## Probability help for a beginner

Hi all,

I've spent a long time analysing football (soccer) matches to rate teams and try and work out probabilities of various teams winning.

So, taking English Premier League as an example. My system analyses the last 5 seasons and based on that rates each team from 1 to 3. If we then have say Arsenal at home (team rated 1) vs. Sunderland playing away (team rated 3). Taking the home win market as an example.

Arsenal at home vs. 3 rated teams won 35 out of 50 (70%)
Sunderland away vs. 1 rated teams lost 30 out of 45 (66%)

So currently my system would (more or less) give probability of home (Arsenal) win of 68%... (35+30) / (50+45)

However, I also know that in the general rating stats show that of all matches featuring 1 rated team at home vs. 3 rated teams then the stat is 305 home wins out of a total of 415 total matches which creates a baseline / general stat = 73% probability

This isn't a particularly extreme example but they do crop up and what I would like to know is how to use this baseline rating to smooth out my team specific probabilities.

I tried a very basic method of just adding them into my calculation e.g. in this case (50+45+415) / (35+30+305) = 1.38. In this case it looks OK but I feel like it weights the baseline stat too heavily due to larger number of matches.

I appreciate that this is all rather basic but any help would be greatly appreciated. Any other suggestions on how I might improve on any of the above would also be welcomed.

Thanks!