Mathematics Awareness Month 2010
As April comes and goes, so too does Mathematics Awareness Month. Every year, the Joint Policy Board for Mathematics swirls mathematics with a different delightful discipline: last year it was climate, and the year before was voting.
This year's theme is mathematics and sports, a topic which has inspired a number of articles here on this site. As usual, there are a number of essays that discuss this theme from various perspectives; while usual suspects such as football and baseball play a central role in many of the essays, other sports get to mingle with mathematics as well, including track, golf, and tennis (also NASCAR, if you consider that a sport).
This dude always thinks about math when he is golfing.
There are too many articles to discuss, so I'd encourage you to go take a look and see if anything strikes your fancy. However, here are a few highlights:
If football is your game, Chris Jones of St. Mary's College of California has written an article about NFL overtime rules and offers a mathematical model for determining the winner in overtime based on the winner of the coin toss at the beginning of overtime. Since overtime ends after any team scores, one would naturally expect that winning the coin toss carries with it a significant advantage, and this is born out in the data. Jones offers an alternative rule scheme whereby the winning team is the first one to score six points, but in this case the team which wins the coin toss still has an advantage, and it is more likely that the game will end in a tie.
Given that the NFL recently changed their overtime rules for playoff games, it's too bad that Jones did not include this scheme into his analysis. Perhaps, gentle reader, this would be a good exercise for you.
If your sports preferences are more varied, you may prefer the article by Rick Cleary of Bentley University, which discusses the probability of rare events in the contexts of football, baseball, and basketball. My favorite example deals with the complaints many people have with regards to playoffs in Major League Baseball. More specifically, the first round in MLB playoffs pits teams into a best-of-5 series, while the remaining rounds of the playoffs use a best-of-7 series. Critics claim that the shorter first round series puts the stronger teams at a disadvantage, but in fact, a 7-series round is only slightly more advantageous for the stronger team. In effect, Cleary argues that it's almost incompatible to say that a best-of-5 series is unfair without also arguing that a best-of-7 series is also unfair. The article is also well suited for a general audience.
Then again, maybe you are more interested in the intricate links between math and golf. If that's the case, you may want to peruse this article by Scott M. Berry, in which he analyzes the question: is Tiger Woods a winner? In other words, does his ability to win transcend his skill level? Does he have a mental game that helps push him to the top because of the influence he has on other players?
Berry modeled Tiger Woods' performance with the affectionately named RoboTiger, and concluded that in fact, Woods' record does not prove him to be a "winner" - he's just a very skilled golfer. The jury is still out, however, on the mathematical significance of any "winning" label for Tiger woods in the bedroom.
Finally, if you're interested in turning mathematics into cash, you may be interested in this article by Tim Chartier, Erich Kreutzer, Amy Langville, and Kathryn Pedings, which discusses different methods of predicting winners in the annual NCAA Men's Basketball Tournament. While I've discussed this topic before, this article gives more detail on a variety of methods, which, if carefully applied, will make your bracket a sure fire winner. Just make sure no one else in your local pool is so mathematically inclined.
There are plenty of other examples illustrating the intersection of math and sports, so don't let the magic stop here. If you've ever wanted to learn how to bend it like Beckham, or if you've ever dreamed of somehow connecting math to NASCAR, click through to the Mathematics Awareness Month website and read on.
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