# Mathletics

What a dense book! I enjoyed it and dreaded it. It has interesting details, yet is quite heavy in statistics. I encourage anyone who wants to see how stats can be used in life to read this book: Mathletics: How Gamblers, Managers, and Sports Enthusiasts Use Mathematics in Baseball, Basketball, and Football by Wayne L. Winston.

### Z scores

z score = (data point - mean)/(standard deviation)

For example, what is more unusual: the stock market dropping 22% on October 19, 1987 or seeing a person shorter than 30in tall walk down the street?

- mean daily stock return: 0%
- sigma of daily stock returns: 1.5%
- mean height of American male: 69"
- sigma of height of American male: 4"

z score for Stock Market = (-22 - 0)/1.5 = -14.67

z score for short male = (30 - 69)/4 = -9.75

So the stock market change is much more unusual!

### Probability of independent events

Independent events means knowing one result gives no insight into the other.

To calculate, you multiple the probability of each.

For example, what is the probability a pitcher with OBP of 0.34 pitches a perfect game. They need to strike out 27 batters. Each batter is independent and has a probability of 0.34.

Probability is = (1 - 0.34)\^27 = 0.0000134 or 1 in 74,500!

### Regressions

Use regressions to try to predict a dependent variable from a group's data.

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