Chrome: I am assuming that the rating I have includes a consideration of all of the important factors influencing the result which have been used to create a numerical rating. I want to convert ratings to odds. A mean rating and Z score does not convert the rating to a probability of the horse winning, rather it gives the probability that a numerical rating is exceeded. It is not clear how the difference rating scores connected to the frequency of the number of times A beats B gives the probability that a wins. Maybe A and B have never raced.