Strength is the average star rating (with mods) of your 10 hardest plays at 95%+ acc out of your top 200, so it's not just your highest-star maps and a 9★ you only passed at 85% won't count toward it.

Rating works like Arcaea's potential: star rating plus an acc bonus minus a bit per miss, averaged over your top 50. It's just for show, since ranks use strength.

Trip drops you today into each past year and ranks you by how many players were already ahead by the end of that year. From 2015 on that's by weighted pp (today's formula, counting only plays set by then), and before that it's by strength, since old pp comes out too low when later scores replaced earlier ones.

Face-off puts you today against someone in a year you pick, ranking six skills plus an overall rank (pp from 2015, strength before) against that year's players. Ranks are a share of the playerbase, so #1 out of 5k counts for less than #1 out of 1M, and each skill is capped so one big gap can't decide it alone.

Data comes from the osu! database dumps (top 10k plus a random 10k players), with old plays and ranks from osu!track. Deleted and restricted accounts are missing, so old ranks come out a bit generous.