I spent some times on this website trying to figure out how Bayes Theorem works.
Now, from that example, consider The Yankees has a 72% of winning next game based on previous results. When someone (named Bob in the example) predicts a game, he has 55% of choosing the proper winner.
The following formula is being used to know that, combining the win percentage and Bob's prediction, the actual winning chances for the Yankees now are 76% :
$$ p(A_1|B) = \frac {(0.72*0.55)} {(0.72*0.55)+(0.28*0.45)} = 0.76 $$
I just don't get how Bob's accuracy has to do with anything in that... It feel like, the better Bob is getting, the better the Yankees can win... You know what I mean ?
Let me show some stupid example, if Bob's prediction are based on 10 predictions and they were 100% correct.
$$ p(A_1|B) = \frac {(0.72*1)} {(0.72*1)+(0.28*0)} = 1 $$
Now Yankees cannot lose. Where is the mistake here ?