Well, you do have a point. From our vantage point today they are. However, with each win, they rise. How would you set it up?
It's Bayes' theorem extended by law of total probability. Interesting topic. An often cited example of the intuition is:
A cab was involved in a hit and run accident at night. Two cab companies, the
Green and the
Blue, operate in the city. You are given the following data:
(a) 90 per cent of the cabs in the city are
Green and 10 percent are
Blue
(b) a witness identified the cab as Blue
The court tested the reliability of the witness under the same circumstances that existed on the night of the accident and concluded that the witness correctly identified each of the two colors 80% of the time and failed 20% of the time. What is the probability that the cab involved in the accident was
Blue rather than
Green?
answer = (.8*.1)/(.8*.1+.2*.9) = 0.26
There is a lot of cognitive psychology research showing that people are very bad Bayesians. We are not good at updating probabilities to reflect the flow of information. This insight is being developed by financial economists and the effects on financial markets, security pricing, etc. (the authors of the blue-green cab example won the Nobel prize in economics for their work in this area - well, the one author who was still alive won the prize)
