Almost all of the games we play are based on math in some way or another. Card games, board games, and computer games are designed using statistics, probabilities, and algorithms. Begin by reading about games and game theory. Then you can choose your favorite game and investigate the mathematical principles behind how it works. Can combinatorial game theory help you to win two-player games of perfect knowledge such as go, chess, or checkers? (Weisstein, 2006; Watkins, 2004) In a multi-player…
What makes a winning team? Getting all the best players? Good coaches? Good chemistry? This project will show you how you can use math to help you test your hypothesis about what makes a winning team.
The Pythagorean relationship is a fundamental one in sports: it correctly predicts the records of 98% of all teams. But in 2% of cases, it fails. Why does it fail? Find teams that deviated substantially from their expected Pythagorean record (this information is available for baseball teams…
Here's a project that combines sports and math. You'll learn how to use correlation analysis to choose the best team batting statistic for predicting run-scoring ability (Albert, 2003). You'll also learn how to use a spreadsheet to measure correlations between two variables.
Is winning correlated with fun? Pick a video game which has different difficulty settings, for example easy versus hard mode. Ask volunteers who have never played the game before to try it out. Some of them should use the easy mode and others should use the hard mode, this will ensure that you have a range in the amount of winning and losing among your volunteers. Keep track of how much each player is winning. Survey the volunteers to find out if they like the game. Do people who win more like…
For this project, you'll use a baseball as a pendulum weight, studying the motion of the ball with and without spin. Wrap a rubber band around the ball, and tie a string to the rubber band. Fasten the string so that the ball hangs down and can swing freely. Mark a regular grid on cardboard, and place it directly beneath the ball to measure the motion. You can also time the oscillations with a stopwatch. Lift the ball along one of the grid axes, and let it go. Observe the motion and record…
Have you ever wondered how playing in a certain stadium affects how well the athletes perform? Major League Baseball (MLB) is played in ballparks that have their own individual quirks when it comes to the exact layout of the field. How an individual ballpark affects player performance, which is known as ballpark effects, is heavily investigated in the field of baseball. To name just a few parks and their different traits, Fenway Park (the long-time home ballpark for the Boston Red Sox in…
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Short (2-5 days)
Basic knowledge of Microsoft Excel, statistics, and baseball
Many sports skills require quick reaction times: think of hitting a 95-mph fastball, returning a 100-mph tennis serve, or blocking a slapshot at the net in hockey. (The Experimental Procedure section below has one way to measure reaction time.) Is your right hand faster than your left? Can you improve your reaction time with practice? Do both hands improve if you only practice with one hand? Try relating your reaction time to real situations in your favorite sport. For example, calculate…
How high can you throw different types of balls, like a golf ball, a basketball, and a football? Would one of them go higher than the others? Do factors like mass, shape, and volume influence the final height? You can measure the approximate maximum height a thrown ball reaches by measuring the time it spends in the air.
To do this project, you'll need at least one ball and a helper with a stopwatch. Your helper should start timing just as you release the ball, and stop right when the ball…
Tennis racquets, baseball bats and golf clubs all vibrate when they hit the ball. You can often feel it in your hands, particularly if you "mis-hit" the ball. You can find the point(s) on your racquet, bat or club—called the "sweet spot"—that minimize unwanted vibrations. Low-tech method: hang the racquet or bat straight up and down with a string from its handle. Lightly hold the handle with your thumb and forefinger and have a helper sharply tap the bat, strings or club face…
You may know Lewis Carroll as the author of Alice in Wonderland, but did you know that in real life he was a mathematician who studied symbolic logic and logical reasoning? How can math help you solve Lewis Carroll's Logic Game? (Bogomolny, 2006) How are algorithms for solving the game Sudoku similar to solving a logic problem? (Hayes, 2006) For the super-advanced mathematical genius, try to evaluate currently available, logic-based computational tools, or design a better one!…
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