Data-Driven Deck Optimization in cEDH

Data-Driven Deck Optimization in cEDH

Introduction

Optimizing a cEDH deck often relies on intuition, meta predictions, and personal experience. However, I recently conducted a data-driven win rate analysis based on card choices to determine which inclusions or exclusions have a statistically significant impact on performance. Let’s take a closer look at the results.

Methodology

For this first iteration, I analyzed Tymna/Kraum decks over the past eight weeks (January 6th to March 3rd), gathering results from 486 decklists that played a total of 2,285 matches. The overall win rate for these decks was 32.19% (W/L/D: 569/1061/615). To account for drawn games, I assigned each draw a value of 25% of a win.

I then examined each card in the decklists to determine whether its presence or absence had a statistically significant impact on win rate. At each step, I applied the findings from previous steps—continuing to include or exclude cards—until no further statistically significant decisions remained.

This process ultimately results in a subset of decklists, from which we can construct a merged decklist that should, at the very least, provide interesting insights.

Determining Statistical Significance

The method used involves sampling from Beta distributions, where the alpha and beta parameters sum to 20 and are chosen so that:

alpha/(alpha+beta)=win rate of subset.

This approach simulates the effect of observing 20 additional games for each card at the win rate of the total population still under consideration.

From these sampled distributions, we calculate the probability that one population has a higher mean than another. Some might refer to this probability as a p-value, although that would not be technically correct in this Bayesian framework.

For this analysis, we accept a decision if its p-value is below 0.05.

Results

Analyzing all 486 decklists, the most statistically significant decision (p-value: 0.0013) is to exclude The One Ring.

• Decks with The One Ring (307 decks, 1411 games): W/L/D: 327/706/378 → Win rate: 29.87%

• Decks without The One Ring (179 decks, 834 games): W/L/D: 242/355/237 → Win rate: 36.12%

The next step is to analyze only these 179 decks without The One Ring and determine the next significant card decision.

Step 2: Inclusion of Swords to Plowshares (p-value: 0.0181)

• Decks with Swords to Plowshares (163 decks, 761 games): W/L/D: 230/316/215 → Win rate: 37.29%

• Decks without Swords to Plowshares (16 decks, 73 games): W/L/D: 12/39/22 → Win rate: 23.97%

Step 3: Exclusion of March of Swirling Mist (p-value: 0.0160)

• Decks with March of Swirling Mist (17 decks, 78 games): W/L/D: 14/41/23 → Win rate: 25.32%

• Decks without it (146 decks, 683 games): W/L/D: 216/275/192 → Win rate: 38.65%

Step 4: Exclusion of Wooded Foothills (p-value: 0.0325)

• Decks with Wooded Foothills (86 decks, 397 games): W/L/D: 111/164/122 → Win rate: 35.64%

• Decks without it (60 decks, 286 games): W/L/D: 105/111/70 → Win rate: 42.83%

Step 5: Exclusion of Miscast?

The next possible exclusion would be Miscast, but its p-value (0.0811) exceeds our 0.05 threshold, so we stop the analysis here.

For those interested, here are the stats for Miscast:

• Decks with Miscast (11 decks, 39 games): W/L/D: 10/21/8 → Win rate: 30.77%

• Decks without Miscast (49 decks, 247 games): W/L/D: 95/90/62 → Win rate: 44.74%

The merged deck

Analyzing these 60 decks, we find that 51 cards appear in all 60 decklists.

Core 51 Cards:

[[Chrome Mox]]
[[Demonic Tutor]]
[[Thassa's Oracle]]
[[Vampiric Tutor]]
[[Enlightened Tutor]]
[[Bloodstained Mire]]
[[Scalding Tarn]]
[[Underworld Breach]]
[[Rhystic Study]]
[[Mystic Remora]]
[[Command Tower]]
[[Tainted Pact]]
[[Polluted Delta]]
[[Sol Ring]]
[[Flooded Strand]]
[[Brain Freeze]]
[[Sevinne's Reclamation]]
[[Grand Abolisher]]
[[Lotus Petal]]
[[Dark Ritual]]
[[Fierce Guardianship]]
[[Force of Will]]
[[Flusterstorm]]
[[Esper Sentinel]]
[[Silence]]
[[Mental Misstep]]
[[Orcish Bowmasters]]
[[Arcane Signet]]
[[Lion's Eye Diamond]]
[[Scrubland]]
[[Mox Diamond]]
[[Deflecting Swat]]
[[Ranger-Captain of Eos]]
[[Ancient Tomb]]
[[Mana Vault]]
[[Intuition]]
[[Marsh Flats]]
[[Arid Mesa]]
[[Pact of Negation]]
[[Mana Confluence]]
[[Swan Song]]
[[Lotho, Corrupt Shirriff]]
[[Force of Negation]]
[[City of Brass]]
[[Gamble]]
[[Borne Upon a Wind]]
[[Demonic Consultation]]
[[Chain of Vapor]]
[[Mindbreak Trap]]
[[Hallowed Fountain]]
[[Swords to Plowshares]]

To complete the remaining 47 slots, I sorted all other cards by their inclusion rate within these 60 decks and filled the decklist accordingly.

Does this result in the perfectly optimized deck? Probably not—but it's an insightful and structured approach to deckbuilding. So, let’s see the remaining cards:

[[Tundra]]
[[Imperial Seal]]
[[Fellwar Stone]]
[[Smothering Tithe]]
[[Simian Spirit Guide]]
[[Wishclaw Talisman]]
[[Watery Grave]]
[[Red Elemental Blast]]
[[Diabolic Intent]]
[[Underground Sea]]
[[Badlands]]
[[Volcanic Island]]
[[Plateau]]
[[Gemstone Caverns]]
[[Misty Rainforest]]
[[Mox Opal]]
[[Exotic Orchard]]
[[Mockingbird]]
[[Otawara, Soaring City]]
[[Mystical Tutor]]
[[Final Fortune]]
[[Ragavan, Nimble Pilferer]]
[[Rite of Flame]]
[[Ad Nauseam]]
[[Mnemonic Betrayal]]
[[Windswept Heath]]
[[Verdant Catacombs]]
[[Talisman of Dominance]]
[[Valley Floodcaller]]
[[Opposition Agent]]
[[Spire of Industry]]
[[Cabal Ritual]]
[[Professional Face-Breaker]]
[[Into the Flood Maw]]
[[Mox Amber]]
[[Pyroblast]]
[[Necropotence]]
[[Cyclonic Rift]]
[[Cavern of Souls]]
[[Talisman of Progress]]
[[An Offer You Can't Refuse]]
[[Wheel of Fortune]]
[[Drannith Magistrate]]
[[Path to Exile]]
[[Toxic Deluge]]
[[Culling the Weak]]
[[Steal Enchantment]]

You can find the complete decklist here: https://moxfield.com/decks/jFY-ZRtOIECksBK0M9XwyA

Conclusion

Is this the scientifically best version of TnK? Certainly not. It overlooks many factors that influence this incredibly complex game. Even within this highly specific, data-driven approach to deckbuilding, it’s not the only solution.

In fact, at the very first step, there were 24 statistically significant choices we could have made instead of excluding The One Ring. One alternative, for example, would have been excluding Ad Nauseam instead.

There’s still a lot to explore, so let’s take this a step further—what happens if we force the exclusion of Ad Nauseam first? Let’s find out.

Excluding Ad Nauseam

Excluding Ad Nauseam leads to the inclusion of Swords to Plowshares and the exclusion of Angel's Grace. This results in 52 decks with a W/L/D record of 91/92/86, achieving a win rate of 41.82%.

The merged decklist can be found here: https://moxfield.com/decks/N4A3fe06uUCnIc-3lfGZkg.

As you can see, we trade Steal Enchantment, Ad Nauseam, Mox Amber, Talisman of Progress and Culling the Weak for Cursed Totem, Deadly Rollick, Wooded Foothills, The One Ring, Delney, Streetwise Lookout.

This approach can be applied in numerous ways. I plan to develop a more comprehensive method to convey this information and also intend to apply the same technique to other popular commanders. But for now that’s it.