Welcome back to TwistedSpoon Studio! This week we'll continue our series on FUR, the custom Magic set about a beast-folk festival, with some riveting math! Get hyped!
Okay, you think I'm being facetious, but this really is the exciting part. Making the mechanics, building the world, all of that stuff-- that's fun, and it's compelling, but that isn't a Magic set. A Magic set is cards. A lot of cards. Over two-hundred cards. When you're making that much content, it's easy to get lost in the weeds. The important thing to remember is that Magic is statistics. How likely are you to draw the card you need to win? Well, that depends on how many are in your deck. And in Limited, that depends on how many you drafted. And that depends on how many are in the pool, which depends on the ASFAN, which depends on the number of that kind of card in the set.
Are you with me so far?
That's the basic methodology. With the mechanics and archetypes in mind, we're going to take a rough guess of how many cards each archetype wants with each mechanic. From there, we can figure out how many of those cards need to be in the draft pool, and then use that to calculate the ASFAN. Finally, We can use the ASFAN to solve for how many need to be in the set at common.
So let's start at the beginning. How many of each mechanic does each archetype want? Here we're going to look at 12 archetypes (our ten two-color pairs, plus alternate archetypes for two of the pairs for added variety). Note that we primarily care about draft right now.
- WU Flyers is a slow deck that relies on defense and evasion. It wants to draw 1-2 crafting cards by turns 4-6.
- UB Artifacts is a slow control deck. It wants to draw 1-2 crafting cards by turns 6-8.
- BR Sacrifice is a slow resource-management deck. It wants 2-3 crafting cards by turns 6-8.
- RG Vibrant is a midrange deck that relies on muscle. It wants 1-2 Vibrant card by turn 4.
- GW Go-wide is an aggressive tokens deck. It wants 2 traditions by turn 4.
- WB Attrition is a grindy midrange deck. It wants 2-4 traditions by turns 6-8.
- UR Tempo is a fast deck that relies on spells. It wants 2-3 vibrant cards by turns 4-6.
- BG Nine-lives is a graveyard-synergy deck. It wants 2 traditions by turns 6-8.
- RW Crafting is a fast aggressive deck. It wants 2-3 crafting cards by turns 4-6.
- GU 5-Color is a slow ramp deck. It wants 2-3 Vibrant cards by turns 8-10.
- WU Tradition is a synergistic blink deck. It wants 2 traditions by turn 4.
- GU Tradition is a slower blink synergy deck. It wants 2 traditions by turns 4-6.
Okay, so now we know how many they need during a game. How many do they need in the deck?
Hopefully this graph is clear. Using a hypergeometric calculator, I looked for how many cards you would need to have a 50% of drawing one of those cards by a given turn (the blue line). I also calculated how many you would need to draw two (the orange line) or three (grey) of those cards by a given turn. The X-axis is the number of cards drawn (7 on turn 1, 17 on turn 10), and the Y-axis is how many cards you need with the desired quality. For example, if WU wants to draw 1-2 crafting cards by turns 4-6, then you need between 2-6 crafting cards.
That converted cards in game to cards in deck; knowing the number of cards in decks will tell us the number of cards per pool. There are 12 archetypes, but only 8 drafters, so to assume an average number of drafters per archetype, we'll add up the numbers above and multiply by 2/3. To use crafting as an example again, the numbers above tell us that between all twelve archetypes, we want to see 13-27 cards with crafting in the pool. Applying our ratio of 2/3 cuts that down to roughly 8-18 cards.
Now that we know how many cards we need in the pool, we can convert to ASFAN. ASFAN just means the number of the thing you care about per draft booster (or how many you would see if a booster pack was fanned out). There are 8 players with 3 boosters each in a traditional draft environment, so that's 24 packs. to get ASFAN from our pool number, we divide by 24 to get roughly 0.3-0.75. In other words, we want to see a card with crafting in 30-75% of packs. (Yes, that's a pretty big range. We'll address that later.)
The final step is to take ASFAN to the number of cards in the set. For commons, this is pretty easy; There are roughly 100 commons, and there are ten commons per pack, so on average, you expect to see a given common 10% of the time. In other words, you can convert commons to ASFAN by dividing by 10, and ASFAN to commons by multiplying by 10. That tells us that wee need 3-7.5 cards with crafting at common. Generally, you want each archetype to be able to support up to two players, so we'll take the average and double it.
Using the methods outlined above, we get:
- Crafting: 11 cards
- Tradition: 16 cards
- Vibrant: 9 cards
Of course, this all hinges on broad assumptions about archetypes and playstyles that I haven't seen in action yet. We'll revisit this after some playtesting and make corrections as appropriate.
Mathed Out
That's all for this week. Other than game design, what's something you use math for outside of school? What's your favorite school subject? Let me know in the comments below!
We've made a lot of progress so far! Next week I'll be back with another design article about cycles in FUR. Until then, check out Star Wars: Visions on Disney+. They're short and snappy, so there's not much story to sink your teeth into, but the animation alone is so, so worth it.
See you soon!
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