Your problem begs for smoothing splines.

for a continuous univariate relationship -you literally cannot do better than smoothing splines.

no function will ever, EVER provide a better fit to your data than a smoothing spline. Some cool theory is behind this.

When I do sports analysis, xgboost , elastic nets, and MaRS models are my friends. Stack a few together. Tune them well.

Sports data is usually as structured and clean as anything in the world, so I don’t think a big neural network will be necessary or helpful.

Lastly, I recommend modeling the proportion of points scored by the home team rather than winner/loser as a binary outcome, as this is more informative.

I recommend starting with as many variables as you can, fitting your model, and seeing how many variables you can cut out before your cross-validated performance starts dropping substantially.