Bayesian Resume Rating for sports math is explained in PDF https://www.jellyjuke.com/uploads/5/8/0/2/58022979/mathematical_explanation_of_the_bayesian_resume_rating_10-23-18.pdf
The formula used to calculate talent is:

However I am confused with the Pi(x) inside product set. It is stated that it depends on each game, however the probability ecuations found in the pdf only give constants (they contain x but it is eliminated after integration).
If I just calculate the product of these constant it yields unconsistent results.
I found a probability formula that depends on x, but it is the probability that the team have determinated talent, and don't depends on the game but the ligue.
What would be the correct formula Pi(x)?