March 19, 2020
unqualified – adjective : (of a person) not officially recognized as a practitioner of a particular profession or activity through having satisfied the relevant conditions or requirements
As someone with a degree in English, I’m naturally curious about numbers, data, trends, statistics, variables, and probabilities.
OK, look, not every English major can, or wants to, teach. I’ve worked with computers for the entirety of my post-graduation life. My first job out of college (not counting teaching baseball fundamentals to shockingly uncoordinated children during a summer program) was doing computerized data entry. The money was decent (as in, it was greater than $0, which is what I was making before I was hired) and I learned a lot…like how it was better to work the night shift so I could avoid the boss and listen to awful metal music without annoying any coworkers.
But thus began my love of data.
That’s a lie. I’m not actually sure where my love of data started, since I don’t actually love data. With one notable exception:
After returning to Magic in 2017 I started tracking every Magic pack I opened in an Excel spreadsheet. Each entry included:
- Date the pack was opened
- Rare or mythic in the pack
- Value of the rare or mythic on the date it was opened
- Value of the rare or mythic on the date I last checked
- Foil (if any) in the pack
- Value of the foil (if any) at the time it was opened (and current value when last checked)
- Where the pack came from (booster box, bundle or fat pack, single booster, etc.)
It was fun – depressing too, but fun – to maintain this database for a time, though I didn’t add to it often because I didn’t open packs often. There’s a story there, but I’m not ready to tell it.
Yes, withholding stories is becoming a recurring theme on this blog, and yes, I am intentionally building up a backlog of stories to tell. Some I’m not quite sure HOW to tell, and some are more serious and will require a different approach that I’m not ready to wrangle with quite yet. In time…
Anywayhow, back to the database. Though I wasn’t opening a plethora of packs, I was logging the ones I did open faithfully. Then last July my son and I went to a Core Set 2020 2-headed giant prerelease where we combined the cards from the 12 packs we received to build our decks. When we got home, we took turns choosing which cards we wanted to add to our respective collections. I wasn’t sure how to log what cards I ended up with from that prerelease…so I just never did. Nor did I log anything I opened after that because…I don’t know…the database wasn’t up to date, and I didn’t want it to be half-assed and missing entries?
Consequently, the spreadsheet hasn’t been updated since last July. I bring this up not to reinforce how nerdy and pathetic my behaviors are, but because the spreadsheet contains the following entry:
That was, until a few weeks ago, the last Hour of Devastation pack I had opened. Back in July that infernal Apocalypse Demon so infuriated me that I chose not to open any of the remaining HOU packs I had lying about. Why was I so angry at a demon? Was it because it was a bobo rare? No. I mean, it was, but that’s not why I was angry. I’ve opened plenty of bobos and never let it stop me from trying my luck again.
I was upset about that demon because, prior to that pack, I’d opened 22 packs of HOU. And out of those 22 packs I had gotten exactly ZERO mythic rares. That lousy demon made me 0 for 23.
So today, my friends, I am going to delve into the statistics behind this ignominious accomplishment/crowning achievement. What makes me think that I, with my useless-but-expensive B.A. in English, can undertake such a daunting mathematical undertaking? Fury. And hubris. But mostly fury.
Let’s get started!
The odds of opening a mythic rare in a booster pack (in HOU, as well as now) is “approximately 1:8”, or 12.5%. The odds of opening zero mythic rares in 23 booster packs is, therefore, .0023684%.
Crazy, huh?
What do you mean, “that can’t be right”?
Do I have to show my work? What is this, middle school?
Alright. Fine. You want more details about how the answer is .0023684%? Here is the equation I used to reach my mathematical conclusion:
For the mathematically deficient, the above can be used to determine the percentages of getting no mythics from opening various numbers of packs, leading to the following results:
Odds of opening no mythics in:
1 pack: 87.5%
2 packs: 76.5%
3 packs: 67%
5 packs: 51.3%
10 packs: 26.3%
15 packs: 13.4%
20 packs: 6.9%
23 packs: .0023684%
What do you mean, “that’s still not right”? The trend is obvious and the results incontrovertible. You can’t argue with math, friends.
Alright. Fine. I double-checked the numbers, and that last one is just a little off. “Traditional” (i.e. lame) math actually says there’s a 4.6% chance of opening 23 packs without getting a mythic. So I was pretty close initially.
Besides, the math just obscures the point I’m trying to make: I’d opened 23 packs of Hour of Devastation WITHOUT GETTING A MYTHIC!
Whatever number you want to attach to that, it’s absurd. Unheard of. Unprecedented. In what universe does something with a 4.6% chance of happening ACTUALLY HAPPEN?
Fast forward to a few weeks ago, when I opened two more HOU boosters in order to build an Amonkhet-block sealed deck. The first pack I opened contained this:
Twenty-four packs, no mythics. We’re down to a 4.0% chance of pulling that off. Pack #25 is, naturally, a foregone conclusion. We both know where this runaway train is headed. I open it, no longer caring what I get, even starting to root for a standard rare so I can continue this comical parade of ignominy. Here’s what I see at the back of the pack:
It’s not just a mythic. It’s a GOOD mythic. Among the best cards in the HOU set. I actually kind of wish my son had gotten it, since it would be a fun addition to the remarkably solid “draw two” deck he built from a sealed pool of Throne of Eldraine cards. But he got no mythics in his AKH-block cardpool, while I got a planeswalker and a GOD.
The HOU mythic drought ended with a raining crescendo of locusts (well, one huge one, anyway) and I’m conflicted. I’m happy to get the card, don’t get me wrong. And this is positive momentum towards shattering the bobo-rare shackles still clinging to my ankles. But a streak is over, and there’s a sadness to that. That streak was special. I mean, yeah, it was “specially bad”, but it also felt right somehow.
No one remembers baseball players with career batting averages of .230, but spend your career below the Mendoza Line*, and you WILL be remembered. And I wasn’t just cracking packs at a below-the-Mendoza-Line rate here. I was in a 2019 Chris Davis, 0-for-56 slump. It was ghastly, and it was glorious, and I was strangely sad to see it end.
Coming soon – the kid actually built his deck! How will two grizzled gladiators (read as: total incompetents) fair in a AKH-block sealed pool showdown?
(It’s clearly not possible to hype up a sealed deck match with a 12-year old. I apologize for lamely trying.)
* Apologies to non-American readers; let me know if there’s something analogous in football/cricket/rugby/curling.**
** Apologies to readers from countries whose national sport wasn’t listed; let me know what I should be referencing when I pretend to know lots about sports in future posts.
Casual Magicking 
One thought on “An English Major Learns You Some Statistics”