Yes, the points to make the offspring have either good, or bad points and genes. I believe that if you breed 2 super good pets together the child will also have a big chance of getting those kinds of stats. About the green stars, that is called the Genetic Power. Genetic power is basically the strength of the GOOD genes, and they make the child have a better chance of getting good genes. (GP-3 pets are really good) On the other hand, degeneration is basically the opposite. With degen, the child has a better chance of getting BAD genes.
Green star-GP 1-3
Red star-DG 1-3
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