I was looking at the Vintage Challenge results for October, and noticed that four different archetypes had between 10-20% of Top 8 appearances (with a 5th, Survival at 9% of the metagame), but none exceeded 20% of Top 8s.

That's the first time all year those two conditions have been met. There hadn't been a month all year where at least one archetype wasn't more than 20% of Top 8s until October.

I was wondering if the mathematically inclined might be able to propose a formula that could measure 'metagame inequality,' much like the Gini Coefficient measures income inequality.

It would have to be sensitive to the performance of multiple archetypes. And since we lack consistent win percentage data, it couldn't be based on that.

In other words, I'd like a formula that could detect, and scale, a metagame that is more 'equal' and balanced, and one that is more 'unequal' and imbalanced.

So, here are two possible extremes:

Balanced Metagame:

Deck 1: 17%

Deck 2: 16%

Deck 3: 15%

Deck 4: 12%

Deck 5: 11%

Deck 6: 8%

Deck 7: 7%

Decks 8-11: under 5%\

Unequal Metagame:

Deck 1: 40% of Top 8s

Deck 2: 30% of Top 8s

Deck 3-11: Under 5% of Top 8s

The "Unequal" metagame is not actually a hypothetical - it was the metagame in the summer of 2017, before Mentor and Thorn were restricted, based upon Top 8 Vintage Challenge results.

Anyway, I'm wondering if there is a formula that could detect these two differences, and give us a scaling value.