A Formula for Determining your Deck's Power Level

[Aetherium Slinky]

Also, your Kinnan deck has, like, 16 pieces of ramp. It's probably that, not the 4 tutors.

Count again, my good friend. 17 tutors. (And yes, 16 pieces of ramp.)

[WWolfe]

Interesting theory. Id do my decks but I’m tired of calculations at the moment with how many I’m doing in my statistics class.

[Aetherium Slinky]

Also my Kami of the Crescent Moon gets 8.8 on this scale. I think that's a little bloated by the 18 draw spells that are very expensive.

[Schau]

The power of my Sek'Kuar, Deathkeeper deck is 9.65710306407.
That being said, I did not know whether or not I should count creating tokens as "card draw" (because they are giving me extra token "cards") so in the end I didn't.

[robort]

My question is for the card draw which it says "D = Draw that either allows you to see 3 cards". I would say that seems fair but however if you are in black which there was a discussion about and lets say you use Ancient Craving that draws 3 but cost more mana compared to Foreboding Fruit that draws 1 less card but cost 1 less mana. The formula is pretty decent by the way and it gives another way to give out a general idea of power level of a deck.

[Aetherium Slinky]

My question is for the card draw which it says "D = Draw that either allows you to see 3 cards". I would say that seems fair but however if you are in black which there was a discussion about and lets say you use Ancient Craving that draws 3 but cost more mana compared to Foreboding Fruit that draws 1 less card but cost 1 less mana. The formula is pretty decent by the way and it gives another way to give out a general idea of power level of a deck.

Imagine that Preordain gives you a point in that category. (And Brainstorm. And Serum Visions.) I feel like a Night's Whisper is more powerful than a Serum Visions but I might be wrong there.

[Morganator 2.0]

Everyone keeps mentioning how they don't like doing math, so I made something for you. Attached to this post you'll find an excel sheet that will calculate the power for you. It seems a little unbelievable that anyone could dislike math. After all...

Do you know what my favorite thing about Deckstats is? The stats.

Power levels of my decks
Current decks are in bold. All the others are retired decks. I've ordered them by what I think is strongest to weakest.

Captain Sisay: 9.70
Edric, Spymaster of Trest: 11.75
Krenko, Mob Boss: 9.77
Atla Palani, Nest Tender: 12.69
Ruric Thar, the Unbowed: 11.57
Narset, Enlightened Master: 7.23
The Scarab God: 10.13
Haldan, Avid Arcanist + Pako, Arcane Retriever: 9.15
Kynaios and Tiro of Meletis: 11.50
Ezuri, Claw of Progress: 8.67
Brudiclad, Telchor Engineer: 7.86
Mishra, Artificer Prodigy: 11.87
Vaevictis Asmadi, the Dire: 6.43

So... yeah. I don't think this formula is much good as it stands. The high value on tutors makes sense for proactive decks, but any sort of interaction is hugely undervalued. I like that this is a legitimate attempt to quantify deck strength, but it needs a lot of work.

The infinitely many parameters trap

So everyone is already pointing out a lot of the glaring flaws with this formula. Some cards like Demonic Tutor and Diabolic Tutor are weighted as the same. It seems to over-value tutors and undervalue interaction. Let's remember that like most models, this is based on arbitrary values. I don't know why twenty, out of all numbers, was used to lower the relevance of interaction, but whatever. It's nice to see this as a starting point. And sure, we can try to make changes to get a more accurate rating, but then you run into a problem called the infinitely many parameters trap. Let's use an example:

I also think the removal portion could be separated into more variables, lending different weight to stax effects, targeted removal, and board wipes. I would even go as far as to say that certain kinds of board wipes should be given higher value than others (symmetrical v asymmetrical, types of permanent hit, destroy/exile/bounce).

First we need to add weights to give different values to stax, counterspells, targeted removal, and boardwipes. Then we need to weigh wipes that exile, destroy, and bounce differently. Then we need to differentiate between wipes that are one-sided, ones that leave commanders, ones that let you select targets, ones that give -X/-X, ones that deal damage...

Infinitely. Many. Parameters.

You can literally go on forever with adding variables and weights. Unfortunately, there has yet to be a consensus on the best way to stop the infinitely many parameters trap. It's a huge debate in stuff like phylogenetics where you can measure things in different ways ad nauseam. There are some models that are able to stop the trap, but they are beyond my understanding (these models also don't work in every situation). Instead, most people decide that at some point, what you're measuring is mostly irrelevant. I don't know what that point is for this model. Should the difference between an exile and a destroy boardwipe be relevant for this formula? I have no idea.

[Schau]

I personally think that it should count ramp with cmc 3 or less instead of just two because things like cultivate, kodama's reach, and wood elves are fairly good cards in almost every green deck.

[Aetherium Slinky]

I personally think that it should count ramp with cmc 3 or less instead of just two because things like cultivate, kodama's reach, and wood elves are fairly good cards in almost every green deck.

Sadly it seems like anything above cmc 2 is just suboptimal and slow. Most higher power decks don't play Cultivate or Kodama's Reach anymore. This is probably due to a lot of reprints (Three Visits) and new efficient ramp (Arcane Signet) and finishing up old cycles (Talismans). Any three colour deck can now ramp with all cmc 2 or less cards and not even bother with higher costed cards. Two colours and monocoloured still struggle if they don't have green but it's not like they're helpless either. Maybe just slightly slower.

[WizardSpartan]

Do you know what my favorite thing about Deckstats is? The stats.

I've been anticipating it and I was not disappointed.

I think a larger sample size like yours, Morg, definitely says a lot more about the formula than my 4 decks. One thing I would like to point out is that all your bolded decks are actually mostly in order. How long has it been since you looked at your retired decks and tweaked cards? Do you think that the fact that your current decks are mostly in order is just a coincidence?

The 'infinitely many parameters' is super interesting to read about, so thanks for explaining that a bit. I think one way to "solve" (not really solve, though) that is to change our expectations of a power level formula. I think it will be impossible to determine a deck's exact power level, but do we really need that? To me, all we need is a system that isn't subjective and can give a ballpark estimate of a deck's power level to create more even-matched games.

If we can agree that a ballpark estimate is all we want from a formula like this, then we don't need all these infinite paramaters. We might need to add a few (i.e. for protection/recursion, commander-specific cases, or price of deck) to cover glaring weaknesses, but we don't need a million different sections for targeted removal, symmetrical stax, asymmetrical stax, board wipes, etc., as the part of the formula dedicated to interaction is just trying to get a metric for how much you will be interacting on average. In the big, big picture, a removal spell, boardwipe, and stax spell all have the effect of disrupting other players, albeit in different ways.

[Morganator 2.0]

One thing I would like to point out is that all your bolded decks are actually mostly in order. How long has it been since you looked at your retired decks and tweaked cards? Do you think that the fact that your current decks are mostly in order is just a coincidence?

The order shouldn't be a coincidence. If the formula is good, we would expect it to give a power level relative to how the deck performs. It has been a while since I've updated the older decks, in some cases years. The strong factor on the deck power level is the number of tutor cards, and less so the amount of interaction they use. This is why decks like Atla and Mishra scored high, while decks that don't need tutors (Narset, Sisay) scored low.

[Dumb Luck]

Charix: 8.22

Out of curiosity, do you think your Charix deck is an 8.22 in reality? (An actual question, not being mean)

No problem at all. I think it may have to do with the definitions set out in the formula, in particular the section for 'Control' or 'Disruption' (that may not be the actual name of that part, can't be bothered to look at it). The deck has a number of cards that fall under that category, even the main crab himself to some degree, I guess. I think that has skewed things, somewhat.

What surprised me more was my Arcades deck coming out as considerably lower than this deck, as it is far more consistent in my view. But again, I think this is down to the limitations of the formula. I recall commanders contributing a value of two to any section they are involved with and comparing my two commanders, I think the two points Arcades contributes to card draw is worth considerably more than the two points Charix contributes to control for his first ability. Although handy, the formula is limited because it assumes that all commanders are equal - I don't think there is any way to mitigate that really. At least for someone with my maths skills anyway!

I'd actually rank Arcades a little higher (7) and Charix a few points lower (a high 6 perhaps). Even Arcades can get disrupted and that blows, I think it is somewhat more resilient than Charix. Charix has all the typical weaknesses of a voltron build and if I don't get any of my ramp/miss land drops, it sinks. It does have the advantage of being an underdog though and it rarely gets targeted early on, unlike Arcades can.

Charix: 8.22

Out of curiosity, do you think your Charix deck is an 8.22 in reality? (An actual question, not being mean)

I was honestly thinking the same thing until I looked at the deck. I don't know if it's really an 8.22, but that is a sick Voltron deck. Nice build.

Thanks! I've run a few Voltron builds in my time but this is easily my favourite. It's so goofy and doesn't just play tons of artefacts to smash face (which is fine, to clarify, but I've been there and done that a ton).

[ApothecaryGeist]

The originator of this equation alluded to the fact that this equation was geared more toward casual decks.  But then made it work around a more competitive build.  Only ramp with CMC 2 or less is counted.  Having Commander's Sphere is counted the same as not having ramp at all in this equation.  Recursion isn't really counted at all.


The mathematician in me wants to revise this equation, adding in factors for recursion, ramp with higher CMC, tap lands, card synergies, etc.


But the reality is, even if we came up with an equation that could precisely and accurately quantify the power of an EDH deck, most casual players would not take the time to tabulate which of their cards go in to which categories and actually run the numbers.  We play casual commander because we like the subjective fun of the experience.  Not because we want to quantify it.

[Aetherium Slinky]

I've been playing around the commander issue with the formula and a couple of other tweaks, too.

If you add a term "2/(cards needed in hand or play to win in addition to your commander)" you get +2 for all combos like Heliod&Ballista, +1 for all regular two-card combo decks, 0.66 for all three-card combos and creature decks get almost nothing at all.

You could also devalue tutors by 2 making the entire formula a bit more balanced. Tutoring is surprisingly expensive to use.

For commanders you could count the commander as 9/CMC (from a hypergeometric calculator: it's like having half a card of the respective category in your hand every game at the start of the game) for the respective categories - Scion of the Ur-Dragon gets 1.8 in the tutor category, Edric, Spymaster of Trest gets 3 in the draw category and The Scarab God gets 1.8 in both draw and interaction categories. Merieke Ri Berit gets 3 in the interaction category.

Maybe tweak the interaction to 15 since it's more reasonable. I don't see many decks use 20 interaction spells.

Finally I think we should adjust the coefficients for the extra term added so that the overall feel stays around 10. So let's divide ramp, draw and tutors by 5.

This would leave us with:
2/(CMC of the deck) + (draw spells + tutor spells + ramp spells)/5 + (interaction)/15 + 2/(cards needed in hand or play to win in addition to your commander) = power level

My Merieke Ri Berit now gets a much more reasonable 8.5.
My Kinnan, Bonder Prodigy now gets a much more reasonable 13.4.
My Kami of the Crescent Moon still gets a bloated 8.2.
My Rosheen Meanderer gets a reasonable 7.1.
My Sygg, River Guide budget Merfolk tribal gets a whopping 5.0 which is definitely in line with the deck's power level.

A "generic deck" would get probably
2/3.5 + (10+0+10)/5 + 10/15 + 2/4 = 5.7. So that's the floor.

The Edgar Markov precon gets 4.9 so that's the true floor for this formula in terms of power level. Looks like anything below 6 is a fairly low power deck, anything above 10 is a high power / cEDH deck.

[WizardSpartan]

Hmm. With your formula, my Ezuri goes down to a 7.88, Kumena down to 7.31, Alesha down to 6.49, and Meren down to 6.57.

Problem is, that formula only works for a deck with an infinite combo that wins the game. My Meren deck just doesn't have one, so I had to guess that Avenger of Zendikar, a sac outlet, and Zulaport Cutthroat effect would be good enough to fit the last section there. I get what you're going for, as combo decks with 3-4 card combos should definitely be punished in this formula rather than being rated the same as a 2 card combo.

I went ahead and plugged my decks back into your formula, MustaKotka, and I found that they dropped a lot. I really don't think that an Ezuri deck that can extremely consistently win on T 5-6 should be a 7.88. So, I tried replacing the 5 with a 4, and put all my results into a handy dandy table.

	OG	With 5	With 4
Ezuri	9.6	7.88	9.28
Kumena	7.4	7.31	8.4
Alesha	7.8	6.49	7.49
Meren	7.7	6.9	8.05

Yeahh, I don't think dropping to 4 is the right choice. Hmm. I'm just trying to think how could Ezuri get back up there. I think that while the bit concerning how many cards you need to win is good, it may just not be a good idea for EDH as a whole. Most EDH decks don't just run a 2-3 card combo for shits and giggles in my experience. They can still be very strong, but having an "oopsie I win" combo isn't really effective in my eyes.

Idk, my brain hurts and it's only 8 in the morning.