For some time, I've been interested in building a Commander deck with a rotating group of commanders. The simplest version of this would be to take two similar commanders with the same color identity, like Brokkos, Apex of Forever and Otrimi, the Ever-Playful, find 99 cards that work well for either, and you're done.
The Magic: the Gathering Data Science version of this is to use EDHREC data to find bundles of ten similar commanders, start your deck with those ten, and then find the 90 other cards that appear most often in decks helmed by those commanders.
The trick is in identifying similar commanders. I decided to do it on the basis of cards in the 99. For each commander, I looked at the EDHREC data to see what proportion of decks featured a given card. As an example, consider the fun new commander Ivy, Gleeful Spellthief.
You can see on the "Table View" on her EDHREC page that Command Tower appears in 86.2% of Ivy decks, Gemrazer in 76.0%, Sol Ring 75.7%, Shielding Plax 75.1%, and so on. You can represent each commander as a vector of these inclusion rates for all cards (there will be lots of zeros!), and represent all commanders as a #commanders × #cards matrix of these inclusion rates.
From there, it's a matter of a "simple" matrix multiplication to get a distance metric between each pair of commanders; essentially, a weighted sum of inclusions rates for cards they have in common.
As I said, I want to try building a deck around ten swappable commanders, so for each individual commander, I looked at the 10th most-similar commander, sorted by this distance, and picked one for each color identity. This will make more sense when you see the lists below.
UR is the color identity with the most cohesive bundle of 10 commanders, where the central commander is Veyran, Voice of Duality. These are all variations on Spellslinger decks, and they tend to start with a fairly consistent set of spellsling-y staples: cheap cantrips, Storm facilitators, and nonlegendary creatures that also carry instant and sorcery triggers.
The next five most-closely-bundled commander/colors are all monocolored, followed by the remaining two-color pairs, then three colors, then five. This is pretty much what I expected, given that expanding a deck's color identity increases the number of cards it has access to.
This table lists, for each non-colorless, non-four-color color identity, the commander at the center of the tightest bundle, the 9 other commanders in that bundle, and the 15 cards that appear the most frequently in their collective 99. Some observations follow, but for now, enjoy a huge list!
The decks are instant- and sorcery-focused, with lots of card draw, ways to copy spells, and control elements. The commander bundle cares more about Devotion to black, and it has some aristocrats elements. has a bit of Elf tribal, along with tutoring for huge creatures that you can cast thanks to ramp. wants to copy things, sling spells, burn, and Storm. Finally, is a collection of every kind of hatebear.
Beyond those single-color themes, the two-color bundles do a great job of showcasing the typical strengths of those guilds. The three-color bundles are a little looser, arguably defined more by what they are not.
"...build a Commander-legal deck that showcases something that other players may have never seen before. For instance, it could feature an underutilized commander, be designed around a spicy combo, or offer a new take on a popular deck."
I figured that building a ten-commander-swappable amalgamation might be sufficiently novel, so I started with the cards most frequently found in the collective 99s of the 10 blue-red Spellslinger commanders listed above.
From there, I eliminated many expensive or salty cards and tuned it down to focus less on Storming off and more on cantrips and cards that could, themselves, be cast more than once. Here is what I ended up with:
If and when I build this deck in real life, prior to playing, I will pull all of the blue/red legendary creatures out, shuffle them, select one to be my commander, then shuffle the other 9 in as part of the 99.
I think this will run best with Veyran at the helm, since essentially all of the permanents have spell cast triggers, but Niv-Mizzet, Jori En, Mizzix, Melek, and Neera should also run pretty smoothly. I think I included enough cantrips to make Eruth work, although I'm not sure there are enough high-MV cards to really take advantage of Zaffai and Vadrik. At any rate, it should be pretty fun to see what happens!
Thoughts? Questions? Critiques? Suggestions?
Let me hear them! Is this just data-wrangling for the sake of data-wrangling? Are these decks too generic to even compete? Or, is the philosophical satisfaction of playing very near to an archetypal center worth the effort? Let me know what you think, and if you have tried to build a deck like this. As always, if you aren’t already, please follow me on Twitter.
MtGDS
decks are instant- and sorcery-focused, with lots of card draw, ways to copy spells, and control elements. The 
commander bundle cares more about Devotion to black, and it has some aristocrats elements. 
has a bit of Elf tribal, along with tutoring for huge creatures that you can cast thanks to ramp. 
wants to copy things, sling spells, burn, and Storm. Finally, 
is a collection of every kind of hatebear.