Nope - nothing to do with sheep. But the Kirkwall Ba' 0r the Ba' as it is more simply known, has been played in the streets of the town for generations. It's basically a game of street football, but with fewer rules! There are two teams - the Uppies and the Doonies. Your membership is defined by where you live or family allegiances. The Ba' refers to the game and also the "ball" - the ba' is thrown up in the town centre (outside the St Magnus Cathedral) then the teams scramble for possession and form a scrum with the aim of pushing through to their goal (in the south end of the town for the uppies and the north end of the town for the doonies). It actually looks more like rugby than "football". Only the "game" lasts for hours - averaging four or five hours, sometimes more. Lots of folk also go to spectate, but it is something of a hazardous spectacle - you need to make sure you keep well out of the way of the mele!
I'm not sure I can explain it any better so suggest you take a look here for details and here for photos of this year's Christmas Ba'!
As we don't have a ferry service (due to public holidays) I've never actually witnessed the event myself - though if I did I would want to doing so from a window high up! I remember the first year I was in Kirkwall at Christmas - stout thick barricades were being put over windows and doorways and I thought - Blimey this is a bit of a rough place I've moved to! Not then understanding that this was all in preparation for the Ba'! The barricades get taken down after the New Year event and the town returns to "normal"!