Problem Bot Index

I'm not sure, but I think PBI with Elo/Glicko was based on some magical formula between the ratings. Maybe an APS-based measure would just be the average score your neighbors get against that bot. So like if you're ranked #25, the average score against bot B for ranks 15-35 is your expected score.

Of course, if you're #1, you can only go from 2-11, but that's probably still useful info. And in that case (or in every case), you could shift everything so your average PBI is still 0.

PBI is the difference between expected score and real score. The expected score is based on difference between ratings.

Zero difference is 50% expected score

-800 difference is 1 to 20 odds, which is 1/(20+1) or 4,76% expected score

-1600 difference is 1 to 20^2 odds or 0,25% expected score

-Infinite difference is 0% expected score