My guess is that depending on the jurisdiction, yes you can patent an algorithm to predict sports outcomes. Whether you should is a different question. Eighteen months after you file an application it will publish which means everyone can see your algorithm. I'm assuming most people would use it for themselves such that it would be very difficult to prove infringement. On top of this, patents cost money both to draft if you use a lawyer or agent (and you should) and file. The process usually takes at least 3 years.
Perhaps better is to provide a service providing picks. People pay you for the pick. You aren't gambling yourself so it could likely be legal where you live. This way you can monetize your invention without disclosing it. The technical term for this is Trade Secret.