Data Mining to Evaluate the Magic the Gathering Arena Economy

With the release of the NDA for Magic: the Gathering: Arena, there has been a lot of discussion on the viability of the economy. Wizards (of the Coast) has decided to implement their own economy for the platform.

The latest update has led to outcry on the Magic: Arena Reddit page and the Arena Forums. I felt for my first article for Cardsphere.com that I could analyze and compare this new economy with one that is very well documented: Hearthstone.

To begin with, I can already imagine the rage from you, dear reader. “Why Hearthstone? What about [INSERT ONLINE TCG HERE]?! It is soooo much better!” Allow me to expand on why I chose this particular comparison point.

The goal of this article is to compare these online TCGs for new and Free-to-Play (FTP) players. Anyone can do well investing large sums of money into a product. One of the major complaints about Arena has been on the economy being too slow for casual players. There is a lot of well-written documentation on the best and worst online TCGs for the FTP community. Unsurprising to some players, Hearthstone, while being the most innovative, is the worst for new or FTP players. As such, if Magic Arena mathematically is below Hearthstone, then it becomes evident that the current setup for the economy is flawed. Luckily, since the program is still in Beta, there still is plenty of room for improvement. We proceed to analyze the daily rewards and extrapolate them to analyze how long it takes a FTP or casual player to build a top-tier deck.

Hearthstone Baseline

We begin our analysis with a brief overview on Hearthstone rewards. Disregarding special events, a normal week of Hearthstone rewards consists of the following:

• 7 Daily quests, each providing between 40 and 130 gold (the currency for purchasing packs)
• 1 Free Pack for winning a Brawl
• 10 gold for every 3 wins

For the sake of this argument, let’s have a player, Harry, play enough to complete the daily quest and play until they get their third win every day. Supposing Harry only swaps gold for packs (for 100 gold each), we will now analyze how long Harry has to play to build a top-tier Standard deck.

For the remainder of the article, all the mathematics have been demonstrated in a spreadsheet. You can view/download it here so you can tweak the numbers as you see fit.

Using the above numbers, Harry nets between 350 and 770 gold per week. Combined with the Brawl pack, this means Harry gets 4.5 to 7.7 packs per week.

We now seek to convert this income as a rate for the creation of a top tier standard deck. Hearthstone has a crafting system in which any (non-locked) cards may be disenchanted for dust. This can then be used to craft new cards. Disregarding premier (golden) cards, the exchange rate is shown below.

Hearthstone Pack Statistics have been extensively analyzed. Using this data, it is assumed that the average value of a pack in terms of dust is 102.71 dust per pack. (As an aside: there exists a “Pity Timer” in which you are guaranteed to open an Epic every 10 packs and a Legendary every 40 packs. This is taken into account for the above number). This means, for our hypothetical player, they earn somewhere between 462 and 894 dust per week. For the sake of simplicity, the remainder of the article will use an average value: 695 dust per week. This takes into account the distribution of the quest gold values.

Hearthstone decks consist of 30 cards, of which there is a 2-card maximum for non-legendary cards. Legendary cards are only allowed to be singletons. Deck values (in terms of dust) can vary widely based on the number of legendary and Epic cards. For comparison purposes, three different top tier decks at the time of writing are used; a cheap deck with a single legendary, a medium-cost deck with a few, and an expensive deck with several legendary and epic cards.

Thus, using the above income rate, we see that our hypothetical casual player will complete these decks (assuming 0 cards were opened, only crafted) for the following timeline.

Given that new sets are released approximately every four months, we see why Hearthstone can be difficult for the FTP player. There exists an extensive grind, often with subpar cards just to complete a deck. For any deck with numerous expensive cards the possibility to build it is not feasible in a reasonable timeline without purchasing product. We now seek to compare this to Magic: the Gathering: Arena.

Magic: the Gathering Arena

With the current implementation of Magic Arena in the Beta, a normal week consists of the following rewards:

• 7 Daily Quests, each providing between 225 and 500 gold each
• Daily Victory Gold: 200 gold for the first win, 50 gold per win for the next 3 wins each day
• Weekly Packs: Up to 3 packs per week
• Up to 30 commons per day, with a chance at uncommons/rares
• Progress on opening the Vault

The key difference that makes this difficult to track is the fact that there does not exist a global crafting system. Rather, there exist Wild Cards at each rarity that may be exchanged with any card of that same rarity. I will proceed to break down each of these rewards in terms of deck progression. Note: these values are all subject to change. This is the goal of the Beta, to offer feedback and adjust appropriately.

Again, we combine the Daily Quests and Daily Victory gold in order to estimate the number of packs per week. We assume now we have a different player: Allison; a casual player that will complete all daily quests that provide gold. Since there does not exist a crafting system, Allison can only complete a deck by purchasing packs. Following the same process (glory be to spreadsheets!), we can calculate that Allison will net about 7.34 packs per week.

Without a dusting system, it is difficult to evaluate how useful the random cards given for victories will be. In a massive simplification, I will assume that these daily rewards will allow a casual player to complete their collection of commons. While there exist fringe cases in which a chase rare will be obtained, with most cards designed for limited the odds of a strong card for constructed is small.

Preliminary data on the Vault is that it takes approximately 15 packs opened in order to get the bonus. Opening the Vault nets a player 1 Rare Wild Card, 2 Uncommon Wild Cards, a random Mythic, a random Rare and a random Uncommon. Assessing the value of random cards is going be beyond the scope of this article. (That’s engineer-speak for “I don’t want to deal with this right now.” This could be mapped as a Poisson process with probabilities of usefulness to a deck, but there’s already too much math here). In the future there will be an update to the Vault including Mythic Wild Cards, until the rate is known I cannot assess how impactful it will be.

So, in order for Allison to construct a top-tier Standard deck, they need to either open the cards they desire or save up Wild Cards. The rarity of these Wild Cards is CRITICAL to maintaining the Magic Arena economy.

Luckily, the forums from Magic Arena also allowed for data-mining to be able to figure out per-pack probabilities for Wild Cards. They are shown in the table below: (note that Magic Arena also has a “Pity Timer” and you get a Wild Card at rare or mythic every 15 packs)

Combining this data with the Vault probabilities gives a weekly Wild Card Rate of:

To provide a timeframe for completing a top-tier deck, I pulled three different Standard deck lists from MtGGoldfish to help provide intuition behind these numbers. For the purposes of simplification, all Kaladesh cards were removed from the deck lists and assumed that those slots are of the same rarity. (No sideboard cards were included in the calculations). Also, all commons are treated as owned, and all cards provided from introductory decks are deducted from the needed card list.

Using these decks as case-studies, we can estimate how long it will take to complete them.

We see that there still exists a long period of time needed just to complete decks that need approximately 30 cards. Note how the limiting factors are Mythics, due to their high appearance rate in top-tier decks, and very low appearance in Wild Card form. I'm certain that with the Vault update it will improve, however it is possible it is still too slow.

Conclusions

In my opinion, Magic: the Gathering is hands-down the best TCG out there. I want nothing more than to have Magic: the Gathering Online be the best possible digital representation of the game. Growing the player base, having an entertaining stream option, Magic Arena has the potential to be a game-changer. However, the lack of a true crafting system means that players are forced into tedious grinding to complete individual decks. Many of the changes and reasoning for this reward scheme are great (frontloading gold, having both daily and weekly incentives to play, etc.) but there needs to be something more. Daily card rewards do nothing for deck progression. A digital economy is arguably the most difficult thing to balance, but it needs to be flawless. The margin for error is incredibly small: either you don’t reward players enough and all but the most dedicated leave, or you reward players too much and you lose out on your profit margin. I can’t say I have all the answers, but I can leave on an uplifting note.
Wizards (of the Coast) is listening. I’ve seen nothing but positive feedback from them about how to improve the game. Here is a quote from MtG Arena Producer, ‘Gyant’: “Finally, anticipate more communication in the forums and expectation setting around economy changes as we move forward with each release. We’ll be better about letting you all know what we’ve intended so that you can continue to give us your best, honest feedback about how the game feels.”

I remain optimistic that this step backward will ultimately propel us forwards.