76.6% sensitive - 76.6% of wins are predicted as wins: p(predict win | win)=.766

89.2% specific - 89.2% of losses are predicted as losses: p(predict loss | loss)=.892

Bayes Theorem: (|) = (|)() / ()

a) Suppose There are 22 teams, P(win) = 1/22 = 0.045. Calculate p(win | predict win) and p(win | predict loss).

b) Plot the posterior probability, p(win | predict loss), as a function of p(win) from 0 to 1. At what value of prior probability is p(win | predict loss)=.5?

c) new prior probability p(win)=.15. Recalculate p(win | predict win) with this new prior information.

d) What is the accuracy of this test using p(win)=.15?

e) Plot p(win | predict win) as a function the specificity from 90% to 100%. Qualitatively describes what happens.

f) Is accuracy a good metric to describe the performance of this model? Why or why not?