I have a problem that I have been racking my brain to figure this out and I just don't have the background to know if I am correct or not so I am hoping that you can help me out, OK here it goes so bear with me. I am going to try and make it as simple and clear as possible. I am going to start with a horse racing example and then go into my dilemma
Horse A and Horse B are going to race against each other in a to horse race.
They have raced each other 12 times before and Horse A has won five times and horse B has won seven times. So horse A has won 41.7% of the time but....
There are two Jockeys RED and BLUE
3 out of 5 of those wins came when Blue Jockey was riding horse A. However Blue Jockey rode him only once on the days horse A lost.
Today Blue Jockey is riding horse A so we get a 60% chance if we just use that Blue jockey 3 out of five fact. But I know we need to consider the total amount of races as well
So far I have this then
P(horse A wins given blue jockey rides) = .60 X .417 /.333
because 60% of 3 of the 5 wins were when Blue was riding. 41.7% win over all and .333 cause Blue Jockey has ridden the horse 4 times out of twelve races.
Now here is where my question with changes
Two horses A & B but five jockeys. so lets just use some quick made up stats for the sake of time.
Horse A has a 66% chance to win but when Jockey Black rides the horse A, horse A wins 70.5% of the time.
now the colors of the jockeys are put in a jar to be pulled out to see who is going to ride horse A. the following are the chances in % of color being pulled out
Red 19% Black 21% Green 13% Blue 37% Pink 10%
Would my formula to see the actual percentage that horse A wins be:
Horse A wins given Black rides = .705 X .66/.21
which then gives me 2.21 which is WHAT?? what does that mean?
if it were a different rider lets say pink and for the sake of simplicity same win% would the denominator then be .10
This is causing me to lose sleep , just kidding(kinda) :)