I too have considered this [0]. You don't really need to scrape, old data is there via retrosheet and current data is available as XML and JSON via gdx.mlb.com (e.g. for 2017 [1]). Of course, beware the terms of use, but if it's just for yourself, I'd say no prob.
As for predictive analytics themselves, you can dig into all the metrics you want, but training/backcasting is how I'd approach it.