Scottish term for a child molester. Stoat is a verb meaning to hit hard and the ba' refers to a ball. Literally thump a football (soccer for you N American eejits). A stoater is something great, especially a goal in football.
How this relates to child abuse I'm not sure but that's what they call it. Stoat the ba's may be in danger of getting chibbed up Bar-L following conviction.
Irate parent to shifty looking character loitering at a playground:
"See you ya cunt, you some kinda Stoat the ba'? Beat it or I'll kick yer heid in!"