Even if your chances are influenced somewhat by level, I would still head for the shrine as soon as possible, and save before clicking on it. The stat bonus will have a much better effect earlier in the game than waiting until heading to the wastelands. I re-loaded about 10 times (I got a strength bonus first, but then re-loaded to see if the effect was random, and had to keep re-loading to get strength again, and had mostly positive bonuses. Others reported getting mostly negative penalties. The possibility that the shrine was influenced by level or reputation was discussed, though nobody did any rigorous testing, AFAIK.
