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Casually Infinite – Understanding EV, Part 1

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My editor says that articles are best at around 1500 words. My problem is that I’m a teacher. I teach sixth through twelfth grade students. In teaching we use something called the Zone of Proximal Development (ZPD) dictates what students are and are not able to learn based on what they currently know. I want to make sure that I don’t start off talking about things that are out of another person’s ZPD because they don’t have the groundwork laid to begin in a new direction. As such, many of my articles are likely to be in series of multiples, like this one.

Basic Business

Understanding estimated value (EV) is vital to pinching pennies or tickets (‡) on Magic Online. It is the most common catch-all term for Return On Investment (ROI) in MTGO. ROI is a business term that indicates how much money is made by one investment over another. If you were to stick money into a bank account, your expected ROI would be <1% per year. If you were to instead purchase a five-year CD, you could expect around 3% per year. It may be even better to spend the money than save it—something like replacing the windows in your home with higher quality windows might save you $30 per month in heating costs. When you have something that you are looking at in business terms, you have to consider what your expected ROI is for various ways to spend it. In Magic, calculating EV is how you do this.

Let’s assume you have six boosters and 4‡ (tickets) in your account. You have a number of options for what you can do. First off, you can sell the six boosters and have more tickets. This isn’t a very exciting option, since the way you probably got the boosters was by paying tickets for them in the first place. So you decide you’re going to enter a queue. But which queue you enter can drastically alter your expected results. For the sake of this article series, I’m going to assume you are likely to have average results regardless of the queue you enter. While there is a documented difference in the quality of players in 8-4 versus Swiss Drafts, and there tend to be better players in large premier events, I’m going to work under the assumption that you are in the middle of the pack for every queue you join. The reason for this is that if you’re better, most of the same advice still stands, and if you’re worse than average, you are going to lose money regardless. In this case, you should only play Swiss queues in order to minimize your losses.

I also can’t take into account the possibility that you happen to crush triple RTR drafts but happen to be really bad at M14 sealed. I’ll note that the differences from one queue to another is small enough that if there is a format you specifically don’t enjoy playing (triple DGM anyone?), it is probably not worth the advantages of playing it over a format you enjoy. Generally, as humans, we dislike things we’re bad at and enjoy things we’re good at. But three hours of your time to play Sealed over Draft when you really just want to draft isn’t worth the .32‡ it might save you. But it is important to understand how the choices you are making affect you.

The Math

If you don’t have strong math fundamentals, this may be a difficult article series for you to understand. I’d say you need a decent grasp on algebra to work through all the numbers. Unfortunately, I don’t have time to explain these fundamentals to you. If you’re having trouble grasping the math, just skip the confusing parts and move along to the results. We’ll be calculating a lot in the next article, so bear with me. If you want to skip the math, that’s okay, but today’s article is about the math specifically.

Terms

Queue EV = (What you pay to enter an event) – (what the average person gets from an event)

How exactly people calculate EV on queues varies slightly but it stands to reason you want to play the queue with the best EV and avoid those with the worst. Your EV is heavily affected by your win percentage. If you’re winning less than 50% of your matches, then a prize structure for winning a queue matters less to you and the prize structure for winning some matches will matter more. Regardless of where you stand, high EV basically means the queue is better for you, low EV means worse. However, queue EV is frequently negative. This means the average player will walk away with fewer ticets in card- and pack-value after playing a queue than they had before playing the queue. The key here is to pick the queues where you lose as little as possible, or if available, play in queues with a positive EV. Increasing your win percentage will increase your EV significantly.

Pack Cost – The market price to buy a booster pack of a given set.

The cost of purchasing a pack of a given set from a bot. Following Rule #2 (never buy packs from the store) from my article 10 Rules for Profit, we learn that the cost per pack is not $3.99 and playing a draft doesn’t cost you 14‡. Pack cost fluctuates wildly over the course of a set’s run and is even less predictable when dealing with flashback Draft formats (drafts where out-of-print formats return on MTGO). During prereleases, prices fall as people want to jump back into another queue and are more than willing to unload their draft winnings to do so. As release events finish up, prices tend to stabilize unless there ends up being a number of expensive rares in the set. Core set pack cost drops very quickly once the queues stop and the next core set comes out. The third set of a block often has a lower pack price because it is main set given as prizes but is primarily being used in block drafts, meaning more are being won than are being opened. The first set in a block will often rise in price later in the block as people go back to needing it to play full block drafts. Overall, packs can range as low as 1.25‡ all the way up to over 4‡.

Also note that there is a buy and sell pack price. You can generally sell packs for about 5% less than you can buy them. I generally use only the buy price because I rarely sell packs that I can still use to get into another queue.

Pack EV = (The value of each card in the set) / (How likely that card is to be in a single booster)

When you open a pack of Return to Ravnica, you have a chance to pull a Sphinx’s Revelation worth 30‡ or a Volatile Rig worth .03‡. Before the pack was opened, it had a potential value that included both of these cards. Once the pack is opened, there’s no more guessing.

The pack value can be calculated by adding up the value of all the cards in the set, adjusting for rarity, and dividing by the potential you’d see in each pack. Individual high-priced cards heavily impacts pack EV, but a number of other factors play a role as well. Currently, M14 has a very high pack EV due to Mutavault being a rare instead of a set with a similarly-priced mythic like Voice of Resurgence out of Dragon’s Maze. Cards like Wasteland (an uncommon worth somewhere around 60‡) or even Ancestral Mask (a 6‡ common) will increase the Pack EV way more than a 60‡ mythic. After all, there are 80 commons opened for every mythic.

There’s a few Excel spreadsheets with this already calculated out and all you have to do is punch in the totals for the set. If you want to know the current pack value, take a look at MagicEV, which calculates it for you (down on the bottom right). Pack EV generally ranges from about .75‡ to 1.5‡ for sets in Standard.
An example that makes a clear point about how pack value works is an unopened booster of Beta costing about $2000. There’s only one card you could open out of 117 rares that would provide you with a value that would be more than your initial cost. You could open a $5000+ Black Lotus or a $6 Warp Artifact. With so many rares and only 30 or so worth over $100, your pack EV is probably in the $500 range.

Pack Spread = Pack Cost – Pack EV

The difference between the pack cost and the pack EV is the pack spread. The greater the spread, the more packs you need to win to make up for your loss in opening up packs. If the spread is small enough or negative, then you can almost make a profit just by ripping packs open and selling the contents. For almost all packs on MTGO, you’ll find the pack cost is significantly above the pack value. The price for a pack doesn’t generally drop below 2‡ while there are active queues for it. In general, a 2-3‡ pack spread is common in MTGO. This means that you have to win about two packs for each three packs you open in the tournament to come out even after you pay entry fees. As I’m writing this, the pack spread on Theros is 2.23‡, M14 is 2.09‡, Modern Masters is 3.99‡, and Mercadian Masques is 1.10‡. While the high value of cards in Modern Masters makes it inviting and it has a significantly above average pack value, the pack spread is so high due to the cost of purchasing the packs. Thus, Modern Masters is one of the least profitable packs to open. You’re actually better off playing M14 or Theros.

Prize Structure

There are a number of different rewards for playing in various tournaments and queues. Sometimes the names of the event speak about the prize structure, such as 8-4 and 4-3-2-2 events, which indicate the number of packs given to each place. The reward for taking first place is significantly affected not only by the prize structure, but also the pack cost of the packs you are winning. If you win an 8-4 Draft at a 3.8‡ pack cost, you pick-up about 30.4‡ in prizes. Meanwhile, an 8-4 with a 2.8‡ pack cost will only give you about 22.4‡ in prizes.

Some events have a prize structure that rewards the players that did well significantly more than others in the tournament. Other events seek to reward everyone who performs decently, and still others reward everyone that plays and manages a win. Larger events will reward the top eight, 16, 32, or 64 players, regardless of how many enter. This could provide either a fantastic chance to a very mediocre chance of winning prizes based on the number of players. Prize structures based on number of wins are often much better than prize structures based on place, because the number of players doesn’t change your chances of winning. In an event that rewards the top 32 players, your chances of making it with 65 players is much better than with 256. On MTGO, premier events frequently have the same prize structure regardless of number of players.

Entry Fee = (Tickets) + (Pack Spread * Number of Packs)

Various events—from Draft queues, to dailies, to premier events—have entry fees. Entry fees for most events can be paid in tickets (bad idea) or a combination of some small number of tickets and product (good idea). The posted entry fee in MTGO isn’t the real entry fee you end up paying. When calculating potential winnings, you need to understand the portion of entry fees that you’re essentially paying to get into the prize structure as well as the fees you’re paying in pack spread. You end up paying the tickets, but you still get the value from the cards in the packs you open. If I have to open six packs to play in a Sealed event, I lose my pack spread six times instead of the three times I’d lose opening a draft. This means the prizes in a Sealed event would have to be almost twice as good as in a draft to have the same EV.

Next Time

Since I’ve probably already given my editor a heart attack, I’ll stop here and pick it up in part two where we’ll discuss what to do with all these numbers. This article gave you the basics regardingthe terms I’ll be using and we’ll get into the gritty details in my next article. I’ll break down each queue as well as some historic prize structures and explain why they good or bad value so you can be on the lookout for changes in the future that provide you with good opportunities.

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Marc DeArmond

Marc DeArmond

Math Teacher at Coupeville School District
@Masticon     -     Email     -     Articles
Marc DeArmond is a currently a Middle School Math Teacher and the host of the Casually Infinite podcast. He started playing Magic back in Unlimited during 1993. His interests are trading up in value and playing limited on MTGO. He is the author of Casually Infinite, which discusses how to continue to play Magic Online without spending money. He is currently a Level 2 Magic Judge.
Marc DeArmond

About the author

Marc DeArmond

@Masticon     -     Email     -     Articles
Marc DeArmond is a currently a Middle School Math Teacher and the host of the Casually Infinite podcast. He started playing Magic back in Unlimited during 1993. His interests are trading up in value and playing limited on MTGO. He is the author of Casually Infinite, which discusses how to continue to play Magic Online without spending money. He is currently a Level 2 Magic Judge.

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  1. Jason Alt

    I am glad you split this up as opposed to trying to cut 3,000 words down to 1,500.

    Did the editor tell you “Brevity is the soul of wit” like I asked him to? Because I think that’s hilarious given that I routinely writer 3-4,000 words every week on QS.

  2. Steven Rich

    Very informative article. Look forward to the next part. One thing, Ancestral Mask – $6 card? I was about to sell all my copies.

    1. Marc DeArmond

      They were buying for 6‡ right up until Christmas. Now they’re back down to 2‡ due to flashback drafts. I’d assume they’ll climb back up if mono-black keeps decreasing in the Pauper meta.

  3. Anonymous

    Ancestral mask has fallen recently to around $2 (mtgo)

  4. Anonymous

    comment is @Steven

  5. Jeff

    Great article, starting with a solid foundation and building up from there, almost like a Math proof! I hadn’t heard of ZPD before, and it makes a lot of sense to me.

    Thanks also for mentioning MagicEV (www.magicev.com)! I intend to keep it updated as a useful resource for anyone playing in any Magic Online events – as well as adding paper Magic (SCG Opens, GPs, common FNM prize structures, etc.) in the near future!

    1. Marc DeArmond

      MagicEV has caused me to let my own spreadsheet become somewhat outdated. I don’t have to go back and recalculate Pack EV each time I want to see the changing values of cards in each set. I’m sure you’re doing all the same math that I’m talking about here. I just want people to understand where the numbers come from and why it matters.

  6. Kirsin Koch

    “In teaching we use something called the Zone of Proximal Development…” Hey! Vygotsky! I’m a huge proponent of Vygostsky in developing my information technology training classes.

  7. swegen9

    Nice to see you bringing Vygotsky to the MTG finance world.

  1. Casually Infinite – Understanding EV, Part 2 » Brainstorm Brewery

    […] my last article, I discussed all the parts that play into estimated value (EV). This article is going to have lots […]

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