The Expected Value of Kaladesh

As I'm sure you probably know by now, for every new set, I like to publish an expected value article breaking down just how much value you can expect to open from a booster box. In the past, I've published these articles as soon as the entire set was spoiled, but with the addition of the Masterpiece Series to every set moving forward, it seems better to wait until closer to release day, because it's possible that sets will be overvalued during presales, thanks to the additional value of the very expensive (and very rare) Masterpiece Series cards. 

In fact, the addition of the Masterpiece Series to all Standard legal sets nearly scared me away from doing an expected value article at all for Kaladesh. The issue is that expected value works with averages, which means that the possibility of opening a Masterpiece Mana Crypt or Mana Vault will be evenly distributed thoughout all boxes, even though only about one in four boxes will actually contain a Masterpiece. While this is fine for a vendor opening cases, variance will be a major concern for the average player who cracks a single box. 

To solve this problem, I've decided to publish two different expected values. First, we'll look at the expected value as if the possibility of opening an Invention did not exist. If you, like me, are just planning to crack a box or two, this number will be the most important, because most boxes will not contain a Masterpiece. As a result, instead of includeing the value of Masterpieces, we'll just treat Masterpieces as a free lotto ticket that comes with buying a box. Second, we'll add in the Invention values and have a second expected value, which will apply more to people who plan on opening case after case to even out the variance. 

All in all, the question we are looking to answer is: Iis it worth it to crack a box based purely on the numbers? Basically, if I pay $100 for a box of Kaladesh, should I expect to get my money back, lose money, or come out a little bit ahead? Here, it's important to note that, over the long haul, it's never, ever worth it to crack a box. Even if the expected value is positive on release day, it won't be in a few weeks, because the supply of the cards from the set will increase, driving down prices. As a result, don't expect these numbers to be good a month from now because they will be wrong, and likely very wrong. 

One more thing before getting into the meat of the article: it's important to remember that there are many reasons why people buy a box. Some people buy boxes because cracking packs is fun. Others buy boxes to play limited with their friends. For some people, buying a box is a tradition or they enjoy the lottery aspect of the potential to open a foil full-art Mana Crypt. All of these (and I'm sure there are many more) are fine reasons to purchase a booster box, even a low-EV booster box. When it comes right down to it, Magic is a game—there is value in having fun, and EV calculation can't account for this non-monetary value. So, don't let this EV calculation be the only factor in your decision of whether to buy a box. 

What Is Expected Value?

While many of you are probably familiar with the concept of expected value, here's a brief refresher. Expected value tells us just how much value we can expect to open in a booster box. To calculate EV, we first determine the odds of opening a specific card (this is the "multiplier" you'll see throughout the article). Next, we calculate the value of each card. Then, we multiply the odds of opening a card by the card's value, which tells us how much value we expect that card to add to the box. Finally, after we do this for all of the cards in the set, we can simply add up the total and determine how much a box is actually worth.

TCGplayer Market Pricing

Most EV calculations use sell prices—things like TCGplayer mid or the prices that vendors like StarCityGames or ChannelFireball ask for a card. But unfortunately, these numbers do not mean much to me for a couple of reasons: First, I (and most of you) can't get StarCityGames or TCGplayer mid prices when we sell our cards (wouldn't that be nice?). Instead, we get things like eBay minus fees and shipping or buylist prices. As such, in calculating the value of the cards in the set, I'm trying to use the number that I realistically think I can get for the card tomorrow (this is important because new sets tend to decrease in value quickly). For this, I used the TCGplayer Market price (minus 15% for fees), which is essentially the "completed listing" of the TCGplayer market, showing the average price of cards that have actually sold and not the price that sellers are asking. This is why the prices listed in the charts in this article are lower than the MTGGoldfish price: I'm making deductions that take into account the "hidden" costs of selling the cards.

Timing is everything when it comes to making a profit by opening boxes, as prices drop quickly once a new set starts being opened. A set can go from positive EV to negative EV in less than a week, sometimes even overnight. Basically, by opening boxes on release day (or release weekend), we can take advantage of the excitement for the new cards (new demand) and the fact that the freshly opened cards haven't had time to reach the market yet (lack of supply).

Methodology Notes

1. Commons (except in very rare cases) are considered to be bulk, which I value at $5.00 per thousand. This means that an entire booster box worth of commons adds $1.80 to the expected value of the box.
2. Most uncommons are also worthless for the purpose of calculating EV, since they cannot be reliably sold as singles. Apart from a handful of "chase" and "semi-chase" uncommons, everything else at this rarity goes into the bulk pile along with the commons.
3. Foils get their own section, but it's important to remember that there is a ton of variance in opening valuable foils. The odds of opening a foil Chandra, Torch of Defiance is somewhere around 1 in 3,200 packs; however, every box should contain some number of foils (typically a handful of commons, a couple of uncommons, and one rare) and these lower-rarity foils do represent some amount of guaranteed value. 
4. As I mentioned before, we are calculating two expected values this time around: the expected value of boxes without taking Inventions into consideration and the expected value with Inventions. Hopefully, this will help account for the increased variance brought about by the new ultra-rares. 
5. These prices won't be good for long. Remember: the idea is to determine if Kaladesh is worth opening on release weekend. If you buy a box six weeks from now, don't blame me when these prices are wrong because I can tell you right now they will be wrong, and likely very wrong. Remember that the EV is a snapshot based on current prices, and not a prediction of where prices will be in the future.
6. Another reminder: you don't actually make a profit until you sell the card. So, just cracking boxes on release weekend isn't enough; you need take the next step and actually trade away the cards, list them on eBay / TCGplayer, or sell them to a buylist.
7. Finally, be aware of variance. These numbers will be accurate if you open enough packs. But, like most aspects of Magic, variance can have a huge impact in small samples. In theory, a booster box could contain zero mythics and all bulk rares, or it could contain a complete set of foil mythics. The more packs you crack, the more accurate the EV will becomebecause you smooth out these outliers. 

Kaladesh: Mythics

$ 0.00 $ 0.00 $ 0.00 $ 0.00 $ 0.00 $ 0.00

Before calculating the expected value, my assumption was that the mythics from Kaladesh would be average to below average in value; this is what we saw in Battle for Zendikar, the first set containing Masterpiece Series cards, with the average mythic value coming in at only $6.81. Thankfully, I was wrong. In fact, the average mythic value in Kaladesh is the highest of any set in the past year at $8.35, meaning the mythic slot adds a massive $37.85 to a box of Kaladesh. 

Why is the average Kaladesh mythic so valuable? Two reasons. Most importantly, it has a true chase mythic in Chandra, Torch of Defiance. While we've seen cards like Jace, Vryn's Prodigy, Gideon, Ally of Zendikar, and Liliana, the Last Hope spike to a similar value, in most cases, this didn't happen until after the set was released, often leading up to (or as a result of) the Pro Tour. The other reason Kaladesh is significantly above average in mythic value is that there are essentially no bulk mythics. The lowest-value mythic in the set is Metallurgic Summonings at $1.28, but otherwise, the cheapest mythic is $2.28 and 13 of the 15 mythics are worth over $3. 

Kaladesh: Rares

$ 0.00 $ 0.00 $ 0.00 $ 0.00 $ 0.00 $ 0.00

The rares from Kaladesh are an entirely different story, with the average value of $1.09 being extremely lacking, especially for a set with a Modern-playable rare land cycle. For comparison, when we did our Eldritch Moon expected value calculation, the average value of a rare was $1.52, 30% higher than that of Kaladesh. Here, the big problem is the bulk rare rate. A full 66% of the rares from Kaladesh fall into the bulk or semi-bulk groups—the highest rate I've seeing since I started calculating expected values. 

So far, one thing is becoming abundantly true about Kaladesh: it's the highest-variance set of all time. The Masterpiece Series naturally creates a ton of variance, but that's to be expected. What might not be as obvious is how the addition of Inventions drives up the variance of the rest of the set as a whole by driving down the prices of rares. In Kaladesh, there are a total of six rares that are worth at least the price of a pack, 11 of the 15 mythics will break even, and of course all of the Inventions equal a big win. Let's say you open four boxes—enough where you should get an Invention based on the stated odds. In those 144 packs, you should get 1 Invention, 4 foil rares, 18 mythics (14 of which will be worth the price of the pack), and 126 rares (14 of which will be worth the price of a pack). All things told, only 33 of the 144 packs will end up breaking even or being profitable, which means that a massive 77% of Kaladesh packs will be losers. 

Kaladesh—Uncommons / Commons / Bulk

$ 0.00 $ 0.00 $ 0.00 $ 0.00 $ 0.00 $ 0.00

As far as the lower rarities, Kaladesh has one chase uncommon in Aether Hub and then a bunch of slightly above bulk uncommons. All told, the lower-rarity cards add $7.05 to the value of a box, which is slightly above average but not to the point where it will have any meaningful impact on whether or not it's worth picking up a box. 

Foils

The value of the foils from Kaladesh is fairly typical, adding a total of $7.55 in value to a box. Much like the non-foil printings, the mythics come in slightly above the norm while the rares come in slightly below the curve. If you happen to crack a box, make sure to keep an eye out for cards like Ceremonious Rejection ($9.99 at StarCityGames) and Panharmonicon ($14.99 at StarCityGames), which are more expensive than you'd think due to eternal and Commander potential. 

Putting It All Together

So, there you have it. If we pretend that Inventions don't exist, the expected value of a box of Kaladesh comes in at a lacking $85.50, meaning that three out of four boxes will end up with a loss of about $15, depending on exactly how much you pay for the box. The good news is that apart from Chandra, Torch of Defiance (which adds nearly $11 to the box EV all by itself), the value should be fairly consistent, so a large percentage of boxes should end up yielding somewhere between $75 and $95 in value—not great numbers but also not a huge loss. 

As I mentioned in the intro, if you are a player who is just planning on buying a single box, I'd use this number as a baseline and expect to get back around $85. This way, you shouldn't end up disappointed if you miss out on an Invention, and if you happen to be one of the lucky few to get a Masterpiece, it will be an awesome bonus! On the other hand, if you are planning on opening a lot of boxes, you'll probably want to include the Inventions in your expected value calculation, so let's take a minute to talk about the most exciting and expensive cards in the set. 

The Inventions

$ 0.00 $ 0.00 $ 0.00 $ 0.00 $ 0.00 $ 0.00

While it might seem excessive to write out all of the Inventions individually—and in the future, I'll probably cover this section differently—I wanted to make sure that the point of just how rare these cards are came across. So, what are the odds of opening a Invention Mana Crypt? One in every 120 boxes or one in every 4,320 packs. As a result, even though Invention Mana Crypt is an extremely expensive card, it doesn't actually shift the math on the expected value all that much. In fact, one good uncommon like Aether Hub actually adds just as much value to a box of Kaladesh as Mana Crypt. The difference is that you are unlucky if you don't open at least one Aether Hub, while your odds are heavily stacked against opening a Mana Crypt. 

That said, the possibility of opening an Invention does up the expected value of a Kaladesh box by about $20, meaning that the EV rises to about $105 per box with Inventions included. Unfortunately, even including Inventions doesn't really make Kaladesh boxes profitable for most people, instead just bringing them up to the break-even point, which is a little bit disappointing. 

All things considered, three out of every four boxes of Kaladesh will be losers, with the typical loss being about $15, assuming you pay $100 for the box. On the other hand, this means that one in four boxes will be winners, which means the odds aren't horrible; however, even opening an Invention isn't always a huge win. About one-third of the Inventions will let you double up, while the other two-thirds will leave you with a profit of somewhere between $15 and $45. As such, here's the bottom line: 

Say 12 people at your local gaming store buy boxes and crack them open. The above chart shows what is likely to happen. One player will end up the big winner and essentially double their money on the box by opening one of the top 10 Inventions. Two players will end up small winners (with a $15 to $45 profit) by opening one of the bottom 20 Inventions, and nine players will end up getting less than their money's worth from the box. Essentially, the nine losers pay to support the three winners. Compare this to a non-Masterpiece set like Eldritch Moon:

Things were much more even under the old system. Out of the 12 box openers, four would end up making a small profit of maybe $20 by opening good mythics, four would break even and get their money back, and four would end up slight losers, maybe opening $80 from their $100 box. 

So, which system is better? I'm really not sure; it probably comes down to your tolerance for risk. If you like playing scratch-off tickets, you'd probably have much more fun opening a Kaladesh box than an Eldritch Moon box. Sure, you'll probably lose money, but at least you have a chance to win big. On the other hand, if you're more a fan of the long, slow value grind, opening Kaladesh will be problematic, since the new system more than doubles up the number of losing boxes. All in all, the expected value of the box is about the same—$105 is completely normal—but the way the value is distributed is much, much different. 

Conclusion

Anyway, that's all for today. Personally, I still plan on cracking a box because Kaladesh look sweet and opening booster packs is fun, but I'll be cracking it with the expectation that I'll be losing $15 in the process. If I happen to get lucky and open an Invention, that's great, but I won't be holding my breath. What do you think? Do you like the new lottery system created by Inventions, or did you prefer the old days when you didn't have the potential to win very much cracking a box but it was much harder to lose? Are you planning on opening a box? Let me know in the comments, and as always, leave your thoughts, ideas, opinions, and suggestions, and you can reach me on Twitter @SaffronOlive or at SaffronOlive@MTGGoldfish.com.