A couple of weeks ago I noticed this article on the Yahoo Sports page, which highlighted a statistically rare event that occurred in the American League on Sunday, May 8th. On that day, 7 baseball games were played on the AL schedule, and in all of those games one team scored exactly 5 runs. The post then links to this article from the AP, which gives this rare event the following context:
It was the first time in 18 years that such a quirky thing happened with a full schedule. On Aug. 10, 1993, all seven NL games featured one team scoring precisely two runs, STATS LLC said.
The last time it occurred with five or more runs was July 20, 1955, when all four AL games had at least one team score exactly six, STATS LLC said.
When I read this article, some questions immediately came to mind: exactly how rare is it . . . → Read More: Scoreboard Stats
Now that the World Series is upon is, I thought I might take a moment to discuss the latest results in the field of optimal base running. On the face of it, this may seem like a non-issue; after all, as any decent student of geometry will tell you, the shortest distance between any two plates is a straight line.
In a game of baseball, however, it’s more important to minimize time, not distance. Given this, running a path that consists of four straight lines connecting each base is not optimal, because the runner must slow down to make the sharp turns at each base. Of course, baseball players already know this, which is why they often swing out in their path before crossing first when they are confident that they can reach second or more. But still, the question remains: are these trajectories optimal?
According to a trio of mathematicians from Williams . . . → Read More: Optimal Base Running
If you went to the movies in Los Angeles this summer, you may have seen the following ad from Stand Up to Cancer, a charitable program whose telethon aired last Friday night. A clear homage to MasterCard‘s long-running Priceless campaign, this ad swaps out prices for odds, ending with the sobering fact that 1 in 2 men and 1 in 3 women will be diagnosed with some type of cancer in their lifetime.
Presumably, those cancer odds are taken from The American Cancer society, which has the relevant stats posted here. When it comes to some of the other claims in the ad, though, I couldn’t help but be skeptical.
Take the bowling claim, for instance. This ad would have you believe that your odds of bowling a perfect game are 1 in 11,500. This seems quite high, even when I consider the fact that . . . → Read More: Stand Up to Questionable Odds
As summer reaches its midpoint, we come to the end of another rousing year of World Cup soccer. As with any international sporting event, fans all over the world have undoubtedly had their share of ups and downs. Of all the countries in this year’s tournament, however, I think Germany may be receiving the most attention, for even though they didn’t make it into the finals, the Germans have one thing no other country has: a precognitive octopus.
At least, that is what the media would have us believe. For the past several weeks, Paul the Octopus has captured the hearts, minds, and stomachs of people around the world. He’s a charming octopus, to be sure, but it isn’t his good looks that have gotten him this far. Instead, it’s his seeming ability to correctly predict the outcome of soccer matches. As time has gone on and Paul’s predictions have continued to . . . → Read More: Let’s Make a Deal with Paul the Octopus
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 . . . → Read More: Mathematics Awareness Month 2010
In the aftermath of the Super Bowl, some of you fans may be dreading the next six months. To kick off this football drought, I’d like to highlight this article, which was featured on Yahoo yesterday. The article says that Saints quarterback Drew Brees should hope to lose the coin toss at the start of the game, because in the past 43 Super Bowls, the team that won the coin toss had only won 20 times.
An unlucky coin? Unlikely.
Um…what? Who cares? While 20/43 is slightly less than the expected 50%, this difference is not even close to being statistically significant. Actually, the fact that this ratio is only 1 1/2 games shy of the mean is pretty good. Matt Springer has posted an article that discusses why we shouldn’t really care about this difference.
Of course, the sample size is naturally restricted by the small number of Super Bowls, but . . . → Read More: Lying with Statistics in Football
This is the third in a series of posts about pools used for betting on the outcome of football games (part one can be found here, and part two here). Let me briefly recall the setting, which is probably familiar to anyone who has been to a Super Bowl party. Typically, one bets on the outcome of a football game using a 10 x 10 grid. People can buy any number of the 100 squares on the grid, and when all the squares have been purchased, each row and each column is assigned a random digit from 0 to 9.
Suppose, for example, that you buy four squares, and after the rows and columns have been labeled, you find that you own square 3-7, square 2-5, square 9-0, and square 6-6. You will win money if, at the end of any one of the four quarters, the last digit in each team’s . . . → Read More: Football Pools, Part 3
Update: Part 3 of this series of posts can now be found here.
This post is a follow-up to an earlier post that looked at betting squares for football scores. In particular, we analyzed the distribution of the second digit of final football scores, and compared that to the digital root of final football scores (recall that the digital root of a number is found by iteratively calculating the sum of the digits in that number until you come up with a single digit number from 1 through 9). We found that on average, the final digits of football scores do not distribute themselves evenly – a score ending in 2 or 5 is much rarer than a score ending in 7 or 0, for example. However, the analysis of the digital root suggested that digital roots may become evenly distributed on average.
We now turn to a related question . . . → Read More: More on Football Pools