Baseball is a sport that has used probabilities and statistics since the 1800s. In fact, the statistics of players can determine when they bat, which position they play, and even how much their salary is. Baseball is a sport ruled by math!

#### The Proof Is in the Details

The batting order of many teams is determined by a player's past performance and the likelihood that the player will be able to hit the types of pitches thrown by the particular pitcher he is up against. In general, batters with higher batting averages are placed at the top of the batting lineup, and those with lower averages are placed toward the bottom.

One exception to this is the “cleanup” batter, or the batter in the 4^{th} position in the lineup. He is typically one of the best hitters on the team and tends to hit with a lot of power. Offensively, he is positioned 4^{th} instead of 1^{st} so that if each of the previous batters hit a single *and* got on base, the cleanup batter will hopefully be able to hit a homerun and all four batters will score (this is referred to as a "grand slam").

Typically, each batter's batting average is displayed when he is at bat. This gives a good idea of how he has performed in the past. A batting average is an experimental probability: since the beginning of the season (the experiment), how many times has the batter hit the ball, out of the total number of times he's been at bat (referred to as "at-bats")?

\begin{align*}\frac{\text{Number of Matching Events in Sample Space}}{\text{Number of Total Events}}=\frac{\text{Number of Hits}}{\text{Number of At-Bats}}\end{align*}

See for yourself: http://www.baseball-almanac.com/bstatmen.shtml

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Explore More

If Jackie Robinson hit a baseball 1,518 times and came to bat 4,877 times during his career, what was his batting average? In other words, what was the experimental probability of him hitting the ball during his career?