority of readers. Instead 2009 Topps and Upper Deck are “live”, to use the parlance of our times, and I am woefully behind schedule.

Perhaps it’s a blessing in disguise. In this, the final episode of “the Value of Cards” series, I wanted to explore how we can make smart buying decisions in these tough economic times. Hopefully, I can piggyback on the enthusiasm surrounding the first releases of the year to gather some information that will assist in that exploration. In a welcome break from previous posts, I’ll try to keep this one short and sweet—especially since I’m about 90% sure that I made SIGNIFICANT mathematical errors in the previous post that may invalidate all of the results, although the conclusions still make sense on a conceptual level.

There is no hard an fast formula that a collector can use to make solid buying decisions, in part because every collector is different, in part because the “value” of cards is market driven and in part because there is an intangible benefit that some people get from winning auctions, opening packs, busting boxes etc. When taking those out of play though, the same questions tends to hit all collectors.

What product do I buy? How much do I buy? Where do I buy it? Let’s take a regular Topps release as an example.
Using information from Part IV we can create composite “insert odds”-- in other words, the odds of pulling any of the inserts in a given pack. .200+.167+.167+.111+.111+.083+.055=.894=89.4% chance of pulling an insert in our baseline pack. We already know that the odds of pulling a Gold card are 1:9 packs. Let’s assume that a base card is worth $.10, a given insert is worth $1 and a Gold card is worth $2. That gives us expected values:

E(Baseline) =12(.1)+.894(1)+.111(2)= $2.316 (Hobby/HTA Baseline is $2.116 because of two fewer base cards).

Based on this information/assumption alone, we can determine that buyers are getting roughly 30 cents more value out of a pack than what they are paying for it. That is great news. Now, let’s add in the “pack hits” that really make the difference between Retail, Hobby and HTA.

E(Retail)=Baseline+Odds of Relic(Relic Value)+Odds of Auto(Auto Value)
E(Hobby)=Baseline+1/36(Relic Value OR Auto Value)
E(HTA)=Baseline+1/10(Relic Value)+1/10(Auto Value)*
*I’m assuming that the guaranteed auto and relic WILL NOT come in the same pack.

Because the odds of getting a specific auto or relic card do not change across Retail/Hobby/HTA, we’re going to leave that aside. Instead, let’s arbitrarily assign values for Relics and Autographs. I suggest:

Also, I will only be using odds for the “Highlights” Relics and Autos, and the “Commemorative Patch” relics, as it is tedious and unnecessary to calculate the extremely remote odds “big hits” for this product.
E(Retail)=$2.316+.00052(5)+.00049(10)=$2.324 ($.193/card)
E(Hobby)*=$2.116+.0277(1.06)(5)+.0277(10)=$2.54 ($.254/card)
E(HTA)=2.116(5)+.1(5)+.1(10)=$12.08/5=$2.42 ($.262/card)
*The 1.06 in the “Relic” portion of the equation relays the relative odds of a box holding a relic instead of an auto.


So what does this all tell us? As the value of relics and autos rises, so does the Expected Value of Hobby/HTA packs. If the value of Relics rise relative to the value of Autos, Hobby pack value increases relative to HTA packs. The opposite holds true if the value of Autos rise relative to Relics.

What does this all mean for collectors? Remember, that based on the SRP of packs, buyers pay $.16 per card for Retail, $.19 for Hobby and $.22 for HTA. With our expected values above that, we learn that buyers are getting $.03 more value per card from Retail, $.065 more value per card from Hobby and $.042 more value per card from HTA.

Woah! The Hobby pack is actually the best bet for collectors that are entirely value driven, provided that the average Auto is only worth twice the average relic. If the autographs were more prestigious, that would change the valuation in Jumbo’s favor.
Certianly, there are benefits to purchasing each type of pack: Retail is the lowest cost per pack, HTA has the best chance of pulling an Auto or Relic, but Hobby is actually the best bang for your buck, provided you can get a Hobby pack for the same price as a retail pack (which SRP indicates you can).

Certainly, circumstances will vary based on individual collectors preferences—an HTA gives the best chance for a complete set due to fewer collation variations, retail offers special inserts that may appeal to a team/player collector etc. Depending on how you collect, there are smart decisions and less-smart decisions. In my personal experience, for example, I found that I get what I need (Tigers set) whether I buy Retail, HTA or Hobby. However, both HTA and Hobby fill my sets but leave me with TONS of cards I don’t care about. I can only peddle the relic/auto sometimes and I spend way more than I will in retail. However, retail does not complete my set and I need to devote time and energy to making trades, and shipping cards. That is the tradeoff.

So before you order that Jumbo box or head to Target for that blaster, think about what you really need for your collection. As appealing as a guaranteed Auto or Relic is, what are the odds that you’ll pull a card you need, or a card you can flip as opposed to a Nyjer Morgan Auto? Assess your needs and spend wisely so that you can build your collection more cheaply and efficiently.

I know that this post may seem somewhat anticlimactic, given the buildup, and for that I apologize. I was basically testing theories on the fly, and rolling with the punches. Still, I still whole-heartedly believe that we, as bloggers, can save the world. Well, the collecting world at least.


When you buy a pack or box of ANYTHING, post all of the information that comes with it. Price, odds, players in Group A, B etc. After you post it (or if you can’t post it) send it to me in an email. Don’t want to email it? Send me the wrapper.
This industry has suffered from a major lack of transparency, and too few people pay attention to the printed odds on packs. This information is there for a reason, and can actually be used to help collectors of all types decide whether to buy cards individually, by the pack or by the box. As I get more and more data from the collecting world, I will tweak my equations and hone my math skills to be able to create meaningful valuations of what products are worth your hard earned dollar.

I expect that this will be most valuable for mid- and high-end packs, where there are fewer cards per pack and a higher ratio of hits. With this information, we can decide how many packs to open, boxes to break or cards to purchase individually online. This will, of course, be a work in progress, but if you do your part (send me the info) I’ll do mine (make sense of it). So let’s get moving and start sending me those odds!