Expected Value is a term that is thrown around the MtG community frequently. “+EV” has become synonymous with “profitable” and grinding has an air of pride attached to it, and that’s whether you’re grinding events or trade tables. While the short-cut term is certainly good enough for communication between people who speak the same language, using its actual meaning and underlying calculations, we can find some interesting things.
Rare drafting is a Science, not an Art. The reason being, there are actually correct times to take a rare for its monetary value, and times when there isn’t. For years, at a standard LGS draft, $5 was the minimum monetary value a card would need to have for me to pick it over another playable. I figured, for a $15 draft, with 3 packs, if I get a $5 card, that pays for that pack, and recoups some investment.
I felt this way until Aaron Forsythe posted some very interesting information about M10 limited using extensive data from MTGO. You can find the data here:
A quick recap for those to lazy to click the hyperlink: He lists the top 25 cards in M10 limited, based on win% of the decks they were included in, during round 1 of sealed events.
In this particular set, 17 of the 25 listed are Rares and Mythics, 5 are Uncommons, and 2 are commons! Also of note, the entire range of the top 25 leads to win% >51%.
Here’s where things get interesting, with regards to Expected Value. In short, Expected Value is simply a weighted average, where we calculate the average outcome of a decision, based on the likelihood of each outcome. The problem with Magic (or reason for its success) is the probabilities of such outcomes are not known. But now we have an idea of the range of how good some of the best uncommons can really be in a limited environment.
Keep in mind, these probabilities aren’t precise for a couple reasons:
1) The data comes from M10 not M12.
2) Your individual win% is going to vary from the population of MTGO players as a whole.
However, it does give us an idea of how much better some cards can really be, and how much of an impact they can have on your chances of victory.
I’ll start with the LGS I play at, as an example. Suppose we open a pack that has a junk rare (Sundial of the Infinite, perhaps), a Foil Timely Reinforcements, and a Mind Control. If this was Pack-1-Pick-1, using my previous rule, the $5-6 foil would be the pick. But with this new information, let’s see how correct that is. At least in M10, and I think most would agree M12 wouldn’t be much different, Mind Control owners won 54.07% of their matches. How can we use this information to determine if the foil is worth the pick or not? It will depend on prize structure.
At my LGS, an 8-man pod gives 1 pack to a player who loses in the semi-finals, and $15 store credit to 2nd place, and $25 store credit to the winner. It is not uncommon for first and second to split at $20/$20. Supposing the rest of my draft is fairly average, just the presence of Mind Control alone, means I’ve got a 54+% chance of making it to the Semi’s alone, and a 27.61% chance of making the finals, and a 14.93% chance of winning it all.
The possible outcomes are:
1st Round elimination: No Prize, 45.9% likely
2nd Round elimination: 1 booster prize ($3 for simplicity), 24.8% likely
Loss in the finals: $15 prize, 14.4% likely.
Win the 8-man: $25 prize, 14.9% likely.
So, if we can accept these figures are a decent starting ground of comparison, we can calculate the value of this proposition.
$0*(0.459) + $3*(0.248) + $15*(0.144) + $25*(0.149)= $6.629 which, depending on who you are talking to, may or may not be more than a Foil Timely Reinforcements. In this case, I think it is correct to go with the Mind Control, but the prize structure will of course affect the decision. Other things to consider, is there’s an opportunity cost in picking Mind Control. I /didn’t/ get to add the Timely Reinforcements to my deck. So would the $5-6 foil, plus the value it adds to my deck make up the difference? It might, but I’m inclined to think that cards like Mind Control, gain so much edge, that it is tough to reject their strength. That being said, there are only a handful of Uncommons that this applies to. Namely, Mind Control, Fireball, Oblivion Ring, Serra Angel, Acidic Slime (although I’d argue its not as strong in M12 as it was in M11 or M10), Overrun, and I would guess Sengir Vampire belongs on the list too. (Note: if you play Swiss-Pack-Per-Win, the numbers resoundingly favor the $6 card).
I fear that some of this article will be ignored, because the numbers aren’t going to fit your exact scenario. That’s likely true, we have to pick somewhere to start, and the data that’s available is about all we can do. FWIW, my limited match win% is in the 54-56% range as it is, so likely adding a Mind Control to my pool skews my win% up a bit farther (making it even more valuable than a Timely Reinforcements, although making the chances of winning without the Mind Control also reasonable). Finding your win% is easy, and work with it. Obviously, winning in later rounds should be tougher, but again, we have to work with averages here, because it’s all that’s available.
Where does that leave us? Well, my $5 gut-check rule, seems to be a fine ‘rule of thumb’ for the types of prize structures I’m used to, but it isn’t an Art, it’s a Science. It either IS correct to take the Foil Timely, or it isn’t. If you plan on keeping drafting as inexpensive as possible, making the correct choice more often than not, is going to be crucial. The most amazing statistic in Aaron’s post is: “Only 70 of the 229 cards in M10 have win % over 50%.” We don’t know how many of those are Rares, but if the ratio is similar to the top 25 cards, we could expect there to be only 20 non-Rares in that group of 70, meaning that most cards hurt your chances of winning (statistically speaking).
Next week I’m going to interview a local Dealer who moves most of his product on EBay, and does most of his buying through networking at the LGS. He’s able to live completely off this work, and we’re going to pick his brain for how he was able to build such a successful business plan. If there is any questions you want answered in that interview, with respect to networking, buying cards/collections, using EBay/Paypal or anything else, let me know in the comments and I’ll bring them up in the interview.
Thanks for reading, and happy drafting!
Chad Havas (@torerotutor on twitter)