6 minute read
With the eye watering prices of premium MTG sets such as Commander Masters, and WotC pushing the limits of what we’re willing to spend in general, the question ‘is it worth it?’ has never been more important than it is now.
While The Professor’s and other content creators’ videos go a long way to address the wider community impacts of such high prices, neither the ‘booster box game’ nor the ‘is it worth it’ series actually answer the question correctly from a mathematical standpoint. The sample size of cracking a few boxes is not close to enough to determine the value in a product.
In this article, we’re going to show how to calculate the true expected value of a Commander Masters Collector Booster Pack, as well as run some probability simulations to see if they are actually worth it from a monetary cost vs contents perspective. Buckle up, it’s about to get nerdy!
Table of Contents
What we know about the Commander Masters pull rates
In order to do our calculations, we must first know what a Collector Booster Pack contains. Luckily, WotC has a handy infographic explaining just this.
From the above image we can gather that each Collector Booster contains 16 cards and enough information to determine which cards can appear where. If we think of each card in the pack as a slot, then the pack can be broken down as follows:
Slot 1 - Traditional Foil C
Slot 2 - Traditional Foil C
Slot 3 - Traditional Foil C
Slot 4 - Traditional Foil C
Slot 5 - Traditional Foil U
Slot 6 - Traditional Foil U
Slot 7 - Traditional Foil Retro Basic Land
Slot 8 - Non-foil Borderless C/U
Slot 9 - Non-foil Borderless C/U
Slot 10 - Traditional Foil Borderless C/U
Slot 11 - Traditional Foil R or M
Slot 12 - Etched Foil R or M
Slot 13 - Traditional Foil (20%) or Non-foil (80%) Extended-Art R or M from Commander Decks
Slot 14 - Non-foil Borderless R or M
Slot 15 - Traditional Foil (96%) Borderless or Textured Foil (4%) Borderless R or M
Slot 16 - Traditional Foil Double-Sided Token
Yep, that is quite the list. Thanks to WotC for making ever more complicated Booster packs!
What we don’t know about the pull rates
What’s left ambiguous is the frequency of Commons vs Uncommons and Rares vs Mythics when both can appear in the same slot. For our calculations, we assume that there is no ‘forced pull rate’ (unless stated) outside of the natural ratio of Commons vs Uncommons and Rares vs Mythics in their respective pools of cards. This is a big assumption, as forced pull rates have been observed in the past. But, without knowing what those might be, we will keep things as simple as possible.
Being in the UK, we will also be using the lowest NM price on Cardmarket for our data, regardless of the seller’s reputation or any other factors. Prices will vary depending on where you are, but the good news is you can customise your own data set with parameters and a source of your own choosing; the methodology will remain the same.
Let’s get started…
For the sake of simplicity and a workable data set (more on that later), we will assign 0 value to Slots 1 through to 7. A quick look tells us that any value in those slots is negligible so this will have minimal impact on our final numbers. Similarly, we will assign no value to the double-sided foil token in Slot 16 due to a lack of reliable price data for those cards.
This means that the first slot of interest is, in fact, Slot 8. To work out the value of Slot 8, we must begin by making a list of all possible cards that can appear in the slot, find the price of each card, then find the average (mean) price of all cards in this pool.
As the table shows, 30 potential cards can appear in Slot 8 with an average value of €0.62. With Slot 9 being identical to Slot 8, we move on to Slot 10 which contains a ‘Traditional Foil Borderless C or U’. The pool of cards for Slot 10 is the same as the previous 2 slots, with the only difference being the foiling. This comes out to an average value of €2.18.
We can then repeat this process for all slots that require a simple calculation of the average: Slot 11, 12, and 14. With 170 possibilities for both Slot 11 and 12, we will refrain from posting an image, but the final results are:
|Number of Cards||Average Value (€)|
This leaves us with Slots 13 and 15 which are slightly more intriguing. Slot 13 contains an Extended-Art Rare or Mythic from the Commander Masters Commander Decks, with the card being a Non-foil 80% of the time and a Traditional Foil 20% of the time. To calculate the expected value of this slot, we have to find the average value of both a Non-foil and Traditional Foil Rare or Mythic from the Commander Decks. Once we have the 2 averages, we weight them by 0.8 and 0.2 respectively to get our Slot 13 expected value of €6.08.
For Slot 15 - you guessed it - we can apply the same approach, weighting appropriately for the 4% chance of a Textured Foil and 96% chance of a Traditional Foil. This leaves us with a Slot 15 EV of €22.14, by far the most valuable slot in the pack. The expected values of all slots are summarised in the table below.
|Number of Cards||Expected Value (€)|
From the table, we can easily see where the bulk of the value is coming from and, more importantly, that the overall expected value of a Commander Masters Collector Booster Pack is €64.66! With the price of a pack going for around €50, we can tentatively say that, at least for now, it is worth the cost.
Wait, there’s more?
At first glance, with an expected value of €64.66 and a cost of €50, it may be easy to conclude that you should be cracking packs all day to sell the singles but, in practice, things are not so simple. Expected value does not mean that every single booster pack or booster box will contain this exact value. Packs will be above or below EV, but over a large enough sample, the average value you get will approach the true expected value. Just how many packs it will take to get close will depend on the spread of the value across the cards in the pack.
To get an idea of this spread, we need to plug in our data and run some booster pack simulations - 10 million of them, to be exact! 10 million may sound like a lot, and more than was printed, but it is just a random sampling of the entire population of unique packs that could be generated from the slots we deemed of value - a staggering 100 trillion unique packs. You can see now why we had to cut the low value slots from our calculations! From these 10 million theoretical packs, we get the following distributions:
|Mean Value (EV)||Median Value||Standard Deviation|
Interpreting the results…
If you aren’t adept at reading strange probability graphs, then fear not. The key takeaways from the data are:
The Pack EV is €64.73 - €0.07 higher than the value we calculated due to the 10M sample size. We are very close, which is a good sign.
The Pack Median is €51.20 - literally the middle of all 10M pack values generated. This means that each pack has a 50% chance of being higher or lower than this Median value.
The Box EV is €259.01 with the discrepancy again coming from the sample size.
The Box Median is €236.84, meaning that 50% of boxes are above this value, and 50% below this value.
The EVs are higher than the Medians due to the skew from super high value cards such as the Textured Foil Jewelled Lotus. Most of the packs and boxes you open will be below EV. If you hit one of the top value cards then you have struck gold!
Not shown in the results above but there is a: 90% chance a pack contains a value of at least €24.70, 80% chance of €31, 70% of €38, and 60% of at least €44.
So, there we have it - the mathematical value of Commander Masters Collector Packs. While the value in the packs is currently strong, if you are only after a choice card or two then it makes much more sense to purchase Singles due to how unlikely you are to pull those cards from your packs. However, if you are looking to crack some packs for fun, then you can currently do so in the knowledge that you are not taking a -50% EV loss the moment you break the seal.
It must also be mentioned that prices, especially in the first few weeks after release, are extremely volatile. No doubt the prices have already moved in the 2 days it took to gather the data and put this article together! The assumptions made at the beginning of the calculations will also have an affect on the end results. Nevertheless, we hope we have shed some light on how true value is calculated and how that translates to the chance of a good pack vs a dud pack. If you enjoyed this write-up then please consider checking out our other articles and product reviews.