## Slowly, But Surely: the Long Term Finances of Your MTGO Deck

#### by Drake Builta // Apr 16, 2015

A frequent occurence in Magic involves making a marginal investment during the beginning of a game and then reaping the benefits of that investment as the game progresses. For example, by investing a single blue mana to cast Delver of Secrets on turn one, a RUG Delver sets themselves up to kill their opponent three points at a time. Strategically, the three point clock over the course of the game was worth more to that player than the one blue mana on the first turn. Not all that differently, players can look at the financial lifespan of their Magic deck and consider whether or not the long term benefits of owning a particular deck are worth the initial cost.

Whether you're grinding for tickets online or playing primarily for entertainment, selecting your deck can be a huge financial decision. One of the great things about playing on Magic Online is that you can partially or completely pay off the cost of a deck by participating in tournaments and converting your prize packs back into tickets. This process is especially important for people who play on a budget or are maximizing their financial value. For that reason, understanding the financial behavior of a deck in the long term will pay back, quite literally, in dividends.

So, the age old question arises: do I shell out the money required to build the "best deck," or do I opt for something that's less competitive to save money. This article will attempt to answer that question and hopefully a couple more.

### The Search Begins

One quick way to figure out if building a deck is worth your time is to look at the payback period: how long it will take you to turn a profit on your initial investment. Payback period analyses are often used in industries that deal with significantly uncertain markets (much like Magic Online). They help to understand the expected cash flow of a financial decision over the course of its lifetime. A payback period analysis in the context of Magic Online will be used to look at how likely you are to earn back your invested value given your deck choice and your skill level. The goal of this article is to demonstrate a mathematical approach to show that sometimes the expensive "best deck" is the way to go, but sometimes it's just not.

Before moving on, there are a few quick points I'd like to address.

Possibly the best way to improve your skill level as a player is to play with the most competitive decks. Unfortunately, there's no way around that. Favoring budget decks in the short term may not be the best financial decision for the very long term as you will be sacrificing gains in skill level in order to save some money right now. Unfortunately, this aspect of benefiting from a skill-testing deck is next to impossible to model, so I'm choosing to ignore it.

### Building a Model

For the sake of this article, I'm going to assume that the financial lifespan of a deck will more or less follow these steps:

- You build the deck.
- You pay the entry fee for playing in a tournament and then play in that tournament.
- You win games for a profit or you lose some games and your entry fee.
- You repeat 2 and 3 for however many tournaments you want to play.
- You sell back singles to a bot for less than you bought them for once you're done.

### Steps 1 & 5: Your Marginal Investment

The first number you'll need to look at is how much money you expect to sink into the deck. This quantity will vary wildly depending on the particular deck you're looking at. While some decks cost a lot at first, they may be full of format staples which you expect to remain stable throughout the deck's use. In order to figure out a quantity for how much money you're sinking into a deck, you'll need to look at the deck's inital price and its expected buylist value at the time you plan on selling back your singles. I'm going to call this difference the "sunk cost." The reason sunk cost is important is that it's essentially the net price of the deck you're and it's the amount of value you're looking to earn back over time.

Predicting the exact price of singles on the Magic Online market is difficult to do a week in advance, let alone a couple months; we'll use ballpark estimates for the purpose of completing this analysis. The particular cards you're looking at buying are not specifically important; the payback period model only cares about the sunk cost associated with those cards.

To make this article less abstract, I estimated the sunk costs of a few standard decks for buying them now and reselling them at the end of the summer. It should be noted however that the sunk cost I'm assigning to each deck is just for comparison and isn't meant to be an exact estimate.

Deck | Current Sticker Price | Approx. Future Value | Sunk Cost |

RG Dragons | 250 | 100 | 150 |

Abzan | 220 | 80 | 140 |

Atarka Sligh | 185 | 100 | 85 |

UB Control | 170 | 75 | 95 |

Jeskai | 150 | 65 | 85 |

Budget Mono Red | 30 | 5 | 25 |

While there are many ways that you can play in tournaments on Magic Online, I'm going to be specifically looking at Daily Events as that is the most popular form of tournament play. In a Magic Online Daily Event, prize packs go out to all players that finish 3-1 or better. As of last Wednesday the prize support for finishing 3-1 is now 4 packs of DTK and 2 packs of FRF; the prize for finishing 4-0 is 7 packs of DTK and 4 packs of FRF. Let's assume that the average price of DTK packs will remain in the ballpark of 2.5 tickets and the price of FRF around 4.1. Considering the value of all packs won minus the 6 ticket entry fee, here are the marginal benefits of each possible finish: a 4-0 finish will net you roughly 28 tickets worth of profit; a 3-1 will net you 12.5; and an 2-2 will net you a 6 ticket loss. These numbers will fluctuate over time with the market price for packs, however, they're likely to remain around these values.

Steps 2 - 4: Your Incremental Payoff

While repeatedly winning with a 4-0 record would be awesome for your wallet, this is not likely to happen. What each player should therefore expect from their tournament winnings is somewhere between 28 tickets and -6 tickets depending on their skill level. One simple way to look at this probability is Match Win Ratio. MWR is essentially the proportion of matches a player has won out of the number they've played. An alternative way to think about this as a probability is to say "for every match I've played, it's X% likely for me to have won that match." While this isn't completely true, it will make our calculations much easier and isn't that far from being accurate. Given that we're looking at winning games in Dailies, it's better to think about an MWR as calculated only from performances in Dailies. Let's also assume that a player's MWR remains relatively constant over the time span we're looking at (a couple months).

Taking MWR into account, we can calculate an expected profit (EP) for each event you enter. Your EP is going to be a combination of your expected tournament record and the associated profit for each possible record. Here's an example: A player with their MWR in Daily Events equal to 70% is therefore 70% likely to win any given match in a Daily. Their probability of finishing 4-0 is (70% x 70% x 70% x 70%) = 24%. The probability of finishing 3-1 is 41%. Finally, the probability of finishing with no prize payout and losing your entry fee is 35%. Given the marginal profits of each record discussed in the previous paragraph, this particular player should expect an average marginal profit of (24% x 28 tix + 41% x 12.5 tix + 35% x -6 tix) which is 9.6 tickets per event. The table below shows the EP calculations for several MWR values.

80% MWR | 75% MWR | 70% MWR | 65% MWR | 60% MWR | 55% MWR | |

Probability of 4-0 Record | 41% | 32% | 24% | 18% | 13% | 9% |

Probability of 3-1 Record | 41% | 42% | 41% | 38% | 35% | 30% |

Probability of 2-X Record | 18% | 26% | 35% | 44% | 52% | 61% |

Expected Profit (Tickets) | 15.3 | 12.4 | 9.6 | 7.0 | 4.68 | 2.55 |

This essentially shows that your EP is going to be higher with the higher MWR you have. If you have a MWR equal to 75%, you can expect about 7 tickets worth of value in a Daily. That being said, the EP calculation is very sensitive to MWR, so consider these to be approximate estimations. They should not be taken as definitive solutions, but more as "if I play in 100 Dailies, I'm likely to make this much on average."

One cool thing worth paying attention to is that the first three rows will remain the same regardless of pack prices. You can adapt this model to different packs as new sets come out. Even cooler though, is that you can apply this to paper tournaments if your LGS operates on a store credit payout schedule.

### Drumroll, Please...

Without further adieu, below is a table that shows the expected number of tournaments you'll need to participate in before you earn back your sunk cost. The way to read it is to look at the intersection of your deck's expected sunk cost and your expected MWR with the deck. For example, I'm looking at getting an Atarka Sligh list and I think I can win around 67% of my matches with that deck. This means I'll need about 29 tournaments before I should expect to make a profit on the investment.

Sunk Cost | Example Deck | Required 4-0's | Required 3-1's | 80% MWR | 75% | 70% | 65% | 60% | 55% | 50% |

25 Tickets | Budget Mono Red | 1 | 3 | 2 | 3 | 3 | 4 | 6 | 10 | 38 |

50 Tickets | 2 | 5 | 4 | 5 | 6 | 8 | 11 | 20 | 75 | |

75 Tickets | Atarka Sligh, Jeskai | 3 | 7 | 5 | 7 | 8 | 11 | 17 | 30 | 113 |

100 Tickets | UB Control | 4 | 9 | 7 | 9 | 11 | 15 | 22 | 40 | 150 |

150 Tickets | Abzan, RG Dragons | 6 | 13 | 10 | 13 | 16 | 22 | 33 | 59 | 225 |

200 Tickets | 8 | 17 | 14 | 17 | 21 | 29 | 43 | 79 | 300 | |

300 Tickets | 11 | 25 | 20 | 25 | 32 | 43 | 65 | 118 | 449 |

Overall, the results are consistent with what you might expect. It takes longer to pay off a larger initial cost. But the marginal benefit of having a higher MWR can definitely add up. Assuming you are able to consistently hold your MWR above 65%, you can earn your investment back in due time; knowing how many tournaments that will take can help you decide between two decks.

If you're using this to compare the long term prospect of two different decks, you'll want to look at the difference in expected number of tournaments. For example, I may want to play Atarka Sligh, but I think I can win more games with an Abzan deck. I tend to win 65% of my matches when I play aggro decks, but I'm expecting a slight bump (maybe 5% up to 70%) in MWR by choosing the "better" deck. I should look at the chart and recognize my expected number of tournaments with Atarka Sligh and with Abzan to be 11 and 16 respectively. If I think I can only play in less than 16 tournaments before selling back the deck, then I should pick the cheaper one (Atarka Sligh). However, if I can play in more than 16 tournaments, I should pick the one that gives me the biggest expected MWR (Abzan) since I'm likely to accumulate a big enough profit over time to overcome the sunk cost.

There's another way to use this chart if you don't like committing to a deck for several months. You can think about getting a deck for a couple weeks while it's the best deck, and then selling it when it's less favored. When doing that, your sunk cost will probably be around 25 to 50 tickets regardless of the deck. You'll want to figure out the number of Dailies you'll be able to play in during that time period, and then figure out what MWR is needed to earn back your value. For example, for a two or three week period, 8 events seems like a high number for my schedule. I'll probably want to err on the side of picking a deck that will help me sustain a MWR of 70% or better. Otherwise, I'll probably end up losing money before I switch decks again.

### Conclusion

As much as I'd like to give a direct answer for which deck will provide the best long term financial prospect, that answer doesn't exist. Ultimately it depends on the pilot's skill and how much they're willing to play, but this chart should help you out.

As always, I hope you enjoyed the article. Please let me know if you found it helpful or if you have any comments you'd like to share. I can be found on Twitter @Rad_Blast.