A Deck with Extreme Matchups Is Statistically Better than One with Even Matchups

A few months ago, Paulo Vitor Damo da Rosa wrote an excellent piece about several elements of competitive Magic. I’d like to add something to one of his points.

PV wrote about people’s tendency to avoid decks with bad matchups even at the cost of overall win percentage. Specifically, he argued that many would choose to play a strategy that’s ~55% against everything over one that’s just as likely to face an 80% or a 35% matchup. The latter adds up to a higher average than 55% and, thus, is the better pick.“

In this article, I want to show that it is better to run a deck with extreme matchups even when its overall win percentage is not higher.

Note that “better” in this context means a better chance of tournament success. This doesn’t have to be your main objective. There are lots of reasons to play Magic, even competitive Magic, and all of them are as legitimate as the next. Maybe you just feel like taking your pet deck for a walk again or you want to prove the viability of some wacky combo you brewed up. If your goal is to have a good time and you don’t enjoy playing games in which you’re a big underdog or a big favorite from the get-go, then don’t follow this article’s advice.

Simplified Calculations

Real Magic metagames are complex and possibly chaotic systems with way too many factors to allow conclusive calculations. When trying to show a fundamental principle at work, however, it is possible to create a simplified model of reality that disregards non-relevant factors. I’m using the following:

  • We can choose a deck with which we win 50% of our matches, no matter what the opponent plays. This is our boring baseline.
  • Alternatively, we can choose a deck that is 70% to win a match when paired against A and 30% to win a match when paired against B. We are interested whether or not this 70/30 deck yields better results than the 50/50 deck.
  • The only possible pairings are A or B. This is the crudest simplification of them all, but it is a legitimate one. We could do the same math with more matchups instead of just one at 70% and a second at 30%. We could also include the mirror. We’d still see the same effect.
  • We have to assume that overall A has an even matchup against B. If the latter stages and top tables of a tournament were likely to feature more A or more B, then we should pick the deck that has a better matchup against A or B, respectively.
  • We don’t know whether A or B is more popular, but we have to allow for the possibility that one of them is.

How to deal with this final point is the crux. Which deck is more likely to succeed in this setting depends solely on the field composition. If there’s more A around, then the 70/30 deck is better. If there’s more B, then the 50/50 deck is better. In fact, if we expect any tendency in one direction or the other, then the whole discussion is moot.

But we cannot assume that we meet A and B at the same rate, either. This would be tantamount to prescribing a field equal parts A and B. Indeed, if A and B each make up half the field, then the 70/30 deck is exactly as good as the 50/50 deck, and the discussion is pointless once again.

What we should do instead, is to assume that A outweighs B with the same probability that B outweighs A: 60% A and 40% B is as common as 40% A and 60% B. 90% A and 10% B is as common as 10% A and 90% B. And so on, and everything in between. Of course 90% A isn’t as common as 60% A, but each outcome bar in the following graphic is as likely to apply as the one right (or left) next to it.

The above tells us that there’s no difference between the 70/30 deck and the 50/50 deck when it comes to winning a single round. If we get lucky in the matchup lottery, our chance to win improves just as much as our chance declines if we get unlucky to the same degree.

Luckily, it doesn’t stop here.

Where It Gets Interesting …

We don’t want to win one round. We want to win tournaments, or at least achieve one of the top ranks. Incentive structures in competitive Magic have always been set up to reward exceptional rather than consistent performances.

For example, at qualifier tournaments throughout history, the second-place finisher has always been the first loser. Most players that went 12-4 at the latest Mythic Championship received four times as much prize money as the majority of 33 pointers. Winning 16 matches across two GPs will get you nothing if you win eight rounds at each, but if you win 16 matches at one Grand Prix and zero at another you can be $10,000 richer.

It isn’t just the top-heavy payout either. “Spike plays to prove something, primarily to prove how good [they are],” is how Mark Rosewater explained the tournament players’ motivation. Spike is the perfect name for this psychographic profile, because the best way to be seen as a good player is to spike a couple of tournaments. If you land a Top 8 berth at multiple GPs, no one will care about the times you went 0-3 drop.

All else being equal, if we can aim for more extreme positions, we should. Top or bottom? Yes, please. Conveniently, a deck choice with more extreme matchups allows us to do exactly that. The effect is plainly visible even for the smallest tournament unit in existence:

The total length of each pair of bars denotes how likely we are to go 3-0 when we get either lucky with our pairings to some degree or unlucky to the same degree. As you can see, good fortune increases our chances more than bad fortunate decreases them. But if we pick the deck that wins 50% against everything, we rob ourselves of this possibility. Then we’re literally never lucky.

Admittedly, it’s almost impossible to quantify this effect outside the context of a simplified model of reality. A lot depends on how real we consider the possibility for an imbalanced spread of matchups to be. Note though that on average any imbalance, no matter how small, favors the deck with the good and the bad matchups over the deck with even matchups all around. This is true not just for 70% and 30%, which are arbitrary numbers. A combination of 60% and 40% or of 55% and 45% or even all of the aforementioned has the same fundamental advantage over 50%, albeit smaller.

The effect gets more pronounced the longer the winning streak we look for. At some point, this advantage begins to outgrow various other factors. For instance, the average expected performance of a deck with 70% and 30% matchups in an unknown field can dwarf the performance of a deck that wins 51% of its matches against everything. Likewise, even if we expect our favorable matchups to make up 59% of the field with the same probability that our unfavorable matchups account for 61% of the field, the deck with these favorable and unfavorable matchups may still be a better pick than the deck with neither.

For an example of such an extreme case, consider the 13-2 record required to guarantee a spot in the Top 8 of a Grand Prix:

I can’t show a lot of the numbers here because the effect is so strong that I ran out of pixels. Know though that the 70/30 deck’s chance to go 13-2 or better moves from 0.37% in a balanced field to 0.87% when it encounters 60% favorable matchups, whereas its chance only drops by 0.23% when it encounters 60% unfavorable matchups. If it encounters 90% favorable matchups, then the chance moves up to an astronomical 7.19%.

Getting lucky with the pairings in nine out of 15 rounds doesn’t seem like an unreasonable proposition. Specifically, we should consider it quite a bit more likely than to go 13-2 or better with a 50/50 deck. A 0.37% shot at Top 8 is hopeless. At this rate, you reach the playoffs an average of once for every 271 GPs you attend.

The point is that the probability to make Top 8 is so low already that you simply have to take risks. Just as you play to your outs in-game, you have to play to your outs in the pre-game as well. Don’t shy away from decks with extreme matchups. Embrace them.


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