Probability assigns a numerical likelihood to an outcome. In practical analysis, it supports questions such as whether a free throw succeeds, how likely a draft pick becomes a superstar, or how randomness shapes a streak. section 16.3 section 20.6
Probability becomes useful when paired with observed data or simulations. A fair coin uses two equally likely outcomes, independent trials, and sampling with replacement; repeated trials can then be compared with a Laplace probability curve. section 16.3
Common applications include:
- Simulate random outcomes with R's sample() function, specifying outcomes, trial count, probabilities, and replacement. section 16.3
- Compute expected value by multiplying each possible outcome by its probability and summing the products. section 20.6
- Use probabilities in logistic regression and classification, while interpreting results carefully rather than treating apparent patterns as causation. section 14.0 section 16.3
NBA draft expected value
NBA first-round selections were grouped by career outcome and draft position. A top-five pick had a 24% probability of becoming a future superstar, compared with 1% elsewhere in the first round. Multiplying each outcome's probability by its median win shares produced expected values of 57.53 and 21.21 win shares, respectively. section 20.6
