When do the stats in the highscores update?

Almost immediately upon your log out, or sometimes a few minutes after.

ok thanks i was switchin back between playin loggin out and checkin highscores on my woodcutting and i noticed i was movin up in the ranks. I thought they updated em like every night or somethin.

VERY occasionally, it glitches out and doesn't update, and you have to log back in+out, but usually it just updates on log out like icecube said.