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Analyzing the Ban: History, Data, Decision Theory, and Vehicles

Although I dislike bannings in general, I believe WotC made a good call with the Felidar Guardian ban. The combo pushed out a lot of interesting decks, and I expect that we will see more diversity in the new Standard.

It would have been better to ban Felidar Guardian right away on the Monday after Aether Revolt was fully revealed, before it even became legal. This would require an immediate admission that they missed an interaction and a lot of foresight, but if they felt that Splinter Twin reduced competitive diversity too much in Modern, then it was reasonable to expect that a good Copycat version would eventually do the same to Standard. It wouldn’t have been healthy for Standard to keep it in for nearly 2 years.

Given my belief that they would very likely have to bite the bullet and ban it eventually, I think it’s better to ban it sooner rather than later. And don’t get me wrong—I like the existence of a combo deck in Standard. But a 2-card, 6-mana combo with cards that are reasonable by themselves is a little too dangerous, at least in a format without efficient answers like Pithing Needle.

History

A Felidar Guardian ban on Monday would have been… cleaner. Instead, we got the second “emergency ban” in the history of the game, not counting the Peregrine Drake ban in the mostly-MTGO Pauper format. A brief history of the Standard banned list can be found here.

During the 1998-1999 “Combo Winter,” when I started playing competitive Magic, the metagame was dominated by infinite combos and 5-minute turns. To remove the domination of fast combo decks, Dream Halls, Earthcraft, Fluctuator, Lotus Petal, Recurring Nightmare, and Time Spiral were are all banned in DCI’s March 1, 1999 announcement. The announced bans would take effect one month later, i.e., on April 1. (Nowadays, there are only 5 days between the announcement date and the effective date.)

In between the announcement and the effective date, the power of Memory Jar from the brand-new set Urza’s Legacy became clear, and it was retroactively added to the March 1 announcement.

Here’s a sample list to illustrate what the deck looked like back then.

Memory Jar Combo

Randy Buehler, 1999 Standard

This is one of the most ridiculous decks in the history of Magic. If you thought Copycat was bad, imagine sitting down for your first Standard game with a home brew Deranged Hermit deck. Your opponent goes Dark Ritual, Necropotence on turn 1, followed by Mana Vault and Tinker on turn 2. A Memory Jar, Yawgmoth’s Will, and Megrim later, you take 28 damage before you’ve even played your second land. Strangely enough, I kind of enjoyed this, but many players didn’t. Turn-1 kills were not uncommon with this deck, and the sheer number of broken cards is stunning.

One important thing to point out: An emergency ban is an announcement that happens outside of the usual announcement dates but that still goes into effect on the usual effective dates. So it’s an addendum, issued after the original announcement but before the bans take effect. Both Memory Jar and Felidar Guardian were emergency bans in this fashion. This means that you don’t have to worry about an “emergency ban” of Gideon, Ally of Zendikar next week—such a thing has never happened before.

But there is precedent for changing Pro Tour Amonkhet to Modern at the last minute. In fact, the first Modern Pro Tour occurred this way. (Thanks to Patrick Chapin for the reminder.) That Pro Tour, held in Philadelphia on September 2011, was originally scheduled to be Extended, but 3 weeks before, the following announcement was made:

“Recently, we received feedback from some professional players who were testing the Extended format for the Pro Tour. The best deck by far, they said, was Stoneforge-Mystic-based blue control, and nothing could really effectively stand against it. […] ‘Caw-Blade’ decks dominated Standard format play to an uncomfortable degree beginning with Mirrodin Besieged, which caused us to ban Stoneforge Mystic and Jace, the Mind Sculptor in Standard….We discovered that 70% of decks played [in Extended on Magic Online] were blue-based Stoneforge decks, and those decks had a win percentage of 65% against any other deck. That’s not a sign of a healthy format.”

So instead of the most CawBladey format ever, we got our first Modern Pro Tour. I remember that this change personally inspired me to book a last-minute ticket to Philadelphia. With that memory in mind, I enjoyed seeing these tweets from fellow Hall-of-Famers last week.

Data

The announcement on Wednesday included the following fragment:

“Why are we making this call now and why didn’t we make it in our regular B&R announcement on Monday? The answer is data.”

In Star Trek: The Next Generation - S07E09 (Force of Nature), Data commands his cat to go down.
In Star Trek: The Next Generation – S07E09 (Force of Nature), Data commands his cat to get down.

I like data-driven decision making, but two days of Magic Online data, when there was limited availability of Amonkhet cards and hardly any time to tune new brews or for the format to evolve, is a questionable amount of time on which to base big decisions. It’s better than nothing, and it offers a useful indication, but that’s pretty much it.

Perhaps a more telling sentence in the announcement is the following:

“Couple this with consensus among a wide sampling of pros and feedback (and pizza) from our community and we decided to take action.”

I indeed saw a lot of negative reactions and disappointment with the “no ban” decision on social media. It’s good that they listen to feedback and fix mistakes, but the negative outcry should not have come as a surprise to anyone who had paid close attention to public opinion in the weeks beforehand. If this factored into their decision making, then it is likely that their feedback gathering process is flawed. Or maybe they just really didn’t like pineapple pizzas.

https://twitter.com/samstod/status/856967927957831680

It would behoove WotC to reevaluate their process for making B&R changes. I think it would be best if we would have 4 B&R announcements per year, each held 8 days after the conclusion of a Pro Tour after a public poll or online questionnaire. This does three things: first, they could use the data from the Pro Tour, the first Standard Grand Prix, and the poll to make their decisions. (This means that they should make ban decisions on the announcement day itself, not 1 or 2 weeks beforehand as they do now.) Second, it reduces the number of announcement dates by half, which will lead to less uncertainty and player unrest. Third, it moves the date to a point where it doesn’t detract from the excitement of a new set.

Decision Analysis Under Uncertainty

Last week, an article appeared on MTGDash titled “Game Theory Explains Why WoTC Hasn’t Banned Anything.” The author proposed a model and concluded that “the dominant strategy is to not ban.” Although the conclusion was correct given the model, I don’t think the model in that article was useful. I wanted to offer an alternative and address some misconceptions.

Bad format now
Bad format w/ban
Bad format now
Good format w/ban
Good format now
Bad format w/ban
Good format now
Good format w/ban
WotC’s Monday belief 10% probability 40% probability 10% probability 40% probability
WotC’s Wednesday belief 15% probability 60% probability 5% probability 20% probability
Decision: Don’t Ban Customers can play with all their cards.

Format is bad.

Poor outcome (4)

Customers can play with all their cards.

Format is bad.

Poor outcome (4)

Customers can play with all their cards.

Format is good.

Best outcome (10)

Customers can play with all their cards.

Format is good.

Best outcome (10)

Decision: Ban Customer confidence shaken.

Format is bad.

Worst outcome (1)

Customer confidence shaken.

Format is good.

Good outcome (7)

Customer confidence shaken.

Format is bad.

Worst outcome (1)

Customer confidence shaken.

Format is good.

Good outcome (7)

The 4 columns indicate the different possibilities. For instance, “Bad format now, good format w/ban” represents the possibility that Amonkhet Standard would be a bad format without a ban and a good format with a Felidar Guardian ban. MTGDash’s matrix only had 2 possibilities—a banning either creates a healthy format or not—which I think correspond to my second and third outcomes. Although every model (including mine) is an abstraction of reality, I believe that MTGDash’s was an oversimplification.

The two decision rows indicate the possible actions WotC can take. Combined with the 4 columns, this yields 8 outcome cells. I assigned numerical values to the outcomes to indicate that WotC would rather reduce confidence than have a bad format. I consider this to be an improvement over MTGDash’s model, where a bad format was deemed to be just as bad as reduced confidence.

The final ingredient is the probability distribution, as all possibilities aren’t equally likely to happen. This distribution can be based on the best available estimates from expert opinions or beliefs. As you see, it can change from Monday to Wednesday. Note that all numbers I put in are merely there for illustration and for an example calculation.

In contrast to MTGDash, I wouldn’t call any of this a game theoretical analysis—I’d call it decision analysis under uncertainty. While one could view the different possibilities as states of nature and nature as a column player in a non-cooperative, 2-player, zero-sum game, in reality there is no actual nature player that makes strategic decisions. If there were, then belief probability distributions wouldn’t factor in, and a maximin approach would have steered WotC toward the no-ban decision. But in reality, there is no game, and it makes more sense for WotC to use the payoff matrix to choose the decision with the highest expected payoff.

On Monday, the following calculation could have taken place.

Don’t ban: 10%*4+40%*4+10%*10+10%*10=7
Ban: 10%*1+40%*7+10%*1+10%*7=5.8

On Wednesday, the following calculation could have taken place.

Don’t ban: 15%*4+60%*4+5%*10+20%*10=5.5
Ban: 15%*1+60%*7+5%*1+20%*7=5.8

(Note that a more intricate, look-ahead model where an emergency ban comes at an extra utility loss, and where WotC wouldn’t be sure whether extra data would change their beliefs by Wednesday, could be even more insightful. To illustrate: If an emergency ban comes at an additional cost of 0.2 and WotC expects their original Monday belief to remain the same by Wednesday with probability 25% and change to the realized, more pessimistic Wednesday belief in the other 75%, then this would effectively yield an expected ultimate payoff of 25%*7+75%*(5.8-0.2)=5.95 for a no-ban decision on Monday.)

This general way of thinking illustrated by this exercise is useful in many situations, including mulligans, Draft picks, or business decisions. If you often feel overwhelmed by difficult problems, then consider the structured approach of (1) identifying the set of decisions and the set of outcomes, (2) estimating probabilities of the various outcomes, (3) estimating the payoffs for each decision-outcome pair, and (4) then making the decision with the highest expected outcome.

So What Possibilities Does This Open Up for Standard?

The SCG Open in Atlanta last weekend was dominated by Mardu Vehicles. It was the most popular deck by far on Day 2—it put 5 players in the Top 8, and the finals was a Mardu mirror match. But this is not terribly surprising given that the players only had two days to figure out a new format.

Mardu Vehicles

Andrew Jessup, 1st place at SCG Standard Open Atlanta

I would prefer Veteran Motorist over Thalia or Walking Ballista now that Copycat got banned, but overall Jessup’s list is solid.

Going forward, Mardu has a giant target on its head, but it is beatable, especially when you don’t have to worry about Copycat combo anymore. There are even some new Amonkhet tools that can provide additional help. Between Magma Spray vs. Scrapheap Scrounger, Manglehorn vs. Heart of Kiran, Glorybringer and Cast Out vs. Gideon, Ally of Zendikar, I’m sure that Pro Tour competitors can figure it out.

The important thing is that a constricting factor on the format has been removed, and I don’t mean Winding Constrictor. With Felidar Guardian removed, three new directions or main categories of decks open up.

First, you can now realistically tap out for expensive sorcery-speed cards to go over the top of Mardu. Midrange and tap-out control decks with cards like Liliana, Death’s Majesty, Ishkanah, Noxious Gearhulk, and perhaps even Approach of the Second Sun will become viable. Here’s an example.

B/G Delirium

Brennan DeCandio, 5th at SCG Standard Open Atlanta

Second, you can now play a different combo or energy deck. Cards like Paradox Engine or Aetherflux Reservoir weren’t particularly appealing when Copycat was simply a better combo. Likewise, a Temur Energy creature deck without the Copycat combo was just inferior to a version with the combo. Now, such decks might become realistic options. Here’s an example.

Temur Aetherworks

William Heise, 15th at SCG Standard Open Atlanta

Third, you can now run a linear deck without having to dedicate so many slots to interaction against the combo. This leaves more room for cards that synergize with the rest of your deck. I don’t know if improvise, Humans, Gods, Zombies, Delirium, Eldrazi, Tokens, emerge, cycling, or any other theme will turn out to be the best, but here is an example of a linear aggro deck with zero instant-speed answers to the combo. Such a list would not have been competitive in a Copycat environment.

W/R Humans

Zach Stern, 4th at SCG Standard Open Atlanta

It’s a whole new world we’re living in!

Discussion

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