Grand Cards: The Value of Cards (Part IV)

Monday, January 26, 2009

The Value of Cards (Part IV)

I'm sorry for the slow posting around here, this little piece has been tormenting me for a few days. If you make it through this and follow me the whole way though, you will be rewarded! Also, today was a tremendous mail day for me, so there will be all sorts of pretty pictures in the days ahead.

For a refresher, Parts I, II and III

Having wrapped up the “true” value of cards from a market perspective last time, I thought that it would be interesting to view the other side of the coin. I hypothesized that manufacturers actually have an implicit Suggested Retail Price (SRP) for cards in a pack that can be derived through a study of pack prices and printed odds. The odds come courtesy of 25 Years of Baseball and we will perform this whole analysis using Topps Series 1. For 2008 Series 1, Topps produced 5,445,000 packs of cards. Based on what? The odds of a platinum parallel are 1:16,500 packs on average. There is one platinum parallel per player, 330 cards in the set. That is 5,445,000 packs to reach the 1:16,500 average. Let’s break it down further:

Gold Cards = 662,640 (pack odds say 605,000, but 330x2008 says otherwise)
Black Cards=18,810 (pack odds say 57,315, but 57*330…)
All Star Rookie 50th: 1,089,000 (55 Subjects-19,800 per player)
Own The Game: 907,500 (25 Subjects – 36,300 per player)
Year In Review: 907,500 (60 subjects – 15,125 per player)
Campaign 2008: 605,000 (12 subjets - 50,416 per person)
Mantle HR History: 605,000 (34 cards – 17,794 per card)
Trading Card History: 453,750 (25 subjects – 18,150 per card)
Mantle Story: 302,500 (10 cards – 30,250 per card)
Commemorative Patch Relics: 13,216 (35 subjects- 377 per card)
World Champion Auto Relics: 500 – 50 per player (odds say 377)
World Champion Relics: 1,136 (15 subjects – 75 per player)
Highlights Auto—Group A: 170 (5 subjects – 34 each)
Highlights Auto—Group B: 718 (15 subjects – 48 each)
Highlights Auto –Group C: 5,683 (15 subjects – 378 each)
Highlights Auto –Group E: 5065 (5 subjects—1013 each)
Highlights Auto—Group F: 6083 (8 subjects – 760 each)
Highlights Auto—Group G: 1773 (1 subject – 1773 each)
Highlights Relic –Group A: 1513 (3 subjects –504 each)
Highlights Relic –Group B: 256 (1 subject—256 each)
Highlights Relic –Group C: 3156 (3 subjects – 1052 each)
Highlights Relic –Group D: 2770 (14 subjects –197 each)
Presidential Stamp Collection: 2792 (30 subjects – 93 each)

Add all of those cards up and you get 5,596,531 cards. Let’s round that up to 5,597,000 to account for some of the other 1/1 cards, printing plates etc. Assuming 10 cards per pack, that leaves us with 48,853,000 Base cards or, approximately 148,000 per player in the set.

Does this check out? By this math, a Gold card would be 73 times more rare than it’s corresponding base card. Well, considering you get 1 base card in every 9 packs (or 1/90 cards is Gold) then I would say that we’re at least in the ballpark! This is useful because it allows us to create a cohesive set of relative prices for base cards and inserts. For all non-relic and non-autographed cards, the only thing that makes one card more valuable than another card is scarcity. With that, we can create this conversion table:

Base Card=1/7 ASR50=1/4 OTG=1/9 YIR=1/3 Campaign=1/8 MMHR=1/8 TCH=1/5 MMS=1/73 Gold=1/2596 Black

These are the cards that have no intrinsic value—e.g. there is no jersey or autograph that actually affects the cost/value of the card. Let’s say our baseline pack (retail pack) features 12 base cards for $1.99. That, in essence, creates an SRP of a base card of $.166. Now, with our conversion chart, we can extrapolate that to SRPs of other cards!

Campaign= $.49
Gold= $12.16
Black= $430.9

Clearly, our equation starts to fail at the extremes. However, it actually does a surprisingly decent job of estimating the market prices of base and insert cards. I would say that many of us, especially those that need it for a specific collection, would be willing to pay the “SRP” prices for these cards. So, for “regular” cards, the manufacturer’s “SRP” and the market price seem to match pretty well.

Can that same logic convert to “the hits?” Autograph and Relic cards create an actual cost for the manufacturer, and you would expect that cost to be reflected through higher “SRP” prices and higher market prices. Let’s use our ol’ friend Albert, who started this whole ruckus a few weeks ago. Based on what The Sportscard File has told us, you would expect the SRP for a Pujols autograph to be at least $250—the $200 cost plus a 25% profit margin (this ignores production costs). Let’s see if our data can help here.

Pujols happens to have a Group A autograph in Series 1, and we find, via pack odds that there are 34 Pujols Autographed cards in this set. We have already established that our simple relationship fails in extremes, and that holds true here. The Pujols card would have an SRP of $4,376.47—clearly an absurd figure. So what else can we do?

Let’s go back to the basics. There are three types of packs that exist: Retail, Hobby and HTA Jumbo. Let’s assume that the only difference between these is the number of cards in a pack and the relative likelihood of receiving a Relic or Autographed card. The SRP of a Hobby Box is $70 and features 36 packs with 10 cards per pack. SRP of a Retail Box is also $70 but has 12 cards per pack. The SRP of an HTA box is $100 and has 10 packs with 46 cards each. Just dividing SRP by number of cards we get:

Retail: 16 cents per card
Hobby: 19 cents per card
HTA: 22 cents per card

A retail box has 72 more cards than a Hobby Box—or the equivalent of 6 packs ($12) worth. To make up for that difference, the Box provides $12 of additional value, on average, through a relic OR an auto. To get the 460 cards that come in an HTA box via Retail would cost only $73.60, a difference of $26.40. Accordingly, the HTA provides the additional value of a relic AND an auto.

What does this mean? The guaranteed Relic or Auto in a Hobby Box has an average value of $12. The guaranteed Relic AND Auto in an HTA box has an average value of $26.40. Using these numbers, and the group odds, we can at least figure out the value of a card from a particular group.

Lets assume that the values of cards within a Group are constant and that relative values are proportional to the card’s scarcity. I realize that this may be a stretch, but it’s all we’ve got for now. In this case, a Group A autograph is the scarcest, and most valuable. With 34 cards per subject it is worth 1.41 times more than a Group B card, of which there are 48 cards per subject. Using that logic, we can make another relative value equation for Autos:


I do not know why there is no Group D breakout in the odds that I found online, so we’ll have to deal with what we’ve got.
Similarly, for Relics, where Group D is the scarcest at 197 cards per subject:

There are 19,492 autograph cards and 20,911 relic cards (using only Highlights Autos/Relics and Commorative Patch relics for simplification). In other words, there is one relic card for every 1.07 autograph cards. Earlier, we calculated that there are 5,445,000 packs. In a Hobby Box 1/36 packs has either a relic or an auto. That means that 151,250 packs have either a relic or an auto.

r=1.07a OR a=.935r

Knowing how many relics and autos there are tell us that there is a 51.68% chance that the “hit” is a relic and a 48.32% chance that it is an auto. Almost there…

The Expected “Value” of our Auto is .4832*12= or $5.80 Let’s use the median instead of the mean to determine that the median card falls in Group F. If F=$5.80 and A=22.35F, then A=$129.63

Clearly, this is well below the $200 that Albert charges for an Autograph. There could be two reasons. The first, is that I don’t know what I’m doing mathematically and that I even ended up with the proper number of figures is a miracle in and of itself. That is the most likely probability. The other reason is that Topps is using Pujols to sell the product (he is on the box after all) and is willing to take a loss on the box to entice people to buy. This is what The Sportscard File has called a “loss leader.” It is a card that entices people to buy the product, but actually costs the manufacturer more money to produce than they expect to get back off that card.

You see, markets rarely lie. They tend to incorporate all of the available information to determine prices. Would you be surprised to see a 2008 Topps Pujols Autograph sell on eBay for $129.63? How about a Pujols Autograph #/34 for that amount? That sounds pretty darn accurate to me.

My point is, Topps has implicitly set an SRP of around $130 for this card, even though it costs them more to produce it. They make up for it by also inserting cards that have low SRPs (Group C is SRP’d at $4.35—sounds about right for the Lance Broadway auto I pulled from my box), and making the difference back as profit. Interestingly, the relic in the box has an Expected Value of $6.20. This may be due to the fact that the relic cards are almost all stars or semi-stars, whereas the autos can be quite obscure.

I’m not mathematically proficient enough to continue this to figure out how things change by guaranteeing both in the HTA box. I know that r+a=$26, but I kind of fall apart there. Feel free to take this and run with it.
Again, I could be wrong on all of this and I would love it if somebody could correct me or help on any of it, but it makes sense to me intuitively. Next time, IN MY FINAL INSTALLMENT, I’ll talk about how we can use this information for good instead of evil and finally explain how we, as bloggers, can save the world.

Thanks for making it through.

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