Generally speaking, what you describe is only copyrightable with regard to the actual text of your predictions, but excluding the facts within. A similar concept applies to stock picks. Once that mostly technical/factual information is out in the public domain, copyright cannot protect it.
Hence, once you publish your predictions to your website for all to see, the hard data and facts will be in the pubic as well. You may want to instead focus on building your brand value through consistently valuable predictions that can be associated with you and your site. Once that is on its way, you can monetize other ancillary services (such as commentary and advice that is more abstract) and protect that through copyright and other means. However, please be ware that the best way to detemine the protectability of your advice is to consult an IP/Business attorney.
I hope this helps.
Disclaimer: This answer is for informational purposes only and does not constitute general or specific legal advice, nor create an attorney client relationship.
You can copyright your EXPRESSION of your predictions and sports analysis and rationale for your predictions, but not the IDEAS. You can copyright the content of your sports website as online works. Please see the link below.
For your website, you need to take all the proper steps of choosing a viable and available trademark, domain name, and company name, form the right entity, advise your clientele that you're not warranting your predictions, acquire advertising insurance, etc. You also need to get some legal advice about your use of sports teams trademarks in expressing your analyses. See an IP lawyer about this business, it's got a lot of moving parts.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.