Magic Drafts as Markets

MARKET SYSTEMS


Anyone who has taken a basic economics course can decribe a what a "Market System" is. It's a system in which people (sometimes called market "agents") can exchange goods and/or services for other goods and/or services.

For example, any store is a small market where people trade money for goods, such as food, clothes, books, or cards. People with money are refered to as the "buyers" and people with goods are refered to as "sellers". In the one store system, there is one seller and many buyers.

Note that groups of stores (such as all stores within 20 minutes that sell cards) also form markets. Such markets have multiple buyers and sellers. These markets are very useful in most areas of economics, but we only need to consider the one store market for the following analysis.

DRAFT MARKETS

Consider Booster or Rochester drafts as a Market System. In particular, there is one seller (the judge who provides the cards) and eight buyers (the drafters). The judge "sells" cards and the drafters "buy" cards by expending draft picks. Normally in economics we consider the interactions between buyers and sellers, but because there is only one seller, the interaction is trivially a monopoly. Instead, lets consider the interaction of buyers with other buyers. In other words, we're going to use economics to explain how drafters interact with each other in a draft setting.

MERCANTILISM

Mercantilism was an economic belief held by the British government in the 17th and 18th centuries (1600s and 1700s). The idea was that all trade with colonies (eg. America, India) must go through the central government (eg. England). The purpose of colonies was to increase the wealth of the central government.

Note that Mercantilism is very similar to socialism's economic policy of central planning. The ineffectiveness of Mercantilism and central planning contributed to the respective downfalls of the British and Soviet empires.

FORCING COLORS

In the draft market, a Mercantilist economic policy is embodied as the strategy of forcing colors. Forcing a color is intentionally drafting a lot of one color so that others will not draft that color and instead draft relatively worse cards. It's equivalent Mercantilism in that in both cases, one buyer (eg. England, or Jon Finkel) tries to force another buyer (eg. America, or Randy Buehler) to pay a higher price for a valuable commodity (eg. Food, or Saga Black).

FREE MARKET

In 1776, Adam Smith wrote "The Wealth of Nations", a mammoth treatise explaining why Mercantilism was an ineffective economic policy. In "The Wealth of Nations", Adam Smith proposes a new market system, called a "Free Market", and explains why that system produces more economic prosperity.

The basic idea is that when the government leaves a market alone, sellers naturally maximize their profits and buyers naturally maximize their utility. (Maximizing utility is economic jargon for, "do the thing that makes me happiest.")

Suppose all buyers in a market have equal impact on the market, as do all sellers. Buyers and sellers can all make decisions about the market. "I am willing to buy X for any price less than $35." "I am willing to sell X for any price higher than $15." Buyers and sellers know what the best decision for them is. When the government tries to legislate decisions, such as, "All colonists in America will buy X for at least $40," they're forcing buyers and/or sellers to make decisions that aren't optimal. This causes loss of utility for the buyers AND the sellers. (Loss of utility is economic jargon for, "I'm not as happy as I could be.") See an economics text book for a more detailed treatment of why free markets work and what limits exist on them.

SURFING THE DRAFT

In the draft market, the free market economic policy is known as "surfing the draft." Surfing the draft refers to drafting whatever colors people aren't taking. It's like a free market system because you let the whole market (the other drafters) determine what the optimal choice for you is (whatever color exists in quantity).

To understand why draft surfing works, we need to clear our minds of old prejudices of colors. We might say, "In Urza's Cycle, black and white are good in draft, but the red is terrible." Concluding we should always draft black or white, but never red, is a mistake.

View the cards in a draft as providing a certain amount of utility (usefulness) that the drafters can buy by expending draft selections. We can assign point values to each color in the draft. In Urza's Cycle drafts, I personally assign points as follows:

White: 4 Blue: 3 Black: 4 Red: 2 Green: 3

Your milage may vary. In any case, it's no coincidence that the point totals add up to exactly 16. In general, draft decks consist of two colors. Mono-color draft decks naturally have twice as much as one color. There are 16 points divided between 8 drafters, so each deck should contain 2 points-- 1 for each color.

Rather than saying, "Urza's cycle black is good and red is bad," we should say, "Urza's cycle black can support 4 drafters but the red can only support 2 drafters."

FORCED DRAFTS

If a player tries to force a color, there is a good chance that color will become saturated. Suppose I tried to force black and took some white. Lets say that because of this, 5 people drafted black and 4 people took white. Then my deck is worth less than 2 points. The black cards are worth 4 points spread between 5 drafters, so we each got .8 points from black. 4 points of white between 4 drafters gives me 1 point, so my deck is worth 1.8 points. If I had tried to draft mono black, then the table would have 6 black drafters (2 of which were me), and my deck would be worth 4 * 2 / 6 points, or 1.333 points. Of course, others players would be likely to drop black, so perhaps there would only be 5 drafters: 4 * 2 / 5 is 1.6 points.

SURFED DRAFTS

When surfing a draft, each player chooses colors that other players are not drafting. Since no player chooses a color that has become saturated, there will always be 4 white drafters, 3 blue drafters, 4 black drafters, 2 red drafters, and 3 green drafters. In this situation, each player gets 1 point from each color, so everyone's deck is worth 2 points. This is a perfectly balanced draft.

REAL DRAFTS

Real world drafts are a mixture of forcing and surfing. Some player inevitably thinks that the best thing to do is force the draft, and the players who surf take advantage of the situation. Here's how that works.

Lets suppose that all other players at the table have selected their colors but you, and that they are overdrafting blue.

White: 2 (Max 4) Blue: 4 (Max 3) Black: 4 (Max 4) Red: 1 (Max 2) Green: 3 (Max 3)

Note that the numbers add up to 14 because only 7 players have made color selections. The two unclaimed colors are white and red. Incidently, no matter how you break out the numbers, there will always be an underdrafted color if there is an overdrafted color. (For a proof of this, just apply the pidgeon hole principle.)

You must either draft white twice or white once and red once. If you draft double white (100% white), your deck will be worth 2 * (4 / 4), or 2 points. If you draft white and red (50% of each), your deck will be worth 4/3 + 2/2, or 2.333 points.

I think the optimal solution is to draft 67% white, 33% red. Your deck will be worth 2 * (2/3 * (4 / (3 + 2/3)) + 1/3 * (2 / (1 + 1/3))) points. Simplified, that is: 2 * (2/3 * 12/11 + 1/3 * 3/2), or 2 * (8/11 + 1/2). This is 27/11, which is 2.4545 points. The optimal solution can be derived using maximization techniques from calculus.

In any case, the best thing to do is draft heavy white and splash some red. By contrast, the average blue/black deck will be worth 1.75 points, because 3 blue points got spread out between 4 blue drafters.

ADVERTISING COLORS

"If surfing the draft is such a good idea," you ask, "then why do some profession players advertise what colors they like?" It certainly seems like they're trying to force colors.

Well, they are and they aren't. Think of it as letting other players know ahead of time which colors you would like to claim. This encourages the drafters to select colors you have not selected. Advertising colors helps everyone do a better job of surfing the draft.

Remember how Jon Finkel would only draft Red, Blue, and White during Rath Cycle? It doesn't matter which three colors Finkel chose as long as everyone knew what those colors were. Darwin Kastle did as well as Finkel, but Kastle advertised that he played Black and Green. The colors themselves are worthless compared to the information that the other drafters in the market receive. Giving other players information about what colors you draft helps them help you.

BROKEN ASSUMPTIONS: BOOSTER DRAFT

Advertisement helps solve the problem of missing information, which plagues booster drafts. Many pros prefer rochester draft to booster draft because in rochester, it's obvious who is drafting what color. This enables drafters to avoid oversaturating colors. In booster draft, maybe some packs just had a lot of black in them, despite the fact that three people upstream from you are taking black. You could accidently oversaturate black because you didn't have all the information.

So if you try surfing a booster draft and things just don't work out, it's probably because of this. The Draft Market assumes that each player knows how much of the colors the other players are drafting, and this isn't true in booster draft.

BROKEN ASSUMPTIONS: ROCHESTER DRAFT

Rochester draft breaks a different assumption. The Draft Market also assumes that each player starts with identical resources. This is not true in rochester draft, because some players have to take their first picks earlier than other players.

Normally rochester drafts don't get oversaturated colors. Sometimes, however, the drafts are more suceptable to color forcing. If I have the very first pick in the draft and draft corrupt, I'll want to play black. But after that, I only get 8th/9th pick, and then 7th/10th pick. It's quite likely that I won't get any decent black cards for a while, if the players to my left force black.

Of course, even in this situation the players who force colors don't get decks worth that much more than 2 points. The players who really win from this situation are the players in seats 6-8, who haven't expended their early picks on a card it turns out they can't play.

In either draft format, someone can screw you if they want to, but it's better off for both of you to help each other and not draft the same colors.

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