When we speak of “decks” or “archetypes,” we’re really using a shorthand to refer to a generally-consistent set of specific cards that are often played together. In Limited, for example, archetypes often align with color pairs, since Wizards designs them that way and because player card pools are, well, limited, and can’t typically be focused much further than the overarching color-identity-based synergies.
This does make card and archetype-strength evaluation somewhat more difficult. What we really care about in deckbuilding is the strength of each card, in conjunction with the other 39 cards being run alongside it. But even things like 17Lands Card Performance data are really aggregating two things – the strength of a given card, plus the strength of the cards most typically run alongside that card.
There are ways of extracting card strength and synergy from more granular data, including one I’ve developed called Adjusted Win Rate, but that relies on knowing the deck list of every deck, and that data does not become publicly available until many weeks into a given format. So, while we wait for the Public Data to be released, I’ve come up with a method that does the same thing, more approximately.
If we want to know the strength of a specific card, just knowing the win rate of decks in which that card appears does not give us the answer, because those win rates are a function of the card + the deck.
In Dominaria United, for example, Shield-Wall Sentinel rates out as the top common by Game-in-hand Win Rate (GIHWR), at about 62 percent! But a huge part of its value is the ability to tutor for other creatures with defender. The Empirical Vanilla Test calculator (see my previous article) suggests that a colorless 1/3 with defender and no upside “should” only cost about 1.3 mana to cast; the Sentinel costs . If you run it in a deck with no other defenders, you’re just paying a terrible rate for a pretty poor card. Most drafters know this, obviously, but the 181 games on 17Lands in which Shield-Wall Sentinel appears in red/green decks have only been won 50 percent of the time when the card is drawn (17Lands average win rate in DMU is around 57 percent).
Red and green have almost no creatures with defender for which to tutor. Many more drafters (over 7000 games played) have run Shield-Wall Sentinel in WUB decks, taking advantage of those three colors’ defender creatures. GIHWR in that case is almost 65 percent.
So, as I am one to do, I built a model to try to decompose the win rate data into
win rate attributable to the card +
win rate attributable to archetype. Even though there will be some time before 17Lands releases data with the contents of specific decks, it is possible to filter their high-level win rate tallies by deck color.
The deck color selection filters for performance numbers of cards only when played in that main deck color combination. This helps understand, for example, which red cards perform better when paired with green than with blue. Splashes are included, so selecting RG also includes RGu and RGb decks, for example.
Using all of the (game in hand) win rates, for each card in each deck color, I fit a linear mixed model with the following basic formula:
win_rate ~ (1 | name) + (1 | deck_color) + (1 | name:deck_color)
So that’s: one random effect for card strength, one for color/archetype strength and one for any notable interaction between the two. Predicting out of this model gives me shrunken expected win rates for each card/archetype pair, and I can just look at the card strength estimates to get what I’ll call
Isolated Card Win Rate.
This table shows, for every card in DMU, the Isolated Card Win Rate (Card WR), the number of games played by decks with that card, and the modeled win rate of decks with that card, for any color/archetype in which the card has been played at least 1000 times.