Welcome back, speculators!

Today I want to go over a concept I'm tentatively calling the Card Desirability Index (or CDI). The basic idea is that if the player base is roughly known (going by DCI numbers) and the number of rares in existence is known, then we can determine the desirability of a given card based on the number of copies played.

Print Runs

Unfortunately, print runs are unknown. But while we can't be exact, we can extrapolate possible print runs assuming a roughly linear growth. (It's likely not linear, but a lack of data doesn't allow for a more complicated model as we do have the print run sizes from 1993-1995.)

Next we need to determine the print run of the rares. Luckily that same set of print run data tells us how many of each rare was printed. Using this data we come up with a ratio of rares to print run. After calculating this ratio we then determine the average over the first few years, called the "Rare Ratio". This will give us an idea of how many rares were printed with each print run.

Last but not least we need to factor in the fact that there were a lot more rares in the original sets (which are what we used to determine print runs). I call this the "rare factor". I took the number of rares in the set divided by the number of total cards in the set. The original printings all had a rare factor at 0.4 but newer sets it's more like 0.2. This means new sets have about half as many different rares as old sets.

Thus assuming our print run calculations are somewhat accurate there are twice as many of each rare printed. Hence why the rare factor is either 1 or 2. Many of the older core sets, Ice Age, Alliances et.al. also had factors of 0.4, but for the most part the other sets printed from 1996 and up had fewer rares per set. If this were to be broken down per set we'd just break down each set here and divide 0.4 by the rare factor.

Player Numbers

The next step is to look at the player growth. Unfortunately we have even fewer data for this.

An article written in June 2011 puts the number of registered DCI numbers at 12 million. Previous search implies that there were around 6 million in 2006. For this article we'll assume the same player growth rate from 2011 to 2013. Assuming a linear growth we can get an idea of how many players were around at each year.

Now to go backwards, we have to extrapolate and we have basically no data to verify or compare with. However, to be conservative I'm estimating a 10% growth per year (from 1993 to 2006), which puts around 656,000 players back in 1993. I think this sounds like a reasonable number.

Knowing both the number of rares printed in each print run and the number of total players we can figure out the number of rares per player that are available.

It's important to note that we are also making the assumption that the print runs are the same. Though in all likelihood the higher selling sets have higher print runs than the lower selling ones. Unfortunately, there isn't enough data to determine what the difference is so we will just stick to the assumption that they are all printed with the same print run size per year.

Putting the CDI Together

With the MTG population increasing we expect to see the Rares Per Player going up as we get closer to the present time (which it does) and this goes in line with the fact that older rares (Legacy) tend to be more valuable (and more in demand) than Standard rares. It's also important to note that the mythics per player count should be around 1/8 of the rares per player count.

Now that we have a general idea of how many rares per player were printed in each year we can determine how desirable a card is based on how many decks it's played in and how many copies are needed.

Unfortunately there's no way to really estimate how many players want to play what deck. We can't really use a metagame breakdown because the metagame often shifts constantly.

However, we can eliminate that as a factor and instead simply use the Rares Per Player or Mythics Per Player in our function. Because the CDI is an arbitrary number the critical factor is that all cards CDI's are calculated the same way.

My equation is as follows: number of decks that run the card * number of cards per deck / rares per player.

The last three results are current Standard cards to use as a baseline comparison. The calculations do appear to be a strong indicator of the price (the cards with the highest CDI's also happen to be the most valuable). The bigger concern is EDH-related cards like Gaea's Cradle, which is played in one Legacy deck (Elves) as a four-of, but appears in almost every green EDH deck that one can build. This is also only done for cards that haven't been reprinted.

The biggest factor, and one of the more difficult to properly assess, is the number of decks played. I didn't have time to go through the entire list of decks on The Source. In all likelihood the CDI numbers for some of the more obscure older cards should be higher.

However the number of rares/mythics per player is the most important as it probably plays the biggest factor. Understanding the estimated number of actual rares per the playerbase will give you a good idea of the demand for an older casual all-star and the the likelihood of it spiking.

In order to determine the CDI of something like Thoughtseize (a highly in-demand reprinted card), we'd need to take a weighted average.

Unfortunately, these calculations will not help breakout cards because they require knowledge of the number of decks played in and how many would be played per deck. However I believe this calculation can be excellent for determining undercosted rares, especially ones that are showing up in a lot of decks but have yet to jump up in value.

But we can use the CDI to speculate on older Legacy cards. To be fair, this is what many of us speculators do subconsciously. However, given how almost everyone on here has limited funds, it makes the most sense to attach a number to rank potential speculation targets in order to best allocate one's funds. Hopefully QSers will use the CDI concept in order to rank them.

I will reiterate that many assumptions were required in order to make these calculations (but often in engineering we are faced with problems that lack perfect information and require assumptions). I admit that the "linear growth" assumption for both player growth and print runs is hard to swallow at best, but I still feel that while they may not be 100% correct, the fact that they are used for all calculations should mean that any error is carried over and thus shouldn't affect the overall outcome.

I personally plan on using these equations on some future speculation targets as a way to verify their correctness.