Recently, Mike Flores used the term “velocity” to describe a certain type of deck behavior. In that article, however, he merely noted it as a conceptual notion, without offering any theoretical context or application. He attempted to demonstrate its presence, but in this author’s opinion and others, he did not accurately describe his observation in terms that have useful application. While what he describes is not deniable, his descriptions are ex post facto observations, and not a theory to be applied in a logistical matter to deck construction or play skill. This article will attempt to define velocity in terms that are more in line with other concrete Magic theories, and identify its application.

Background

Conceptually, velocity describes a scenario where cards constantly shift from place to place throughout the course of play. Any storm-based combo deck relies on playing several spells per turn; and in order to do so it most likely requires a lot of draw, search and mana acceleration. Since the deck is constructed to do so, it can be described as a “high-velocity deck.” The inverse is a “low-velocity”, or inert, deck is one which generally does not do so. The Rock is an example of an intuitively low velocity deck (at least relative to its opponent) – it plays out threats in a somewhat sequential answer and gains card advantage through control rather than through massive draw, tutoring power, or by dumping its hand on the table.

Several questions must be answered in order to determine the usefulness of this description. How do we qualitatively define velocity? Is it merely a descriptive concept, or can it actually be measured? As with any intellectual undertaking, we will attempt to answer these questions through rigorous test conditions and applications of our definitions.

Analysis

Initially, assume that the velocity describes a rate rather than a basic count. In a general test of this assumption, we see it is a pretty fundamental conclusion, even with an imprecise understanding of velocity: it is inconclusive if we only know that a deck drew 7 cards — did they draw seven cards over the course of seven turns, or did they draw seven cards over the course of only one? It should therefore be immediately concluded that velocity at least describes a rate of some sort.

As Flores initially described, it seems that conceptually, velocity is depicted as a measurement of how often cards move from one zone of play to another. Cards that go from hand to graveyard, library to hand, hand to play, graveyard to hand, etc. all constitute valid zone movements. This does not include the initial hand of cards, although it would count a mulligan using Serum Powder. In a similar vein, it will not include the first card drawn during the draw step, since that draw has nothing to do with the deck itself.

With this understanding, the following equation can be used to define velocity as our hypothesis:

Velocity = Total Number of Zone Movements per Number of Turns Accumulated

An illustration: FrummyChick opts to play first. On turn 1, FrummyChick plays an Island and says go. That counts as one zone movement; as a single card, an Island, changed zones; from hand to play. On turn 2, FrummyChick draws a card at the beginning of her turn and plays Accumulated Knowledge for 1. This turn, she has a zone movement count (“ZMC”) of 3: one land played, one AK that goes from hand to graveyard, and one additional card that goes from library to hand. Over the course of two turns, FrummyChick actualized 4 total zone movements over 2 turns. Thus, her rate of velocity is 4 / 2 = 2 movements per turn on average.

This example, however, is merely an illustration. Whether or not this actual definition is true, however, will require some rigorous analysis. This article will study ZMC over the course of actual games, rather than randomly chosen sets of turns. Also note that similar to drawing cards, we divide by “natural” turns, not those that are not the result of a player casting Time Warp, etc. “Artificial” turns are considered part of the originating “natural” turn.

A deck revolved around Fluctuator and Living Death is an example of a deck that strives for a very high velocity, at least according to this definition. Assume the following progression of events in a Legacy Fluctuator deck:

Turn 1: Swamp, Mox Diamond (pitch Swamp) –> Fluctuator; Cycle through 4 Primoc Escapee, 4 Sandbar Serpent, 4 Keeneye Aven, 4 Barkhide Mauler

Turn 2: Swamp –> Dark Ritual –> Living Death

Turn 3: Attack for 52 damage and win

In this example, turn 1 started with a ZMC of 4: 1 for the land, 2 for the Mox and its pitched Swamp, and 1 for the Fluctuator. It then cycled 16 cards — since each card cycled results in a ZMC of 2 (one card from hand to graveyard, one card from library to hand), it accumulated an additional 32 zone movements for a total ZMC of 36 for that turn. Turn 2 begins with another 3 ZMC, but the Living Death returns 16 creatures from graveyard to play for a total of 19 ZMC. Turn 3 has no zone movements, so it has a ZMC of zero.

Plugging in our numbers, we get 36 + 19 + 0 = 55 zone movements over 3 turns; so 55 / 3 = 18.3 “units of” velocity. For the sake of clarity, this article will use term “ampt”, or average movements per turn, to describe this unit of velocity. At 18.3 ampt, Fluctuator.dec clearly has a very high velocity by comparison to your average deck.

For something a bit less extreme, analyze the ampt for a deck like White Weenie (don’t pay attention to the build, it’s just an illustration):

Turn 1: Plains –> Suntail Hawk (ZMC = 2)

Turn 2: Plains –> Leonin Skyhunter (ZMC = 2)

Turn 3: Plains –> Mask of Memory, equip, attack to draw 2, discard 1 (ZMC = 5)

Turn 4: Plains –> Empyreal Plate, equip [5 cards in hand], attack to draw 2, discard 1 (ZMC = 5)

Turn 5: Empyreal Plate #2, equip [6 cards in hand], attack for win. [No card draw since game is over.] (ZMC = 1)

Total ZMC = 2 + 2 + 5 + 5 + 1 = 15 ZMC over 5 turns, for a velocity of 3 ampt. It has a decent velocity, to be sure. Note that it has an interesting correlation to playing a land, a spell, and netting one card off of a Mask of Memory. Regardless, it is clearly not even remotely close in velocity to Fluctuator, even though it ends the game only two turns later.

This prompts further discussion to determine how important this metric is to understanding the efficiency of a deck: what does velocity actually affect? Does it matter at all? Analyzing the same game using Grafted Wargear in place of the Mask will show some interesting results that can be used as a better basis of comparison:

Turn 1: Plains –> Suntail Hawk (ZMC = 2)

Turn 2: Plains –> Leonin Skyhunter (ZMC = 2)

Turn 3: Plains –> Grafted Wargear, equip (ZMC = 2)

Turn 4: Plains –> Empyreal Plate, equip [4 cards in hand] (ZMC =2)

Turn 5: Draw for 5 cards in hand, attack for win. (ZMC = 0)

Total ZMC = 2 + 2 + 2 + 2 + 0 = 8 over 5 turns, for a velocity of 1.6 ampt. This relates to the average of playing a spell along with a land almost every turn. By comparison to example above, though, the difference between 1.6 and 3 ampt does not necessarily translate into a different clock, even though the version running Mask of Memory has a velocity almost 87% more than the version without. Similarly, a ratings difference from 18.3 ampt is almost twelve times “faster” than its 1.6 ampt parallel, but does not necessarily translate into a significantly better deck.

If the equation above actually describes velocity, the indication seems to initially lean on the fact that the measurement of velocity may not even matter. Arguably, that is a logical conclusion — the ampt powered out by a deck do not necessarily translate into a better or faster deck, especially when studying the comparison between the two WW builds. There is reason to believe, though, that velocity actually does matter, and may be an important element in deck construction since it potentially translates into some interesting theoretical elements.

In the Fluctuator example, if it cannot cycle enough cards into the graveyard, it might not draw into a Living Death, or it might not be able to cycle through enough creatures to stock a graveyard for Living Death to be a near-fatal threat. In either case, velocity might be used to describe why the deck might “fizzle” — if its velocity falls below a certain threshold, the deck may fall apart. It must surpass its required minimum velocity, or inertia, in order to succeed. This process will be labeled as “overcoming inertia”.

Consider another Legacy deck (an unsuccessful one at that) which illustrates how overcoming inertia is critical to winning, and failing to do so can be lethal:

SuiDoom v3.6, by njx & JimmyK

//Disruption: 4
4 Duress

//Combo Core: 26
4 Chromatic Sphere
4 Doomsday

4 Tendrils of Agony
4 Spoils of the Vault
4 Night’s Whisper
4 Skeletal Scrying
2 Infernal Contract

//Mana: 30
4 Lion’s Eye Diamond
4 Mox Diamond
4 Chrome Mox
4 Dark Ritual

4 Cabal Ritual
10 Swamp

Although statistically impossible without cheating, it is logistically capable of a turn 1 win. The reason this instant kill is cited is to show the most extreme example of a high-velocity play that could possibly exist:

Starting Hand: Spoils, Doomsday, Petal, LED, Dark Ritual, Swamp, Mox Diamond:
Diamond (pitch Swamp), Petal, LED (storm=3);
Tap Mox, Ritual -> Doomsday (storm=5) for stack:
– Infernal Contract
– Petal
– Petal

– Dark Ritual
– Tendrils
Sack Petal on table -> Spoils for Contract, sack LED in response (storm=6);
Play Contract (-10hp), Petal -> Ritual, play Petal #2 -> Tendrils w/ Storm = 11.

That play has probably the highest velocity level of any turn one play that ends the game. Notably, it’s because you are moving almost your entire library into the removed-from-game zone on turn 1. (For the record, the above play happens to have a velocity of 68 ampt. The author tried to find something even higher, but only Worldgorger Dragon—based combo was even remotely close.) Note how incredibly risky this gambit would be: it has no resilience. Even when going first, a singular Force of Will is an automatic loss. And in Legacy, it’s not impossible for an opponent to use an Elvish Spirit Guide to Oxidize your LED in response to playing that pre-Doomsday Dark Ritual. (This author has witnessed the event several times.) This deck has a tremendous amount of inertia to overcome, as it can “fizzle” at any given step in the process; and it would also be extremely unforgiving if a mistake was made.

Conversely, since a deck like WW might require a very low velocity, it may be able to win even if it plays a turn 1 Skyhunter off of a Chrome Mox (ZMC = 3) and a turn 2 land and Wargear (ZMC = 2). After another three turns of doing nothing but attacking (0 ZMC each), the total velocity may only be 4 ZMC for 5 turns for a miniscule ampt rating of 1.2; which is almost the same as playing nothing but a land for five straight turns. Since WW may have extremely low inertia, it is not nearly as likely to “fizzle” the same way that Legacy Doomsday can.

(An interesting observation is that it is virtually impossible to naturally produce a velocity of zero, since even if one does not play any lands, the player will still discard a card at the end of the turn when possessing a full hand, which is a zone movement. Now, obviously, the player could mulligan to one card and lose in 5 turns, and thus have an actual velocity of 0 ampt, but that is not a natural occurrence. Nonetheless, it certainly describes what occurred: for all intents and purposes, the player became the proverbial goldfish. Similarly, even a velocity less than 1 demonstrates completely idle play on at least one turn of the game, clearly indicating a significant lack of actions performed during the course of a match.)

So clearly, velocity can be related to a deck’s level of risk. The higher a deck’s velocity can go, the easier it is for it to crash. Decks which can produce high velocities often require it in order to execute its strategy; and this is most notable in the case of storm combo decks. If it fails to overcome its relatively high inertia, it will crash and fall apart.

The application of this notion lends itself to actual application of theory: Perhaps velocity is one of the reasons that a deck like Legacy Doomsday is not truly viable while its Vintage counterpart can be. In Vintage, Doomsday has a much lower velocity. One obvious explanation why is related to the permanency of its manabase — real moxen stay in play, and have the same ZMC has lands. Lotus Petals, Chrome Moxen and Mox Diamonds all have at least 2 ZMC. With minor thought one realizes that Vintage Doomsday can play a mox once and use it over many turns, lowering the ampt rating when looking strictly at mana-based ZMC. In the Legacy version, a Lotus Petal only covers one turn, and to get the same mana production as a regular mox would require at least another zone movement (land from hand to play) or possibly twice that (using either another Petal or either of the Legacy-legal moxen).

Even more important, Vintage Doomsday can “artificially” increase ZMC through a single card: Yawgmoth’s Will. YawgWin allows for a massive increase in zone movement all by itself, essentially doubling the ZMC potential in a single play. Since the bulk of the ZMC for surpassing required minimum velocity can be “stored” in one card, it is not required to “keep the pedal to the metal”, allowing the setup portion to be a little less reckless. Legacy Doomsday does not have that luxury, so it cannot survive: it is forced to go at mach speed at each and every point in the process, opening up more holes for disruption. This is clear as to why Legacy Doomsday cannot even think of running Force of Will, whereas its Vintage cousin has no problems doing so. (Time Walk is another factor which allows for ZMC counts to be “stored” in a single card, as since Time Walk provides an “artificial turn” it does not count towards the division in a velocity equation. Thus, two turns’ worth of ZMC can be packed into one turn.)

Noting that high velocities pose certain risks, the rewards should be immediately obvious. A high-velocity deck which overwhelmingly overcomes inertia is basically broken. Long.dec was a great example of that; it could just crush opponents straight through. Pro Tour: New Orleans was an example of how decks had such high velocity the format was just plain stupid. Similarly, the power inherent in ZMC “storage” cards like Yawgmoth’s Will and Time Walk can have game-swinging effects, and for good reason: they are capable of dramatically altering the current ampt when played.

Thus, the definition of velocity that has been provided has significant application to deck construction. Simplistically, when constructing a deck, the deck must be provided the tools necessary to overcome its own inertia. Putting 36 lands in Mind’s Desire may prevent you from being manascrewed by RDW, but it doesn’t help you reach the necessary velocity in order to win. Similarly, Extended Goblins plays Goblin Matron, Goblin Warchief and Aether Vial because they raise the deck’s ampt. You would think that five-mana 2/2 goblins aren’t the pinnacle of speed, but no one doubts how awesome Siege-Gang Commander and Kiki-Jiki are. Both create additional ZMC, so while the decision to put five-mana creatures in an aggro deck should seem counterintuitive, it obviously isn’t. Alternatively, putting 23 mass draw spells in an aggro deck is an obvious waste of time; since velocity is not nearly as critical as killing the opponent.

It also explains why White is rarely a dominant color in Constructed – it lacks many cards that dramatically increase velocity. Astral Slide was a huge boost in the velocity department, as cycling is inherently a high-velocity mechanic and Astral Slide gave white decks a way to double the velocity by piggybacking on it. Eternal Dragon recursion was an extension of this, which also contributed to white’s success. These increases produce the most dramatic swings in White, since most successful White decks generally win through an inverse strategy; maintaining a very low inertia. A White deck can play out four lands in four straight turns and call it great progress, since it will cast a Wrath, and on the following turn drop Temple of the False God and an Exalted Angel. It can then smile and wave at the irrelevant creature or two across the table as it rides the Angel to victory — a victory which is only 7 ZMC over 11 turns. That’s not even .65 ampt, but it remains a viable strategy against a number of aggro decks. We can see how the application holds: White decks normally have low velocity, so they don’t tend to have that “broken” flavor. Yet when even the slightest elements of velocity are introduced — Eternal Dragon — for example — they can easily surpass their threshold for inertia and thus be quite formidable, as was the case with Type 2 U/W Control prior to the release of Darksteel.

So in terms of Magic Theory, velocity is a measure by which one can judge the risk-to-reward ratio of a deck. We see this is intuitively correct, as high-velocity decks like Meandeck Tendrils and 2-Land Belcher are both contain high risk elements but will often reward the skilled and practiced player with a win, even in dire circumstances. Conversely, decks like Fish and Red Deck Wins base themselves on the principles of inertia, and while they cannot easily turn a game around, they are remarkably consistent due to their low inertia and their ability to adapt to the current game state.

Counterarguments and Further Questioning

There are quite a few quandaries that must be directed at these definitions; primarily whether or not velocity is actually a theory in and of itself or rather just a subset of previous theory (namely tempo).

Some would argue that the definitions provided in this article merely attempt to establish a metric for tempo. That question is a legitimate one. If my opponent has played a critter and then I play Man-O’-War, the opponent must now replay the original zone movement. It seems logical to state that we would not recount that zone movement since its first iteration was ineffectual, and thus we have actually lowered the opponent’s ZMC with our tempo-stealing Jellyfish. Early land destruction negates a land’s movement from hand to play, so thus it lowers the ZMC, thereby “forcing inertia” on an opponent. A great card for exhibiting this intuitive comparison is Sunken Hope. It constantly and repeatedly rolls back an opponent’s hand-to-play movements for creatures, but if you control Eternal Witness, you could use Sunken Hope as a means to gain velocity, since you are not truly rolling back your play but essentially recurring a Regrowth, which further increases ZMC. So we can use velocity to measure tempo, something perhaps we previously found elusive.

That may be the most important discovery of this definition, but velocity is not synonymous with tempo. Tempo cannot exist against a goldfish; since tempo can only be gained or lost against an opponent. Gaining or losing tempo, in that sense, should be explained as altering the difference in velocity vs. inertia in relation to the opponent. An example to clarifty:

Assume my deck requires 4.6 ampt in order to overcome inertia, and I am currently operating at 6.9 ampt. My control opponent, who requires 2.3 ampt to overcome inertia, is operating at 4.6 ampt. My opponent clearly has the tempo lead: he or she is operating at twice the minimum required velocity for his or her deck, and I am operating at only 1.5 times my minimum required velocity. This is true even though our actual velocities are identical.

If I play Echoing Truth to remove a hoard of my opponent’s Beacon of Creation tokens, I may be cutting down the opponent to only 2.4 ampt, which puts them on the brink of inertia by comparison to my healthy velocity. On the other hand, if I Boomerang a land it may only reduce them to 4.5 ampt, which may be quantitatively less than mine, but has little impact on his or her tempo. From this example, tempo appears to be about suppressing a deck’s velocity relative to your own velocity. Unlike tempo, velocity can measure an individual deck; although it is possible that might not be important.

Whether velocity is an element of theory entirely on its own or merely a metric for tempo is outside the scope of this article, but it stands to reason that because of its applicability to deck construction, it seems to have enough merit on its own to establish it with the definitions provided.

Velocity seems to converge with other theories as well. Sometimes, it seems almost like we are really discussing an extension of Geordie Tait’s original expositions on Pure Card Advantage and its derivatives — a controversial theory, but worth mentioning. In an example above, the White control deck gains card advantage through Wrath and extra turns through the Exalted’s lifegain, but never experiences what Tait calls PCA — i.e. it never actually draws extra cards. The fact of the matter is, though, that it achieves Effective Card Advantage through sweepers like Akroma’s Vengeance. It might be worth exploring if there is a correlation between velocity and PCA, and/or low inertia and ECA. It is quite possible that decks with low levels of inertia rely on high ECA for card advantage, whereas decks with very high PCA also possess a high velocity. That analysis is also well outside the bounds of this article, but suffice it to say that neither of these theories or correlations harm the definition of velocity but rather show its importance in the deckbuilding process — e.g. inert builds (those with low velocity) must rely on high ECA to compete effectively.

Another line for critical questioning revolves around velocity and its relationship with the theories about the fundamental turn. Some may argue that velocity and overcoming inertia are really about hitting the fundamental turn; and while this author does not feel they are one and the same, some relationship may exist that needs to be explored. This, too, will not be discussed in the context of this theory.

Summary

This article has defined velocity according to the following equation:

ampt = ZMC / t

…where ampt is the unit of measurement for velocity, ZMC is the total sum of all movements of cards from one zone of play to another, and where t is the number of turns the ZMC was accumulated. We discount the normal card drawn at the beginning of each turn, and turns produced through unnatural means (Time Walk, Time Stretch, etc.) are not counted in t.

This article has also shown that all decks have individual minimums of required velocity in order to properly function. This minimum required velocity is called inertia. The process of raising the velocity past the level of inertia is termed as overcoming inertia. The analysis has shown that the metric velocity in ampt is not important, but rather the comparison of the deck’s average velocity to its own inertia determines its viability.

Finally, the arguments presented concluded that velocity and inertia have an application in deck construction by elucidating links between velocity and card selection, as well as connecting velocity with the risk-to-reward ratio offered in a deck’s performance.

Since the summary indicates that velocity has been defined, analyzed, applied, and shown to be informative, it stands to reason that it has sufficient grounds to become an established concept in the annals of Magic theory.

Conclusion

This author is aware that the current definition of velocity is merely a proposed hypothesis and therefore is subject to scrutiny; and may require further analysis or revision. Feedback in the forums will be used, where applicable, to help refine this theory so that it can stand on firm ground with other established theory. The author also encourages others to consider writing on the subject to further determine branches of theory unexplored in this initial review.

Cheers,

– Nathan J

njx on the SCG Forums

(Special thanks for this article go to B. L. Speiser for his contributions to the critical analysis and for his follow-up questions; to Jim Katz for his specific contributions on the comparison between Vintage and Legacy Doomsday; and to Mark Young for his initial recognition of inertia in the SCG forums and his first attempt to apply Flores’ concept.)