The Theory of Profit

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How do we evaluate expected value? How do we calculate whether a risk is worth taking, or whether a deal will turn a profit? Having a constant, accurate, system for determining these will allow you to more consistently gain profit, while minimizing risk. While I talked about the different types of risk in one of my previous articles (“Recapping Risk”), I wanted to revisit this topic, this time covering more strategies to avoid risk, and also ways to measure risk, and conduct a risk-reward analysis.

Let’s start by reviewing the areas of risk a seller faces:

* Price fluctuations

* Finding a market

* Security concerns (fake cards, etc.)

Again, my last article about risk went over ways to minimize the risks you take in these areas while trading, buying, and selling. But without risk there is no reward. In order to determine when the risk is of an acceptable level to do a deal, we just apply a few simple equations.

Example 1:

I’m at my local store, and one of the players pulls a Koth from a booster while drafting. After the draft, I approach the player, trying to buy his Koth for $20, knowing that the store’s buy price on Koth is $25. Let’s start with a simple equation…

profit=sell price+buy price

So by plugging in our variables we get…


Obviously showing that we get a profit of $5. Yet this is only monetary profit. This doesn’t reflect your own time invested. What if that $25 buy price was at a store an hour away? Then you’d be earning a paltry $5/hr, lower than minimum wage. A more effective variable to use instead of profit is wage profit, i.e. the amount of money you make per unit time above the maximum amount that you could be making elsewhere. So if you earn $20 by trading for an hour, while your normal job pays $15/hr, your wage profit is $5/hr. Yet there are also a host of other variables and costs that must be applied to the equation. Let’s hit you with this monstrosity, and then explain it below…

Wage profit=sell price-buy price-(% risk x potential monetary loss)-(investment length x money loss per unit time)-(labor value per unit time x personal time)

So at this equation’s base, we have our profit=sell price-buy price. Wage profit=sell price-buy price-(labor value per unit time x personal time) just expresses what I stated earlier about how to define wage profit. Labor value is equal to the maximum wage you can earn elsewhere, and we adjust that wage for the amount of personal time invested. But making a profit isn’t that simple. There are several other costs that we must factor in to calculate our wage profit. This is where risk comes in, as part of our costs. The % risk is the estimated chance of losing money, which we multiply by the potential money loss that would result from that risk. We also subtract our “opportunity cost”, something that Kelly and other writers have often talked about on this site. Every second that your money is tied in an investment is a second that you lose money. Sure, you might’ve gotten that playset of Frost Titans for only $35, but what if that means you now can’t afford the $250 Mox Jet that popped up on Ebay? While inflation is much less of a factor for Magic, it will apply to more long term investments in the real world. By multiplying our estimated opportunity cost per unit time by the time that the investment is held, we establish another cost. So by plugging in values for all of this, we end with our only variable being our wage profit. Let’s restate that equation again…

Wage profit=sell price-buy price-(% risk x potential monetary loss)-(investment time x money loss per unit time)-(labor value per unit time x personal time)

For that previous example, we can calculate our wage profit quite easily. Let’s assign some values to our variables. We already know that sell price=25 and buy price=20. Our % risk is 0, because we know we can resell the Koth for profit right away. We can assume our time to be fairly insignificant, because we flip the Koth so quickly, so let’s estimate our personal and investment times to be around 1 minute. I would also estimate that your money loss per unit time, or “opportunity cost”, to be 1 cent per hour. Let’s also assume that you took the night off to go to FNM, and you could be earning $6/hr if you hadn’t. so let’s plug in our variables…

Wage profit= $25-$20-$0-(1 minute x $.01/60 minutes)-($6/60 minutes x 1 minute)

Then, we just simplify…

Wage profit=$25-$20-$0-($0.000167)-($0.1)

Wage profit=$4.899833 per unit time

Not a light load of math, and this wasn’t even a complicated situation! Let’s try this again, giving ourselves a source of risk to factor in.

Example 2:

This time, you’ve secured a collection on Craigslist. It’s chock full of great cards, from Aether Vial and Sol Ring, to Revised versions of the original duals. You’re buying it for $500, but you’ve already talked to a friend who wants to start getting into the Eternal formats, and has promised you $750 for it. You estimate there’s a 5% chance that the cards are fakes, in which case you will lose all the value of your investment. The time you’ll have to take flipping it between the two parties is an hour, and you maintain the loss of $.01/hr. it will also take you an hour to drive to the seller’s house, half an hour to check the collection, and an hour to drive back, leading to a total time investment of 2.5 hours. Since it’s a Saturday, you don’t have work, but you could be making as much as $8/hr by helping out your local store while they’re busy…

Wage profit=sell price-buy price-(% risk x potential monetary loss)-(investment length x money loss per unit time)-(labor value per unit time x personal time)

Wage profit=$750-$500-(.05 x $500)-(1 hour x $.01/hour)-($8/hour x 2.5 hour)

Wage profit=$750-$500-($25)-($.01)-($20)

Wage profit=$204.9 per unit time

Again, the math here is not simple, but it’s not overly complicated either. By applying these basic economic principles, we are able to more accurately evaluate the amount of money we make. Ok, one more time, with more risks.

Example 3:

You found a Mishra's Workshop worth $250 selling on Ebay for only $200. You quickly snap it up, thinking you’ll be able to resell it for the normal $250 price. So what are the risks at play here?

1. The card is fake and you can’t get a refund. 5% probability, $200 loss

2. Stax becomes a very bad choice in Vintage because there is too much artifact hate for it to thrive. 7% probability, $50 loss

3. No one in your local scene needs the Workshop for Vintage, so you’re forced to sell it at a loss to the store. 20% probability, $15 loss

Other needed information:

* It will take a week for the card to be delivered and another week to sell it, so your investment time will be two weeks, with the normal loss of $.01/hr (for those of you without the inclination to do the math, there are 7x24=168 hours in a week)

* It took you an hour of your personal time to both find the listing on Ebay, and then resell it, which is time you could have spent working at your $35/hr job.

For this equation, we’ll need to do multiple iterations of our risk loss term.

Wage profit=sell price-buy price-(% risk x potential monetary loss)-(investment length x money loss per unit time)-(labor value per unit time x personal time)

Wage profit=$250-$200-(.05 x $200)-(.07 x $50)-(.2 x $15)-(336 hours x $.01/hr)-($20/hr x 1 hour)

Wage profit=$250-$200-($10)-($3.5)-($3)-($3.36)-($35)

Wage profit=-$4.86

So as we can see, speculating on this Workshop is less profitable on average than just grinding hours at work.

Now of course the calculations I demonstrated don’t take into account every possible factor. There's theft, a possible reprinting, random damage to the cards, getting paid in counterfeit money, ripping somebody off and getting double a card’s value, or an increase or decrease in value of the deck archetype or format that the card is played in. there are infinitely many variations of this, so do your best to simplify it down to it’s four or five key components to plug into the equation.

Well, that’s all for now. After taking a few weeks off I wanted to write a more theory centered article for my comeback, and I think I achieved that fairly well. So let me know what you think about this in the comment section.

Peace, love, and economics,

--Noah Whinston

nwhinston on Twitter

arcadefire on MTGO

baldr7mtgstore on Ebay

10 thoughts on “The Theory of Profit

  1. hahaha, of course John.
    But yes, that's another area that i would need to try and factor into the equation: multitasking. that would be significantly more difficult to assign a mathematical value to though

  2. Flipping from ebay to online buylists can be a total pain in the a. I've gotten some great margins, but I also get burned on condition occassionally which significantly affects a card's buy price. I would say the percentage of risk for a NM card not being NM is 30%+ if it is coming from ebay regardless of seller status. The cost range of this risk could be anywhere from 15-50%.

  3. "* It took you an hour of your personal time to both find the listing on Ebay, and then resell it, which is time you could have spent working at your $35/hr job."

    Most jobs do not allow you to just show up for an hour and get paid. The $35 dollars is only a cost if you are on Ebay when you could be working, but its more likely you are on Ebay when there is no opportunity to be at work.

  4. Great article, going deep into economic theory is always exciting. Takeaways: Buy/sell cards at work, and that sometimes what you would be doing other than trading cards is watching TV or commenting on Magic-related economic theory articles, which have no EV.

  5. A $35/hour job? I'd like to know how to get one if you're using that as an average wage of a magic player. I'm working on getting a college degree and right now the jobs I'm looking at for graduation will only pay $30k a year. 35(Dollars an hour)*40(hours a week)*52(weeks)= $72,800. If anyone made that sort of money it would be no problem to just buy a 4x set of any standard set for $1k and not have any issues.

    1. Furthermore, it does show that unless you're moving a lot of product, it's worth more just to get a min. wage job to supplement this game that we play. The unseen value is getting to know people through trading, you may not be the most liked person in the room, but you'll also actually know people to playtest with and/or play more casual formats and actually ENJOY this game that we play. The social interactions that most "Average Joe" players read about in the pro's articles don't just have to be had at that level, you can find a place in your hometown and enjoy that time with a certain set of friends.

      1. Sorry for triple posting, but I also wanted to say welcome back, its interesting getting a new perspective on the ideas of trading. I also read up above that you suggested the wage to compare to is $15/hour not $35/hour, most likely a typo that slips through everywhere. We all have are interests in this game and this is a great place for people to find out the other aspect of this game "Trading" which is seen by a lot of people as a blemish on some of the more intense traders always trying to get an insane deal on cards. Thanks for all the work you do to try to encourage this understood aspect of the game.

        1. yeah, i accidentally said $35/hr, then used $20/hr in the equation.

          for everyone commenting about specifics, such as the hourly wages i used, or the percentage risks, etc, the important thing to remember is that they're arbitrary. these aren't values that have come up in my everyday life, just values i chose to demonstrate how to apply the equations

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