Getting zero star sons from good kings is known as the wrap-around bug. It seems that when a son gets 10+ stars, the game cannot really handle it and the hier gets 0 stars instead. Thats why the sons got exellent stats in the other areas. My record is 5 out of 6 sons getting 0 stars, when the king was an 8 star.
Getting more than 0 stars on the sons seems to indicate lousy son though. BrSpiritus they had lousy other stats too? Check the influence of your king, might be low.
Piety and influence can bug out occationally too.
If you launch multiple jihads (10+) then you'll basically end up with random piety.
Influence can occationally drop to 0 and then recover back to 9 by itself during some turns. Can be annoying if you gets sons during that time.
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