In Development – The Area Under the Curve

I’ve never forgotten Larry Chen’s description of fighting a talented, quick boxer.

This was a good decade and a half ago when Larry was a second dan black belt and I was still somewhere in the rainbow of colors that says, “I know just enough to get myself hurt really badly.” Larry had sparred with a competitive boxer, and he had this to say about the experience.

“He was so fast, it felt like I was ducking my head into his punches.”

If you’ve been playing Standard for the past few months, this may be a familiar experience. You cast a creature, it gets [card vapor snag]Snagged[/card]. You recast it, they [card snapcaster mage]Snapcaster[/card] and [card vapor snag]Snag[/card] it. You try again and they [card mana leak]Leak[/card] it.

And the whole time, you’re being beaten to death by a [card delver of secrets]flying bug person[/card].

Last month, Paulo wrote a love letter to aggro-control. His big selling point for this class of decks was that their cards are useful at any point in the game.

So what does that mean? Do we have a good way to think about how concepts like “useful at any point in the game” factor into building and choosing decks?

Today, I’m going to talk about cumulative card utility—that is, what your mana curve really looks like.

The Anatomy of a Mana Curve

The concept of “the curve” is one of those core Magic ideas that we tend to run into pretty early on in our development as players. It’s hard not to learn it—you just aren’t casting all those awesome Titans and [card]Wurmcoil Engine[/card]s when your opponent gets there first with [card]Strangleroot Geist[/card]—until you ditch a few of the more expensive cards and drop in some early plays.

But to understand why Paulo loves aggro-control, we really need a more nuanced view of the mana curve.

The Traditional Curve—My Cards Come Online

Our intuitive view of the mana curve idea is that it’s all about our ability to cast our spells. I drop my first land and now I can [card]Ponder[/card]. I drop my second land, and now I can [card]Doom Blade[/card].

The basic question is “When can I cast my spells?”

You can read a lot more about finding the answers to that question here.

Cards Also Come off the Curve

In general, a [card]Rampant Growth[/card] is as awesome on turn two as it is crushingly bleak on turn six.

That is, the value of a card can shift pretty dramatically as the game moves along.

Naturally, all cards shift in value depending on turn, game state, what’s on the board, and any number of other moving elements that make up a game of Magic. But setting aside these detailed considerations, some cards are obviously of extraordinarily less value later on in the game.

Generally, these are going to be acceleration cards such as that [card]Rampant Growth[/card], or a [card]Birds of Paradise[/card]. They can also cover early “fast aggro” creatures that don’t tend to hack it in the late game.

So sometimes we have to wait for cards to come onto the curve, and sometimes cards “drop off” the curve as their relative value diminishes as the game progresses.

Instead, a Cumulative Curve

The easiest way to accommodate cards popping on and off of the curve is to take a look at a deck’s cumulative curve. That is, a sort of moving total that tries to measure how many “useful” cards a deck has at any point in the game.

Intuitively, we already know this is a thing. But what might not be intuitively obvious is just how this works, and how it might inform your choices in deck selection and deck building.

Building a Cumulative Curve

Today I’m going to look at building a cumulative curve as a conceptual idea. This won’t be a hardcore statistical analysis. Instead, it’s just a way to frame knowledge we already have, in a sense, based on looking at decklists. The main issue with that kind of knowledge is that it’s really hard to usefully compare it in your head—and that’s where it can be helpful to draw a little chart and view the knowledge in that context.

So let’s take this idea apart, step-by-step, and figure out how we want to visualize it.

The Rules of the Cumulative Curve

The basic goal is to take something that looks like this:

Delver (as played by Matt Hoey)

[deck]Main Deck:
4 Gitaxian Probe
2 Gut Shot
1 Mutagenic Growth
4 Delver of Secrets
1 Dismember
4 Ponder
1 Thought Scour
4 Vapor Snag
4 Mana Leak
3 Moorland Haunt
4 Snapcaster Mage
4 Geist of Saint Traft
2 Sword of War and Peace
3 Restoration Angel
9 Island
2 Plains
4 Glacial Fortress
4 Seachrome Coast[/deck]

-and turn it into something more like this:

These are the rules I came up with to go from decklist to nifty chart:

•Cards come online on the turn matching their CMC
•Cards that come online 2+ turns after at least 6 ramp cards get “promoted” to one turn earlier
•”Early” cards stop counting from the fourth turn onward
•Decks have “power” and “trump” cards (more on this below)
•Flashback cards become available (again) one turn after their base cost or at their flashback cost, whichever comes later
•Land abilities become available at their activation cost
•Cards are cast at their Phyrexian costs

It might seem like a lot of rules, but it’s really just an easy way to think about when we can usefully cast the cards in this deck. Acceleration makes stuff happen sooner, flashback cards turn up twice, and so forth.

Let’s take a slightly closer look at some of those card categories.

The Early Cards that Go Away

As we touched on earlier, some cards just aren’t worth much in the mid- to late-game. Consider a pretty reasonable Wolf Run list:

Wolf Run (as played by Daniel Samson)

[deck]Main Deck
1 Birds of Paradise
3 Pillar of Flame
4 Rampant Growth
4 Sphere of the Suns
2 Beast Within
4 Slagstorm
1 Viridian Corrupter
3 Huntmaster of the Fells
2 Kessig Wolf Run
4 Solemn Simulacrum
4 Primeval Titan
1 Wurmcoil Engine
3 Green Sun’s Zenith
6 Forest
3 Mountain
4 Copperline Gorge
4 Glimmerpost
3 Inkmoth Nexus
4 Rootbound Crag[/deck]

Very clearly, [card]Rampant Growth[/card] and [card]Sphere of the Suns[/card] are terrible mid- and late-game plays, so we stop counting them from the fourth turn onward. I’ve also chosen to put the Birds into this category—I’ll leave the nerdgument over whether this is legitimate or not as an exercise for the reader.

Here’s the other major “early game” situation:

U/B Zombies (as played by Michael Marlow)

[deck]Main Deck:
4 Diregraf Ghoul
4 Gravecrawler
4 Ponder
3 Tragic Slip
4 Blood Artist
3 Geth’s Verdict
3 Highborn Ghoul
3 Mortarpod
4 Phantasmal Image
4 Geralf’s Messenger
1 Bloodline Keeper
2 Killing Wave
10 Swamp
3 Cavern of Souls
4 Darkslick Shores
4 Drowned Catacomb[/deck]

I called out [card]Tragic Slip[/card] as an “early” card in this list, which is probably a subject for a more legitimate debate than Birds.

As a less controversial choice, I tagged [card]Diregraf Ghoul[/card] as another “early” card. It’s cheap, small, and enters the battlefield tapped. It’s almost comically bad after the early game. In contrast, [card]Gravecrawler[/card]’s recursion powers let you convert [card]Mortarpod[/card] and [card]Blood Artist[/card] into machineguns, after a fashion, and give it a lot of extra value in an aggro deck that wants to just keep attacking.

Power Cards

All cards are not created equal. Even if that [card]Diregraf Ghoul[/card] is a reasonable mid-game play, it’s no [card]Huntmaster of the Fells[/card], [card]Geist of Saint Traft[/card], or [card]Geralf’s Messenger[/card].

Here’s where we get to be fuzzy and qualitative. I’ve defined “power” cards as cards that “strongly advance” a deck’s game plan.

In the case of Hoey’s Delver list, for example, I classified [card]Geist of Saint Traft[/card] and [card]Restoration Angel[/card] as “power” cards. In contrast, Delver is a good card but, on its own, is not a “power” card.

Remember that this entire process is about finding a way to frame our intuitive understanding about each deck. As such, you might have completely different thoughts about what constitutes a “power” card or not.

Trump Cards

If a card is likely to win the game quickly, on its own if unopposed, it’s a trump.

Trumps include [card primeval titan]Titans[/card] in Wolf Run—and those [card sun titan]Titans[/card] that make their home in Solar Flare lists.

[card elesh norn, grand cenobite]Elesh Norn[/card] is a trump. [card]Wolfir Silverheart[/card] is a trump.

Essentially, anything that comes pre-labeled, “deal with me or die,” is a trump.

Actually Building the Curve

The actual guts of building the curve are pretty straightforward.

With all the considerations we just talked about in mind, place the deck’s cards (and land-based abilities) out on the curve, like this:

“Promote” cards forward on the curve if there’s enough acceleration to warrant it.

Then, walking your way up the curve, add the cards together.

Finally, remove any “early” cards from turns four and higher.

-and that’s the general purpose cumulative mana curve for R/G Aggro. If you wanted to convert that into a nice visual, it would look like this:

Curving Out in Standard

Let’s set aside the “power” and “trump” categories and focus on general curves. If we compare a selection of major archetypes from the current Standard, their curves look like this:

You may suddenly find yourself wondering why you would ever, ever play anything other than Delver. Its curve starts earlier and stays “richer” with options than every other deck, right up until Solar Flare barely catches up with it.

Two things are true here.

First, Delver is actually a really, really good deck.

Second, there’s more to this story, and that’s where the idea of power cards and trumps comes in. Let’s check out these archetypes individually.


Again, check out that beautiful curve. The Delver list benefits from the fact that, as Paulo said, its cards are useful throughout the course of the game. This is why the overall curve rapidly rises to more than forty useful cards and then just stays there.

Another way to think about the message here is that “all your non-land cards, and even some of your lands, are useful through most of the game.”

When we turn our eye toward power cards, we see that Delver plugs into them at turns three ([card geist of saint traft]Geist[/card]) and four ([card restoration angel]Angel[/card]), and then trucks along with its not-quite-ten cards just fine into the late game.

Notably, Delver has no trumps.

This is part of why Delver can be a cognitively intensive deck. You dont really get to just slap down your win condition, breathe a sigh of relief, and watch it steamroll your opponent. All of Delver’s cards are useful in the late game and that’s good, because you’ll need them.

Solar Flare

If Delver rises swiftly and maintains its altitude, the Solar Flare cumulative curve is more stately. Taken in isolation, this curve says that you won’t be beating Delver with Solar Flare, and really should have picked another option.

The power cards don’t help much there, either. They’re also just ever so much less abundant than Delver at the same mana costs.


Check out the trumps. Those are why you’d play a Solar Flare list at all. Instead of requiring the dynamic control we see in an aggro-control list like Delver, the Solar Flare list steadily builds up its card quality, generating a wall of resistance that culminates in landing a series of crushing, game-ending blows.

Seen in this light, the reason you’d choose a pure control list such as Solar Flare is much clearer—as are some of the risk you face in the early game.

Wolf Run

Wolf Run is a great example of a deck where many of its cards lack value in the late game. All of those ramp spells spike the deck’s cumulative curve around turn three, then things kind of flatten out after that. All this is in aid of hitting those trumps a little bit sooner and a little bit more than a deck like Solar Flare.

The obvious advantage is just that—you hit those trumps sooner and just a bit more.

The less obvious advantage is that the spike around turn three includes lots of cards that help blunt an early aggro rush. By hitting this spike sooner than Solar Flare, the Wolf Run deck should, on average, be a little bit less likely to get rolled by fast aggro.

Fast Aggro Options

The cumulative curves on the fast aggro lists all feel pretty similar to me, at least in terms of the most general “all the cards” tally. What I find interesting about the aggro lists we’re looking at here is that they don’t particularly outpace Delver.

The Zombies lists, in particular, have a sort of “too little, too late” approach to bringing their power and trump cards online. In contrast, R/G Aggro brings its power and trump cards online much earlier, making it a credible threat against the growing card abundance of decks like Solar Flare and Delver.

The Area under Your Curve

The take-home from this kind of “conceptual” analysis is pretty open to interpretation. It is, after all, really just a way for you to visualize how thoughts you might already have been having about how the decks you’re playing, or playing against, work.

And that can be a big deal, really. Is your deck faltering in the long game in a way you don’t understand? Or maybe you’re finding that you changed something, and now your Wolf Run deck is dying to fast aggro rushes to an incredible degree. Maybe it’s time to try laying your deck out on the curve—the cumulative curve—and seeing how it stacks up against the opposition.

magic (at) alexandershearer.com
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