Data crunching

[FanF]

It's here that we're going to speak about how to make the most of our hard rating work!!!

Ideas and offers to contribute are most welcome!

[FanF]

here's a list of what I have in mind for use of this data set:

• identification of powerful micro-synergies: filtering on the top improvements, what do we find? I'm sure that some pairings triggered light bulb moments - I'm curious to see them!
• identification of clusters: cards which are mutually improving each other would make clusters. Looking at these clusters might be insightful - I'd be looking for odd or underrated cards, off-color spells to identify "innovative" (?!) new deck strategies.
• rating of a deck: adding up the absolute ratings of each card of a limited deck, plus the sum of the rating for specific pairings, weighted by the probability for them to find themselves in a game, should give us a benchmark to compare decks. Not an universal truth by any mean, but at least a view on how (micro-)synergistic a deck is. At the beginning, I'd assume we'd be comparing this measure to how good players do in draft to see if there is some sort of correlation... I'd hope so!
  
• highlighting rating changes when drafting: given your pool at each pick during the draft, how are the ratings of the cards in the pack impacted?

the clustering is probably the most complex, but most interesting use.

[FanF]

Other ideas:

• high picks: it's likely that the common that improves the most other cards will be highly coveted. There will be a correlation as well with how much it improves them. Conversely, what card get improved by the most others? The interest for that one will be dependent on the common absolute grading too. Could we do a ranking of these commons per color? per synergy cluster? how would that affect how we read signals in a draft?
• set ranking: how does the improvements provided by other cards affect the absolute power level of a card? how does this change the P1P1 pick order?

[FanF]

That's it, we've got a first shot at building optimal decks automatically!!!

It's been good Google Sheets fun to get there - feel free to have a look and play with it! If you see that the input change on its own, it might be that someone else is on it, so duplicate it for your own use!

In terms of key lessons (always improving...):

• absolute rankings absolutely need to consider the card for what it is in a vacuum - see the post in the lessons learnt conversation
• all the deck constraints are a matter of taste (minimum number of creatures, curve), and even of color pairs - there's no obvious "one truth"
• non-linearity in synergies (e.g. Party here: a Rogue improves Malakir Blood-Priest, but if you only have Rogues apart from that Priest, that's only 2 members in your Party... but still every Rogue contributed for its improvement!) would require specific - and probably tedious - calculations
• same for DMFCs, that's more specific calcs

and... at the time of writing, the construction of the deck is very basic, it could certainly be massively improved - watch this space!

[FanF]

Useful comment provided online: in the ranking sections, it'd be useful to be able to select a card, and see with what it pairs up well.

[FanF]

Other useful comment provided on the LRcast subreddit: create a line of comment for every item of the ranked lists.

[FanF]

Explanation of the Ranked Lists:

The ranked lists give away 2-cards combos to watch out for when drafting and playing.

Since we're focused on Limited format, we created one that specifically excludes pairings with Rares and Mythic Rares to focus on what pairings are the most likely to come up in sealed or drafted pools. NB: the ratings evaluate how the 1st card makes the 2nd card better, which means that a rather card poorly rated in absolute terms could have the largest improvement with the right conditions (e.g. Chilling Trap with a Wizard in play).

[FanF]

Explanation of the Optimal Decks:

These 23-card lists have been built by picking iteratively, amongst cards from 2 predetermined colors (and colorless cards), the card with the highest compounded rating, i.e. the absolute rating added to the increments in ratings from the pairings with all the previously picked cards. Then we added the compounded ratings of all these cards to get a score. All in all, it means that these decks are optimised for micro-synergies, and that the score is only used to rank them on that basis. Arguably, there are other criteria to make good Limited decks, so this ranking is not necessarily an universal truth! 

We had to put constraints in the building to make the selection relevant. Obviously with 10 mythic rares and 15 rares you'd get away with a powerful deck - but we're not about Richman Draft here. We limited the number of MR/R to only 1, and Uncommons to 8, which is probably where you end up if things go averagely well when drafting the hard way, and which could be a good benchmark. The number of duplicates are limited to 2 at Common, and there is no duplicate at other rarities (it's a strict interpretation of the probabilities to get duplicates at every rarity over the 24 packs of a 8-player draft table).  We had to put constraints on the curve (min and max number of spells of each CMC), on the board presence (min number of creatures) and on interaction (min number of removals).  

[FanF]

Explanation of the Color Comparison:

We've used a number of datasets:

• absolute rating (floor): rating of a card "in a vacuum", i.e. with none of its dependencies or its potential fulfilled (e.g. Attended Healer is a 2/3 for 3W (which is indeed very poor), since neither its triggered ability to create Cats nor its activated ability to give lifelink are considered). NB: a 2/2 for 2 mana, or a 3/3 for 3 mana have different ratings in every set, notably depending on its speed. So the "vacuum" mentioned above is somehow theoretical.

• maximum potential rating  (ceiling): an attempt at rating a card once it reaches its maximum potential. It means all dependencies fulfilled to their maximum (e.g. full Party assembled), but as well leaving space for any additional support from other cards in the set. A concept up for debate, certainly.

• the ratings of each card have been weighted with the probability of getting that specific card in a draft booster, i.e. 0.79% for a Mythic Rare, 1.54% for a Rare, 3.78% for an Uncommon, 9.65% for a Common.

• and of course the dataset of rating improvements.

[FanF]

Explanation of the Top Supporters:

The ranking of each the cards here is inferred from the sum of the rating improvements for all the cards they improve - or make worse. The higher the improvement they give, and the more often they do, the higher they'll score on this list.