Quantitative Risk Management: A Practical Guide to Financial Risk, + Website

2.4 Probability and Statistics

Probability is the science of studying uncertainty and systematizing randomness. Given uncertainty of some form, what should happen, what should we see? A good example is the analysis of streaks, the chance of a team winning a series of games. This kind of problem is discussed in any basic probability text, and Mlodinow (2008) discusses this type of problem.

Consider two teams that play a series of three games, with the first team to win two games being the winner of the series. There are four ways a team can win the series and four ways to lose the series, as laid out in the following table. If the teams are perfectly matched, each has a 50 percent chance of winning a single game, each individual possibility has a probability of one-eighth (0.125 = 0.5 × 0.5 × 0.5), and each team has a 50 percent chance of winning the series:

The analysis seems fairly obvious.²⁷ But consider if the teams are not evenly matched and one team has a 40 percent chance of winning and a 60 percent chance of losing. What is the probability the inferior team still wins the series? We can write down all the possibilities as before, but now the probabilities for outcomes will be different—for example, a WWL for the inferior team will have probability 0.096 (0.4 × 0.4 × 0.6):

It turns out the probability of the inferior team winning the series is 35 percent, not a lot less than ...