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Last week I discussed the importance of taking the time component into account when evaluating the performance of investments. Percentages and absolute Tix amounts only represent one side of the story. With so many variables between the value, number of cards involved, duration of the investment and the size of the bankroll, comparing two specs between each other could be difficult.
Of course, when comparing similar positions based on number of copies, Tix invested and duration of investment, the return on investment (ROI) is probably good enough to evaluate which of the two specs performed the best.
However, if you consider the two following positions, which one performed the best?
- For a 1,000 Tix bankroll, 30 copies of a 0.5 Tix card that yielded 250% profit in 100 days.
- For a 10,000 Tix bankroll, 15 copies of a 4 Tix card that yielded 100 % profit in 70 days.
I tried to come up with a formula that could be used to compare any two positions to each other, which took all the parameters cited above into account.
Disclaimers
I don't have any specific or advanced mathematical knowledge. Here I tried to take as many relevant parameters as possible to evaluate the performances of two positions. I'm not pretending the calculus below are the simplest or the most accurate. I simply tried to put together a formula that could be used for any positions that yielded a positive return. I also chose several values arbitrarily.
Feel free to edit and correct the following if you think I omitted something.
Defining the Parameters
The first thing to define when attempting to evaluate the performance of an investment are the relevant parameters. These parameters must be applicable to any spec.
ROI
With no surprise, the return on investment is one parameter to take into account. I use it as a positive percentage of the initial value of the position.
For instance, +100% means that the position has doubled. The higher the ROI, the better the investment is.
If X is the total initial value of your position and Y the total final value of the same position, the ROI = (Y * 100 / X) - 100.
Duration of Investment (DI)
This number represents the duration of your investment. The shorter the duration of investment the better it is.
Arbitrarily I chose to express it in days.
Number of Copies, Buying Price Per Unit and Bankroll Size
These three parameters are used to reflect a single notion--the relevance of any given position compared to the bankroll size at time of purchase. As I described last week, fewer copies save more time; the fewer copies involved, the better the investment.
The bankroll size (BS) and the buying price per unit (BU) are expressed in Tix. The number of copies is called N.
Derivative Parameters
Annualized ROI
As explained last week, the annualized ROI (ROIa) allows us to compare different specs based on their ROI normalized by a period of 365 days.
Here, ROIa = ROI * (365 / DI)
Theoretical Card Index
The Theoretical Card Index (Ct) is a value I'm introducing to reflect the relevance of the investment to Bs.
Based on Bu and Bs, I first estimate the number of playsets (Pt) needed to represent 1 % of Bs. I chose 1 % arbitrarily as most of my spec are close to representing 1 % of the size of my bankroll (this percentage could be anything of your choice).
The number of playsets is simply the number of copies divided by 4 (rounded up). For instance, 3 copies make 1 playset, 44 copies make 11 playsets, 203 copies make 51 playsets. I'm using the number playsets because in most instances it takes the same amount of time to deal with 1 card or 1 playset.
So Pt = ROUNDUP ((Bs * 0.01) / Bu)
When trying to come up with this Card Index I wanted a value that reflects the fact that the more copies you use for a spec the less efficient it is.
Since dealing with one or five playsets is about the same--it takes a little bit more time with five but won't impact much, if at all, your sell or buy price and won't require significantly more time. For instance, you can easily buy/sell 4 to 6 playsets in a row from/to Mtgotraders' buying bots without changing the price. On the other hand dealing with 50 playsets is not only time consuming but it is likely to affect your buy/sell price.
Instead of directly using Pt I decided to use 1.005^P. This new value increases exponentially (although very slowly) as Pt increases. For low Pt values the value of 1.005^Pt are "relatively" close, for higher Pt values the difference gets bigger and bigger. 1.1 is chosen arbitrarily here again.
I defined Ct as Ct = 1 / (1.005^Pt)
Adjusted Card Index
Now that we have a Ct for each spec, I'll calculate the Adjusted Card Index (Ca), which is Ct adjusted to the number of playsets actually used (P) for any given investment. Similarly to Pt, P = ROUNDUP (N / 4).
With this, Ca = Ct * (P / Pt)
I formulate Ca to be dependent on the size of the bankroll, the number of copies purchased and the price of each copy. This way, the same spec with the same number of copies purchased and for the same buying price will have a different relevance--a different Ca--for a different bankroll.
Higher bankrolls would need to buy more copies to make it more significant, but as you need more copies it is also counterproductive as it decreases the value of Ca. This means that whatever you do, some specs are simply not adapted for the size of the bankroll--you are not optimizing your time, and you should aim for specs that require fewer copies and/or have a higher price per unit.
Speculating with 50 copies of a 0.05 Tix card is not a good investment of your time and your Tix it you have a 10,000 Tix bankroll. At the opposite, the same spec could be totally suitable for a 100 Tix bankroll.
The Performance Score
With all the above parameters defined, here is the formula I came up with for the performance score (Ps) of any investment: ROIa * Ca.
Being fully developed and using the five basic variables ROI, duration of investment (DI), the number of copies purchased (N), the buying price per unit (Bu) and the bankroll size (Bs), here is what it looks like:
Ps = (ROI * (365/DI)) * ((1 / (1.005^(ROUNDUP ((Bs * 0.01) / Bu)))) * ((ROUNDUP (N / 4)) / (ROUNDUP ((Bs * 0.01) / Bu))))
As is the formula can be used in Excel.
Everything being equal, Ps gets higher (better) if:
- The ROI increases.
- The duration of the investment decreases.
- The number of copies decreases.
- The buying price per unit increases, which is likely to also have the number of copies decrease as well.
- The size of the bankroll gets smaller.
As the variations of Ps are not linear (see below for examples), two investments with a Ps of 200 and a Ps of 100 doesn't mean that the first one performed twice as well as the second one. I'm sure with better understanding and usage of mathematics one could come up with a formula that reflects this. Here, the formula I'm proposing only compares different investment performances between each other and tells you which one is "better".
Examples
I'll use the three examples I used last week--Spoils of the Vault, Angel of Serenity and Voice of Resurgence.
- 47 copies of Spoils of the Vault, purchased at 0.12 Tix each, for an ROI of +480% in 244 days.
- 22 copies of Angel of Serenity, purchased at 1.16 Tix each, for an ROI of +170% in 91 days
- 6 copies of Voice of Resurgence, purchased at 15.66 Tix each, for an ROI of +43% in 38 days.
In both cases the bankroll size is set at 10,000 Tix.
- Ps of Spoils of the Vault = 14.53
- Ps of Angel of Serenity = 116.63
- Ps of Voice of Resurgence = 408.92
According to this formula, Spoils of the Vault is clearly the worst performer of the three positions. However, the same Spoils of the Vault investment made with a 900 Tix bankroll this time around would give a Ps of 412.49. This investment is much more relevant for a smaller bankroll.
For another example, applying this formula to Perilous Vault, probably my best investment so far, gives me a Ps of 2136.71.
Comments And Critics
What do you think of it? This formula is supposed to be applicable for every spec (with a positive return) and for every bankroll. I'm far away from claiming it's perfect but it's a first step toward a tool to evaluate and compare specs between each other, and across different bankroll sizes.
Some of you are certainly more mathematicians than I am and you may have seen flaws in my reasoning and my formula. How would you update and modify this? Please share your thoughts and check the Ps of your investments.
Thanks for reading,
Sylvain Lehoux
So I’ve been talking more and more about getting into MTGO with a mid sized bankroll and possibly working together with someone to have a much higher sized (~5-8k) bankroll. The quick and dirty summary I’m seeing is that investing in higher value cards which may generally see a smaller percentage gain but a higher total ticket gain (plus an easier way to out) is a better investment?
Also, you have a high bankroll I believe. Do you not invest heavily in the smaller specs simply for the issue of having to move all of them? That seems to be the factor that a lot of people in both MTGO an paper don’t take into account. Cool, you bought 500 copies of a bulk rare that is now worth $1.50. You made 1000% profit, but how are you going to sell 500 copies of this card? Cards like Voice are easier to move because they are staples and the demand is driving the price up, where as some random spike card is harder to move once the spike is over.
Am I on the right page?
Hi Dylan,
You are pretty right all the way. In my opinion, two big factors that should drive your speculation strategy is the size of your bankroll and your spare time for this activity.
The less time you have the less interesting (and performant overall) cheap card will be. The bigger the bankroll the more expensive cards you need to make a significant difference when selling positions.
With the limited time I have for speculations on MTGO (about 4 to 6 hours a week, and this include buying/selling but also reading a bit, doing some research and looking at prices charts) it makes more sense for me to seek “higher value cards” (which means that for my bankroll I’m looking for cards I don’t need to buy more than 30-50 copies in average to make up for 1-2% of my bankroll).
Modern mid-priced staples (from 2 to 15 Tix) are great for this, they swing very often with 100-200% variations and it’s “easy” to buy 100 Tix worth of them (from 1 playset or 2 to 10-20).
From experience, moving 50 copies of cards without really affecting the selling price is doable, more than that you will either affect the price or you’ll need more time to sell. If the trend is a nice upward trend supporting by real player demand it’s fine. If it’s a spike moving a high number of copies at the same price will be more challenging. And when you want to move a card that is not in demand you will quickly affect the price.
Here is two different examples:
– Hushwing Gryff. To me this card was really great. With a price as low as 0.2 Tix in August I bought 60 copies of it. (But I know I’m already in a situation where it needs to perform well to be worth it, but I really believed it could reach 1-1.5 Tix). Then it dropped down to 0.05 Tix briefly late September, I bought an additional 40 copies and stopped at 100 copies because of what I said above. The price took off and was supported by real demand (it never really went bellow 1 Tix after the initial spike). I sold part of my copies around 1.5 and the rest more recently around 2, and the price is still up! Great investment since I made 100 Tix profit on this cheap card. I know core set cards performed really well (my M15 specs have been terrific) so I knew I could drift away a little bit from the rule. But here is another different experience.
– M14 Junk mythics (Ring of the three wishes, Devout Invocation, Windreader Shpinx…). I bought more than 200 copies of these as part of my experiment on the core set mythics (if you read my articles, I bought all of the 15 mythics for an equivalent Tix amount to see what would happen). None of these mythics really took off and pretty much always stayed in the 0.4-1 Tix range. When a slight spike occurred I decided to sell them all. I sold the first 50 copies with a little profit, the next 50-70 copies breaking even but lost value on the 100 or so last copies. I took me forever to sell all of this without sacrificing to much on the price. When a card is not in demand the market is easily saturated and prices drops.
Hope it helps.
Hello Sylvain, I’m a new member of QS and I’m reading all your articles, since I found your finance reports and points of view really interesting.
Well, regarding this article, I’ve tried to use your formula, but I’m a bit dumb and it’s not working for me.
As for an example let me copy-paste the formula and the data:
Ps = (ROI * (365/DI)) * ((1 / (1.005^(ROUNDUP ((Bs * 0.01) / Bu)))) * ((ROUNDUP (N / 4)) / (ROUNDUP ((Bs * 0.01) / Bu))))
47 copies of Spoils of the Vault, purchased at 0.12 Tix each, for an ROI of +480% in 244 days.
OK
This makes:
(ROUNDUP ((Bs * 0.01) / Bu)= 10000*0.01/0.12= 833.3->834
((ROUNDUP (N / 4))= 47/4= 11.75–>
Then:
Ps=(480*(365/244)) * ((1/1.005^834)*(12/834)) = 0.16
It should have been 14.53 as you say in the article, but unfortunatelly I don’t know what’s wrong.
Maybe you can help me, I would really appreciate it