Collecting MTG Arena: Part 2 (of 2)

Today I want to cover a more few topics related to collecting on MTG Arena. If you want to know the method to collect 4x sets most efficiently on MTG Arena, see Part 1.

• Are Traditional drafts or Ranked drafts better for collecting sets (or better in general)?
• How many gems/$ does it take to collect a 4x Rare set on average?
• Where do I get my data from? (And how you can use that data too, if you want.)
• What small things can MTG Arena do to improve the collector experience?
• What small things can MTG Arena do to improve the general player experience?

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Are Traditional drafts or Ranked drafts better for collecting sets (or better in general)​?

Time for some charts!

Obviously, you earn way more reward packs playing Traditional drafts. But it costs twice as much, so the first graph's not a terribly useful comparison point. It does show that packs won begins at about the same place and is roughly linear, but Traditional has a much steeper slope. 

More useful is the second graph. Net gems is "Entry Fee minus Gems Won;" it's equivalent to "how many Gems did you lose playing this draft?" It's clear that if your win% is terrible, you should avoid Traditional drafts. If you're Rare drafting, your win% will probably be terrible. So you'll lose nearly twice as many Gems per draft if you do Traditional drafts.

Once you get up to 62% win%, they're the same 215 Gems lost per draft, and Traditional grows rapidly from there. You'll be able to "go infinite" with Traditional drafts at 66.6%, which is tough but certainly doable. If you're playing Ranked, you'll need an almost impossible 75% to go infinite.

An even more fair comparison is this third graph, which divides the Gems you lost by the number of packs you won. Essentially, this is how much you "bought" each pack for. I consider drafted packs and reward packs to be the same for this comparison. You'll note that even if your win% is down at 45%, with a Ranked draft you can still "buy" packs for 100 Gems each, instead of the 200 Gems the store charges. So, never buy packs from the store - you'll get the twice the value on average even if you do terribly in a Ranked draft.

Drafted packs and reward packs are of course not the same - drafted packs have 1 R/M, 3U, 10C, while reward packs have 1 R/M with a 1/12 chance of a wildcard, 2 U, 5 C. Drafted packs may have passed Rares, reward packs contain duplicate-protected Rares. But for our purposes of collecting R/M, it's easier to assume they're about the same.

So if you can manage a 58% win%, which is possible even if heavily Rare-drafting, then the two types are equivalent in terms of the number of gems you spend to "buy" each pack. Above that, Traditional rapidly sinks to packs costing 0 (you're going infinite).

But another aspect of this I wanted to examine is the amount of time spent. While that's impossible to measure directly, it is possible to figure out the average number of games you play with each type of draft, shown in the fourth graph. With traditional, you are playing between 60-70% more games with each draft, plus there's 2-4 minutes of sideboarding every match. You can easily do 3 Ranked drafts for every 2 Traditional ones, and it's quite possible for you to do 2 for every 1.

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Ranked drafts have another aspect, that's either a feature or a downside, depending on what you're trying to do. That's the "ranking up" part. As you win more Ranked drafts, the competition will get noticeably better. Once you're Platinum 2 or higher, you'll be facing almost all competent players playing real decks. And it only gets harder from there. Now, it still isn't impossible - I managed to get all the way to Mythic (and stayed top 1000!) while Rare-drafting RNA. (I had a 64% win% through 15 drafts, though it eventually reverted back to 60%.) But if your goal is collecting, you really DON'T want to face better and better players as you go along. But if you do manage to get all the way up to Mythic top 1000, that's probably a worthy goal. So it depends; you might want to put Rare-drafting on the back burner for a while if you make Diamond 3 or so. Traditional drafts match solely based on record and ignore rank (as far as we know) and you'll face the same average level of competition all the time. In my experience, Traditional has similar competition to Ranked drafts if you're Platinum 3ish or lower (best guess, no way to calculate it), but almost certainly Traditional has easier competition on average above that.

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So, to summarize:

• If your win% is below 58%, you should be playing Ranked drafts to minimize losses, regardless of anything else.
• If your win% is between 58-62%, you have a choice of priorities - do you want to minimize the cost of each pack (do Traditional), or do you want to minimize the Gems you lose each draft (do Ranked). As we're trying to collect Rares efficiently, you should lean towards Traditional, as you'll spend less to acquire Rares in the long run.
• If your win% is above 62%, you should do Traditional drafts.
• If your win% is above 66.6%, congratulations, you are a superior being and have achieved INFINITY.

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A few other relevant factoids to help decide what's best for you:

• Ranked drafts are the only way you (currently) can draft older sets, so no choice there. If you're working on collecting the current set, you might have to wait a few weeks for Ranked drafts to become available.
• Ranked drafts has the competition get better the more you play and the more you win, but you might be able to get to Mythic.
• Traditional drafts take 60-70% more games to complete on average, plus sideboarding time.
• Traditional drafts have much higher variance in terms of "making back your gems". I didn't do the full calculation for all win%, but the standard deviation of Gems won in Traditional draft is roughly 3x that of Ranked draft. With Ranked drafts you'll always lose Gems, but steadily and never too much. A few unlucky 0 or 1 win Traditional drafts can wipe out a considerable chunk of Gems. So to do Traditional drafts you need to be able to absorb some losses due to variance without running out of Gems.
• If you've already reached the Critical Point and opened packs to get 4x Rares, you should give some extra weight to Traditional drafts. You don't have to sabotage your own win% by taking a ton of crap Rares anymore, so you might hit 62% win% against normal competition. And if all you need are Mythics, then reward packs are likely more valuable to you than drafted ones. Opening a Mythic you don't have 4 of in a draft becomes more and more unlikely as you collect more of them, and bots usually only pass the bottom 3 Mythics of a set, which you probably already have 4 of.

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How many gems/$ does it take to collect a 4x Rare/Mythic set on average?

Your local tax rate notably impacts what gems cost, anywhere from 200 gems per $1 to 182 gems per $1 (my rate), or even lower. Also, maybe your currency isn't dollars. So I'm going to leave everything in terms of Gems, you can figure out your own conversion from there.

Here's graph #2 from above in table form.

Assuming 55% win% in Ranked drafts while Rare-drafting, and let's say the 47 drafts we calculated last time to collect a 4x set, you'll spend 15,600 Gems. But that's the absolute ceiling, as I said last time. If it's more like 40 drafts, that's 13,300 Gems (and you probably paid for some of those with free Gold). If you win% is 60%, it goes down to 9,300 Gems.

Real-world check: For M19, I started with 38 Rares and 2 Mythics from the tutorial. I ended up needing 31 more drafts, and I ran terribly while Rare-drafting and had an abysmal 49% win%. On average I should have spent 12,900 Gems to collect the 4x Rare set. I actually spent 13,100 Gems, ~$70 for me. Seems very plausible, as the above table is average values, not exact.

(I didn't track things closely from the beginning of GRN and RNA, so I can't give you my exact number of drafts needed there.)

At the same time that you collect 4x the Rares on Arena, you'll get about half the Mythics. To compare to MTGO, if you were buying the equivalent cards (4x each Rare and 2x each Mythic), for GRN it would cost you ~$280, and for RNA ~$240. So you can immediately see that it's way, way cheaper to collect sets on Arena. To be fair, you can't later sell the cards like you can on MTGO, which depending on when you sell them may make that much closer to equivalent. But even if it costs you ~$70 on MTG Arena (and it might be ~$50), it seems unlikely that if you sell that much GRN or RNA in August 2020 (so you can use it through all of standard) that you won't have lost that much value, and you still get to keep all the cards on Arena!

A lot of this depends on knowing your win%. How do you get that? There's really no way to figure it out except to record all your games, and actually figure it out. The spreadsheet from part 1 gives you an easy way to do that. For a new set, you just have to guess based on other sets until you're ~10 drafts in, by which point hopefully it's settled down a bit.

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Where does your data come from?

I'm all about setting up simulations to get answers. Modern computers exist, yo, and while I totally respect those who mathematically derive answers from first principles, it's much faster for me personally to set up "virtual" drafts. That's where this data comes from - I ran 50K virtual drafts at each win% from 45-75% and averaged out the results.

My programming language of choice is spreadsheets (Excel specifically). I'm not a computer scientist, I work with what I know, and that's what I know well enough to set it up quickly and correctly (I believe). Now that it's set up, it only takes about a minute to get data from 50K Arena drafts (Ranked or Traditional). Anyway, I thought I'd share these sheets, in case someone else wants to take it even further, there's a lot you can do with full draft simulation. (Standard deviation of the values/error bars? Are there more fair prize structures to explore?) As before, provided as is, no tech support or warranty.

Calculate Arena Drafts sheet) This sheet simulates Arena drafts, both Ranked and Traditional, and calculates averages for them for a variety of data.

Simulate Collecting sheet) This sheet simulates "collecting in general". I used it to figure out how many packs on average you need to open to get 4x a Rare set without using wildcards or trading. If you only wanted to collect 1 of each Rare, it's the well-known Coupon collector's problem. But collecting 4 of each doesn't seem to have an accurate approximation that I could find, so I set up a simulation for it.

Note that these sheets have real simulations, so they're bigger than your average data tracking sheet. I haven't tested Google Sheets versions, but I wouldn't be surprised if they don't work or are very slow. The data from both sheets is (not surprisingly) very noisy, so it does take a lot of trials to get reliable averages.

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What can MTG Arena do to improve the collector experience?

MTG Arena isn't really designed for collectors at the moment. That's fine! Wizards really needed to focus on the core gameplay, and they really knocked it out of the park. While I imagine there's still several higher priorities (ioS/Mac version, Brawl, human drafts, and chess-clock 3000 player tournaments would be on my list), eventually they'll want to add in a few tools to make it easier to collect on MTGA. And some of these might be very simple and require minimal programming time, so maybe we could get them sooner!

• Somewhere (in the search filter?) there would be an option to turn "Collector Mode" on, just like for "Advanced Play Modes". I'm very conscious that Wizards wants to minimize the interface for the majority of players. So everything I list below would be "hidden" unless you have Collector Mode on, and if you do, it would remember that when you log back in.
• If there's a single thing that would dramatically improve the collector experience, it would be the option to put a small "<4" on cards you have less than 4 of WHILE drafting. Right now, to check whether you already have 4 of a card in your collection and then start drafting again it takes 10 clicks and 25 seconds. For a single card! So realistically, you have to maintain a spreadsheet and continually update that; it takes less time but still quite a bit. If we could just have an icon that would let you know if you have less than 4 of each card while drafting, that would be utterly amazing and most collectors wouldn't have to maintain a spreadsheet anymore! I would, because I like to track everything, but it would still speed up my drafting considerably. More drafts = more gems I (and other players) spend, so it's kind of win-win.
• Right now, the cards in your collection are ordered in what I call "color-blob" order. They're not by collector's number, or alphabetically, or any other system that we can easily sort to on a spreadsheet. The system appears to be "Color->Converted Mana Cost->Alphabetical by name->Set (by release order)", but I wouldn't stake my life on it. After the 5 colors, we get Azorius/Orzhov/Dimir/Izzet/Rakdos/Golgari/Gruul/Boros/Selesneya/Simic, then Esper/Grixis/Jund/Naya/Bant. It appears they sort in WUBRG order by whatever symbol is literally the leftmost printed one. It turns out, that's really not super helpful for anybody. After that, then Chamber Sentry for some reason has a special spot, then non-basic lands that aren't tied to 2 color pairs, then artifacts (including Sphinx of the Guildpact, who for an unknown reason is not special like Chamber Sentry). If you have to sit down and spend an hour analyzing the sorting system to figure out what the heck it's doing, it's probably not serving its purpose. I would really love an option to have the cards in our collection be sorted in a more "traditional" order like Alphabetical or Collector's # or anything that the Arena devs didn't seem to invent themselves.
• The "COLLECTED" and "NOT COLLECTED" selectors would be replaced with "COLLECTED 4x" and "NOT COLLECTED 4x" if you have Collector Mode on. The current system is really only useful if you play Singleton and nothing else.
• There would be an option to "EXCLUDE NON-BOOSTER CARDS" in the card filter. When looking at your collection, no matter the set, there's always going to be massive holes for the "Planeswalker Deck" and "Buy-a-Box" cards, plus a bunch of others if you're a Core set. And there's also a few promos that they've released on MTGA - it really annoys me every time I look at my collection and it shows me I don't have any Firemind's Research, even though I do right next to it, because there's a promo. If you're trying to figure out which cards you still need to get from drafting, it's very annoying to have these rando cards show up in your collection. Without an option to sort by collector's number (which puts them at the end), there's absolutely no way without doing internet research to even figure out WHICH cards are the non-booster ones.
• A counter for how many Rares/Mythics you own of a set. If you have a single set selected, it would show "XXX/212 Rares" and "XX/60 Mythics" in small grey italics somewhere, probably just to the right of the search options.
• A tiny bit of Uncommon duplicate protection. For example, maybe the first Uncommon you get each day from your daily win bonus (the 5th win) would be not a duplicate. Finishing the Uncommons is now noticeably harder than finishing the Rares if you're focused on collecting, and just a tiny bump would bring them a lot closer. Maybe special constructed events that award cards (like Singleton or Momir) could also have one of the Uncommon rewards be protected.

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As long as we're here, what can MTG Arena do to improve the general Arena experience?

Here's some small things that would improve my general Arena experience, not tied to collecting. Again, not as important as the larger stuff, but may be much easier to implement.

• By the time I get to scrying (or putting cards back, if the London mulligan happens), I have completely forgotten whether I'm playing or drawing. Yes, I just saw it 5 seconds ago while mulliganing, but I play lots of games, it's easy to forget. Why can't that info stay on the screen until the first turn actually starts? Is there some reason it disappears as fast as the greatest thief in the multiverse? (*sniff* Dack Fayden *sniff*)
• Have a card filter option for "EXCLUDE UNSELECTED COLORS". When I'm trying to build a B/W deck, it's kind of super annoying that I see every GW card and land that I own, and every RB card and land that I own, etc. If I'm trying to build a mono-green deck, maybe I'd like to include Shalai, Voice of Plenty? Uh no, I would not, thanks. It's especially egregious as we're right in the middle of multi-color sets, so there's a ton of cards you can't use you have to wade through when deck building. You can still allow cards that are hybrid of one of the colors, but please take away the rest, it's super tedious.
• Having to count your mana all the time. Clearly, the game knows how many untapped mana sources you have at any one time. When I'm casting an X spell, why do I have to count everything, and then start all over again if I'm one too high? Or feel really bad if I'm one too low? Why isn't there an option for "ALL MANA" with X spells? (Or for Momir, where it would make it so much faster.) In general, I'd love to have an option to have a tiny number that shows you how much mana you would have if you activate a mana ability each of your lands/artifacts/creatures on the board. That's by far what takes the most math and the most non-thinking time in my games. Especially since the computer already seems to do this calculation but won't share it with us.
• MTGO has a key you can hold down for "Tap a dual land for whatever the first mana is, probably because you just need to spend it for a generic cost." When I do need to tap my lands individually, because I want to keep specific colors up, it takes a lot of time to fiddle with selecting colors when it usually doesn't matter at all after the first color. This is the one (and only) way in which MTGO's tapping is better than Arena's. This would probably save me 20 seconds every constructed game. Maybe there is a way to skip selecting useless colors and I just don't know it?
• I love that the deck stats counts the cards of each color for you, but it'd be nice to have an option to have it count "mana symbols" instead. I've always felt that counting mana symbols is a better way to figure out an appropriate mana base, especially in limited.
• Why aren't all daily quests worth 750 Gold? Right now, "rerolling" the quest has nothing to do with whether you actually WANT to cast 20 red or blue spells while your favorite deck is mono-green. It's only about trying to get 750 Gold quests, regardless of whether you want to do that specific quest or not. I guess part of it is to limit us to X free gold per day on average, maybe, but it feels weird to me to throw away quests I wouldn't mind at all to get quests I don't really want to do in pursuit of extra Gold. But in terms of value, it's always worth trying to do it. Maybe that's their sneaky way of forcing us to try other decks?

That's all I've got to say about my recent obsession with collecting Arena. I know collecting sets isn't for everyone, but it's the most fun way for me to get my Magic fix. Arena is an amazing new tool for all of Magic, and there's a ton of different things you can focus on achieving with it. This is one way you can "play Arena" that's a little more subtle than most, so I wanted to share what I've learned about it.

Promise I'll write a funny article one of these days! Until then, keep on playing Arena and collecting your sets!