We aren't actually sure if anyone was discarded in ancient Sparta, as I explain here. Infanticide was certainly common throughout the ancient Mediterranean, and the Spartans certainly had some overtly eugenic policies, but there is no contemporary evidence for the supposed practice of throwing deformed babies off Mt Taygetos.

In any case, true or not, we hear about this practice only from one source, which does not specify what these Spartan baby inspectors were looking for. We can only guess as to which features they thought disqualified someone from life as a Spartiate. The only thing we can say for certain is that Agesilaos, despite being very small and lame in one leg, still ended up becoming king of Sparta; even if the murder of infants was a real Spartan practice, apparently the conditions were broad and flexible.