Relativity in Magic

Relativity in science is a complex concept. The simplest way to explain it is that when two objects interact their properties only matter in terms of the differences between them. Imagine two balls that are 3 meters apart with a string just long enough to reach connecting them. Now imagine both balls begin rolling forwards at the same speed. The string is still just barely long enough no matter what speed they move at as long as it's the same, since they're still 3 meters apart relative to each other.

Where this gets complicated is when you have more than two objects. If one is still, a second is moving, and the third is moving twice as fast as the second in the same direction, how fast is the first object moving? From its perspective, it is still, but from the perspective of the third object the first one is moving away at twice the speed of the second object.

So how does this apply to Magic? Well, we have cards with comparable properties like mana cost, power, and toughness, and they interact relative to other cards each game. Of course, it's obvious enough that a Rumbling Baloth is twice the size of Grizzly Bears, but I believe the impact of relativity needs to be looked at in more detail in terms of comparing formats.

Dig Through Time saw play in several Standard decks that made the Top 8 of the most recent Pro Tour. However, in Modern and Legacy, Treasure Cruise has seen far more play. Why is this? 

The commonly accepted explanation is that Dig Through Time is more powerful, but in formats where your graveyard fills quickly being able to cast Treasure Cruise for just one mana puts it over the top. However, Louis Scott-Vargas chose to play Dig Through Time in his Vintage deck, as he mentions in his article on Standard Jeskai. Why would you want Dig Through Time over Treasure Cruise in a format where the graveyard fills even faster than in Legacy?

To analyze this, I first listed the differences between Dig Through Time and Treasure Cruise. There are five:

• Colored mana
• Colorless mana (relevant due to delve)
• Instant versus sorcery speed
• Card advantage
• Card selection

Then, I looked at them relative to each of the four formats discussed above and looked at the differences between them.

There's only one difference between Treasure Cruise and Dig Through Time that would make you prefer Dig Through Time in Vintage but not Legacy/Modern: the amount of redundancy available in the format. In Vintage, the restricted list means decks are actually less consistent than in Legacy as the most powerful cards are limited to one-ofs.

Standard, like Vintage, has less redundant cards available due to the smaller card pool rather than a restricted list. So, if consistency in the format determines how good Dig Through Time is compared to Treasure Cruise, what can that tell us?

By playing Dig Through Time over Treasure Cruise you're giving up one card. Since card advantage scales linearly (the difference between one card and two is the same as the difference between two cards and three), we can conclude that powerful card selection is worth card disadvantage. It just so happens that there's a card in standard right now that is seeing no play yet is likely the most card selection ever given by a single card:

Now, in a format where Dig Through Time can be cast for two mana, the card advantage makes it much better. But in standard, Taigam's Scheming is at the very least worth testing. Comparisons to Index are flawed as being able to remove bad draws is what matters here. Scry 3 is already strong, and this is essentially Scry 5. What's more, it enables Dig Through Time as well meaning you can run eight selection spells!

This is only scratching the surface of what relativity brings to Magic. With this kind of analysis we can make statements far more decisively than simply using intuition. Eventually, we could have complete maps of a format and how cards interact with each other to form the metagame. There's an enormous amount of Magic theory that has gone unexplored because it seems impossible to compare such different cards as Grizzly Bears and Lightning Bolt, let alone the hundreds of cards that can appear in a single draft, but we have the tools to do so at our disposal.

For now, here's a few topics I think are in need of more analysis:

• Monastery Swiftspear has made a name for itself in eternal formats. Since I'm pretty sure Raging Goblin with 1 more toughness isn't what Legacy players are looking for, could Seeker of the Way and Jeskai Elder be playable as well?
• Some cantrips that give you card selection are banned in modern, and Brainstorm is format-defining in legacy. How do various types of selection compare, and how powerful does one have to be to see play?
• Standard is in a very unique place in terms of removal right now. Removal that costs two or less mana is highly conditional, usually caring about power or toughness, and for one of the first times in Magic history there's no four mana board wipe. How does this change affect the power level of various types of cards?