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It's not real complicated.
Karma is influenced most by a stars-to-post ratio, with a minor influence from flags.
WATS is influenced most by a flag-to-post ratio, with a minor influence from stars and post-count.
Long term members with a high number of well-flagged threads will achieve a high WATS number -- or -- mid-term members with highly-flagged threads will also receive a high WATS number. It reflects a ranking of those who start quality threads (mostly).
Short term members who create replies that earn stars may achieve a high KARMA number -- or -- those long term members who focus more on adding to existing threads and are starred as a result, will also achieve a high KARMA number. It reflects a ranking of those who add quality to existing threads.
Sure, there may be short-lived abuses to stars and flags, but the intent of the system is to aid in painting a larger picture of ATS content. While, on occasion, some individual posts or threads may receive more flags or stars than deserved, on the whole I believe the system works as intended as a means to showcase important topics and hard-working members.