There was a discussion between
@
Chris Perkins
and myself about a tournament evaluation metric, known for now as the Meta Health Index. With some time on my hands yesterday, I worked up an equation for assessing how healthy a tournament meta was, or essentially "how many different viable armies?" were there for the given format and is on a scale from 0 to 1, with 1 being the highest achievable score and 0 being the lowest. A healthy meta should fall within the .8-1 range.
The equation is loosely based on Jaccard similarity. The equation also weights higher ranking armies better, so that if the top 8 armies were all different but the bottom 8 were all identical, the MHI won't be as negatively affected as if the opposite were true. It again weights based on "player skill" represented by the players' all-time win-loss ratios on .org. Because the M values are point-based, the equation can be applied across all formats.
As an example of the MHI in action, I worked out the scores of Lincoln Seasonal IV and the top 4 of OST S6 Kaiju Wars by hand. I did the top 4 because I didn't want to code it out and it took a while, so the MHI is a little high because there were different lower-ranking armies. But it still serves as a good example.
Lincoln Seasonal IV MHI: 0.953.
Kaiju Wars Top 4 MHI: 0.127.
To reiterate, this is a little unfair to Kaiju Wars. But part of a healthy meta is that there are a wide variety of armies that do well, not just a wide variety of armies. And so while there were hounds armies and soulborg armies and Hydra armies, they would be given much less weight under the tournament placement factor, and so I don't expect that the MHI would increase by much.
I think this equation could serve as a useful tool for tournament directors. Generally, formats with low MHI scores lead to less interesting tournaments and less fun experiences for players. No one wants to play a mirror match. This is also something that would be fairly easy to implement as this information is all freely available on .org, but I would like to refine the MHI first.
I know we have tons of engineers, mathematicians, and statisticians in the community who are much smarter than I am. I would appreciate any feedback on this equation. I'm well aware it's not perfect, especially because there are extreme edge cases that would fall outside the bounds of 0 and 1. (But you don't need to mention that I used J and j in the same equation...blame Jaccard, not me.) ((And yes, I used Word's equation editor to type this up. Sue me.))
If people feel that this is worth its own thread, I will move it to its own thread. In my opinion it would be extremely helpful as a TD to have MHI scores for various formats at various point totals and variations. I would also be fascinating as a player and a scaper to evaluate the MHI of VCheese over the years.