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Combat Research: Decomposing Card/Archetype Strength in MTG DMU Limited

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.

 

 

Shield-Wall Sentinel

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 cardwin 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.

Note that…

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.

That very screenshot

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.

card estimates
1. Wingmantle Chaplain (U)
Card WR: 5.2
Games: 40602
Modeled WR by deck:
63.0
62.5
62.1
61.4
61.3
60.9
60.3
60.1
59.7
58.4
2. Archangel of Wrath (R)
Card WR: 4.8
Games: 13743
Modeled WR by deck:
64.6
62.8
60.2
3. Sheoldred, the Apocalypse (M)
Card WR: 4.5
Games: 6295
Modeled WR by deck:
62.9
61.5
4. Sphinx of Clear Skies (M)
Card WR: 4.0
Games: 7249
Modeled WR by deck:
61.5
5. Shield-Wall Sentinel (C)
Card WR: 3.9
Games: 57177
Modeled WR by deck:
61.9
61.3
60.7
60.7
60.4
59.3
58.8
57.8
57.3
55.2
54.6
54.4
6. Squee, Dubious Monarch (R)
Card WR: 3.7
Games: 11738
Modeled WR by deck:
63.1
61.9
61.2
59.7
7. Vodalian Mindsinger (R)
Card WR: 3.6
Games: 14249
Modeled WR by deck:
60.2
59.9
59.5
58.6
58.5
58.1
8. The Elder Dragon War (R)
Card WR: 3.4
Games: 13071
Modeled WR by deck:
62.0
61.1
61.1
58.9
9. Herd Migration (R)
Card WR: 3.4
Games: 14279
Modeled WR by deck:
59.7
59.5
59.5
59.5
59.5
59.4
58.8
10. Nishoba Brawler (U)
Card WR: 3.4
Games: 43642
Modeled WR by deck:
61.0
60.0
59.9
59.4
59.2
58.9
58.8
58.6
58.6
58.1
57.9
57.3
56.6
11. The Weatherseed Treaty (U)
Card WR: 3.3
Games: 38578
Modeled WR by deck:
60.7
60.0
59.6
59.3
59.2
59.1
59.1
58.9
58.1
57.8
57.6
57.2
56.7
12. Quirion Beastcaller (R)
Card WR: 3.3
Games: 12259
Modeled WR by deck:
60.7
60.3
60.2
59.9
58.4
58.4
13. Haughty Djinn (R)
Card WR: 3.3
Games: 13295
Modeled WR by deck:
60.2
60.1
59.7
57.5
14. Rona’s Vortex (U)
Card WR: 3.1
Games: 46449
Modeled WR by deck:
59.8
59.4
59.2
59.2
59.1
58.4
58.1
57.8
57.2
57.1
56.6
55.1
15. Micromancer (U)
Card WR: 3.1
Games: 48734
Modeled WR by deck:
59.7
59.3
59.2
59.1
59.1
58.7
58.4
58.3
58.0
58.0
55.8
16. Llanowar Greenwidow (R)
Card WR: 3.1
Games: 12962
Modeled WR by deck:
60.1
59.7
59.1
58.8
58.4
57.9
17. Tolarian Geyser (C)
Card WR: 2.9
Games: 147339
Modeled WR by deck:
60.7
59.0
58.9
58.8
58.8
58.5
58.5
58.3
58.2
58.2
58.2
57.9
57.0
56.7
18. Guardian of New Benalia (R)
Card WR: 2.9
Games: 12225
Modeled WR by deck:
62.3
61.4
60.4
60.2
19. Fires of Victory (U)
Card WR: 2.9
Games: 43037
Modeled WR by deck:
61.5
60.2
60.2
58.2
57.9
57.8
57.5
56.8
56.4
56.3
20. Knight of Dawn’s Light (U)
Card WR: 2.8
Games: 40375
Modeled WR by deck:
62.4
60.6
59.6
59.5
58.6
58.4
57.7
57.5
56.8
56.5
21. Serra Paragon (M)
Card WR: 2.8
Games: 6269
Modeled WR by deck:
61.1
22. Phyrexian Missionary (U)
Card WR: 2.7
Games: 41841
Modeled WR by deck:
61.3
60.5
59.3
58.7
58.6
58.6
57.7
57.5
57.4
57.2
23. Balmor, Battlemage Captain (U)
Card WR: 2.6
Games: 35368
Modeled WR by deck:
59.2
56.7
55.1
54.3
24. Phyrexian Espionage (C)
Card WR: 2.6
Games: 79316
Modeled WR by deck:
59.4
59.3
58.7
58.3
58.2
57.5
57.3
56.9
56.8
56.4
56.1
56.0
25. Nemata, Primeval Warden (R)
Card WR: 2.5
Games: 11844
Modeled WR by deck:
59.2
59.0
57.7
26. Tatyova, Steward of Tides (U)
Card WR: 2.4
Games: 37276
Modeled WR by deck:
59.5
59.2
58.5
58.3
58.3
58.0
57.4
57.2
56.8
27. Prayer of Binding (U)
Card WR: 2.3
Games: 40083
Modeled WR by deck:
62.8
59.1
59.0
58.8
58.7
58.5
58.3
57.8
57.7
57.2
56.4
28. King Darien XLVIII (R)
Card WR: 2.3
Games: 11302
Modeled WR by deck:
59.7
57.5
56.9
56.9
29. Sprouting Goblin (U)
Card WR: 2.3
Games: 33558
Modeled WR by deck:
61.0
59.6
59.6
58.6
57.6
57.6
57.1
56.3
55.3
30. Take Up the Shield (C)
Card WR: 2.3
Games: 81329
Modeled WR by deck:
62.1
60.2
59.2
59.0
57.8
57.3
57.1
56.7
56.7
56.3
31. Talas Lookout (C)
Card WR: 2.2
Games: 119943
Modeled WR by deck:
58.8
58.4
57.9
57.6
57.4
57.0
56.6
56.3
56.3
55.8
55.5
55.5
32. Yavimaya Iconoclast (U)
Card WR: 2.2
Games: 32386
Modeled WR by deck:
59.5
58.9
58.7
58.0
57.5
57.3
56.9
56.7
55.7
33. Walking Bulwark (U)
Card WR: 2.1
Games: 20598
Modeled WR by deck:
60.2
59.7
58.1
58.0
56.8
56.6
54.7
34. Anointed Peacekeeper (R)
Card WR: 2.1
Games: 11996
Modeled WR by deck:
61.9
60.5
59.0
58.7
35. Shivan Devastator (M)
Card WR: 2.1
Games: 7091
Modeled WR by deck:
58.5
36. Battlewing Mystic (U)
Card WR: 2.0
Games: 42396
Modeled WR by deck:
58.6
58.2
58.0
57.7
57.5
57.2
57.2
56.2
56.1
37. Clockwork Drawbridge (C)
Card WR: 2.0
Games: 29529
Modeled WR by deck:
60.3
59.0
58.3
57.7
57.2
56.5
56.1
54.7
38. Hurloon Battle Hymn (U)
Card WR: 1.9
Games: 41358
Modeled WR by deck:
60.0
59.2
58.8
58.3
58.0
57.6
57.0
56.0
56.0
55.7
55.4
39. Ertai Resurrected (R)
Card WR: 1.9
Games: 10462
Modeled WR by deck:
58.1
57.7
57.5
40. Argivian Cavalier (C)
Card WR: 1.9
Games: 103924
Modeled WR by deck:
61.7
60.0
59.9
58.8
58.5
57.3
57.0
55.5
55.3
55.2
41. Keldon Strike Team (C)
Card WR: 1.9
Games: 63685
Modeled WR by deck:
61.3
58.7
56.7
56.4
56.0
55.4
54.8
42. Impulse (C)
Card WR: 1.9
Games: 74320
Modeled WR by deck:
59.0
58.2
58.1
57.9
57.3
57.3
56.9
56.5
56.4
56.1
54.8
43. Essence Scatter (C)
Card WR: 1.9
Games: 115390
Modeled WR by deck:
58.5
58.3
57.9
57.8
57.7
57.4
56.9
56.7
56.7
56.4
56.3
56.3
44. Lightning Strike (C)
Card WR: 1.8
Games: 112424
Modeled WR by deck:
61.2
58.9
58.7
57.9
57.6
56.4
56.3
56.0
55.8
55.6
55.4
54.8
45. Ghitu Amplifier (C)
Card WR: 1.8
Games: 81332
Modeled WR by deck:
58.4
57.1
56.8
56.1
54.9
52.9
52.6
52.1
46. Aether Channeler (R)
Card WR: 1.8
Games: 14194
Modeled WR by deck:
58.6
57.8
57.4
57.3
57.1
47. Vohar, Vodalian Desecrator (U)
Card WR: 1.8
Games: 25034
Modeled WR by deck:
57.8
57.7
57.1
56.4
54.1
48. Drag to the Bottom (R)
Card WR: 1.8
Games: 11398
Modeled WR by deck:
59.5
59.2
58.5
58.3
49. Love Song of Night and Day (U)
Card WR: 1.7
Games: 28949
Modeled WR by deck:
61.1
59.4
59.1
59.0
57.3
57.2
57.1
57.0
56.9
54.7
50. Protect the Negotiators (U)
Card WR: 1.7
Games: 24668
Modeled WR by deck:
59.9
58.1
57.5
57.0
56.7
56.7
56.2
51. Temporal Firestorm (R)
Card WR: 1.7
Games: 11567
Modeled WR by deck:
57.9
57.5
52. Frostfist Strider (U)
Card WR: 1.7
Games: 44587
Modeled WR by deck:
58.9
58.5
57.7
57.1
56.8
56.6
56.4
56.3
54.1
53.5
53. Llanowar Loamspeaker (R)
Card WR: 1.7
Games: 11451
Modeled WR by deck:
59.8
58.6
58.4
56.4
55.9
54. Timely Interference (C)
Card WR: 1.7
Games: 92891
Modeled WR by deck:
58.3
57.6
57.5
56.5
56.5
56.3
56.0
55.5
54.8
54.7
54.5
55. Tolarian Terror (C)
Card WR: 1.6
Games: 111983
Modeled WR by deck:
59.1
59.1
57.1
57.0
56.1
55.5
55.3
54.8
54.5
54.3
54.0
54.0
56. Territorial Maro (U)
Card WR: 1.6
Games: 36897
Modeled WR by deck:
58.6
58.3
58.0
57.9
57.8
57.2
57.1
56.9
56.9
56.2
55.9
55.7
54.8
57. Raff, Weatherlight Stalwart (U)
Card WR: 1.5
Games: 30398
Modeled WR by deck:
58.9
58.6
56.3
55.8
54.7
58. Electrostatic Infantry (U)
Card WR: 1.5
Games: 36479
Modeled WR by deck:
59.4
58.5
58.1
56.9
55.7
55.4
54.4
59. Destroy Evil (C)
Card WR: 1.5
Games: 59588
Modeled WR by deck:
60.7
60.0
58.5
58.0
58.0
57.8
56.8
56.6
56.5
56.1
55.3
60. Defiler of Vigor (R)
Card WR: 1.5
Games: 11888
Modeled WR by deck:
58.2
58.1
58.0
57.4
57.2
56.7
61. Bortuk Bonerattle (U)
Card WR: 1.5
Games: 38495
Modeled WR by deck:
59.2
58.3
57.7
57.5
57.3
57.1
56.8
56.8
56.8
55.5
62. Citizen’s Arrest (C)
Card WR: 1.5
Games: 86867
Modeled WR by deck:
61.1
59.6
58.3
57.8
56.0
56.0
55.7
55.6
55.1
55.1
63. Defiler of Instinct (R)
Card WR: 1.4
Games: 11108
Modeled WR by deck:
60.0
59.4
58.2
56.7
64. Keldon Flamesage (R)
Card WR: 1.4
Games: 11772
Modeled WR by deck:
60.4
58.3
55.7
65. Strength of the Coalition (U)
Card WR: 1.4
Games: 25991
Modeled WR by deck:
59.7
59.1
57.8
56.2
55.8
54.6
66. Radha’s Firebrand (R)
Card WR: 1.4
Games: 11481
Modeled WR by deck:
60.8
58.7
58.1
57.4
67. The Cruelty of Gix (R)
Card WR: 1.4
Games: 11806
Modeled WR by deck:
59.1
58.5
57.4
56.8
68. Evolved Sleeper (R)
Card WR: 1.4
Games: 11513
Modeled WR by deck:
59.5
58.8
58.4
58.0
55.7
69. Tear Asunder (U)
Card WR: 1.4
Games: 35994
Modeled WR by deck:
59.5
58.3
57.4
57.3
57.2
57.1
57.0
57.0
56.9
56.6
54.8
70. Tail Swipe (U)
Card WR: 1.4
Games: 32922
Modeled WR by deck:
58.8
58.8
58.5
57.9
57.8
57.8
55.8
55.6
55.5
55.0
71. Magnigoth Sentry (C)
Card WR: 1.4
Games: 77479
Modeled WR by deck:
58.7
58.1
57.8
57.7
57.6
57.6
57.0
56.7
56.4
56.2
55.8
55.2
55.2
72. Tribute to Urborg (C)
Card WR: 1.4
Games: 95890
Modeled WR by deck:
58.5
58.3
58.1
57.8
57.6
56.6
56.5
55.9
55.4
54.9
54.8
54.4
73. Urborg Repossession (C)
Card WR: 1.4
Games: 82168
Modeled WR by deck:
58.5
58.3
57.8
57.6
57.5
57.5
57.3
57.1
57.0
56.9
56.3
56.1
55.3
54.4
54.3
52.3
74. Mossbeard Ancient (U)
Card WR: 1.3
Games: 35883
Modeled WR by deck:
58.1
58.1
57.6
57.4
57.0
56.8
56.7
56.3
55.9
54.8
54.0
75. Baird, Argivian Recruiter (U)
Card WR: 1.3
Games: 22661
Modeled WR by deck:
60.7
54.8
54.7
53.9
76. Vineshaper Prodigy (C)
Card WR: 1.3
Games: 93175
Modeled WR by deck:
58.4
58.1
57.9
57.5
57.5
57.5
57.2
56.8
56.6
56.2
56.0
55.5
54.4
54.3
77. Benalish Sleeper (C)
Card WR: 1.3
Games: 60821
Modeled WR by deck:
61.0
59.4
58.4
57.0
56.2
55.3
54.9
54.6
78. Sol’Kanar the Tainted (M)
Card WR: 1.3
Games: 4358
Modeled WR by deck:
55.0
79. Extinguish the Light (C)
Card WR: 1.2
Games: 95161
Modeled WR by deck:
59.4
58.8
57.9
57.9
57.6
57.2
56.5
56.2
56.0
55.9
55.6
53.0
80. Sunbathing Rootwalla (C)
Card WR: 1.2
Games: 91578
Modeled WR by deck: