I’ve been interested in prediction markets for a while, and have a lot of questions about how they work that I think could be answered through some pretty simple data analysis. Unfortunately, there aren’t a lot of publicly available datasets for sites like PredictIt, Manifold Markets, etc. I previously did a project where I
"I decided to correct this for my analysis, and normalize the implied probabilities so that they sum to 1"
This makes sense, but you need to be careful how you normalize for tail events. If a sportsbook's market on a huge underdog is 1%-3% (i.e. they offer the underdog at 3% and the favorite at 99%) then their fair price is much closer to 1% than 3% (for similar reasons to tails trading rich in prediction markets).
Also as far as some sports being harder to predict than others... I think about this much more in terms of win probabilities tending much closer to 50% - higher Brier scores are downstream and that framing feels less intuitive to me. Of course with a reasonable forecaster and a large sample size these converge, but the Brier measurement is quite a bit noisier for small samples.