Are the 49ers skilled, or just lucky? Part 2.

In my previous post, I asked whether the San Francisco 49ers’ improbably successful season was due more to luck (say, by being granted a relatively easy schedule), or due to real improvements in the skill of the team. By comparing the 2011 season with the 2010 season and correcting the schedule for the number of wins and losses each team accrued, I concluded that the level of difficulty of the team’s schedule year over year was roughly the same, and therefore more of their success should be attributed to skill rather than luck.

In this follow-up, I’d like to dig a little deeper into measurements of the 49ers’ skill, in an attempt to further bolster the above claim. If you are a football fan, then you are fortunate to have me write two football-themed posts in a row. If you are not a football fan, fear not; with the season . . . → Read More: Are the 49ers skilled, or just lucky? Part 2.

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Are the 49ers skilled, or just lucky?

Fans of the two football teams who face off in the Super Bowl will no doubt spend the weekend filled with nervous anticipation – hopeful that their team will emerge victorious, but certain of the knowledge that there can only be one champion. For the rest of us, we must hang our heads with relative degrees of shame, and bide our time until the next season brings with it the promise of new opportunities for all 32 NFL teams.

For a San Francisco 49ers fan like myself, most of the last decade has been spent in a fairly constant state of disappointment. But after ten years without a playoff appearance, the team blossomed this season under the influence of new head coach Jim Harbaugh, and came within one game of their first Super Bowl appearance since 1995.

This poster hangs proudly in our apartment.

Despite a great season, in . . . → Read More: Are the 49ers skilled, or just lucky?

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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 . . . → Read More: Mathematics Awareness Month 2010

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Lying with Statistics in Football

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 . . . → Read More: Lying with Statistics in Football

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Football Pools, Part 3

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 . . . → Read More: Football Pools, Part 3

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More on Football Pools

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

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A Variant of the Traditional Football Pool

Update: Part two of this three-part series on football betting pools can be found here. Part three is here. During this month’s Super Bowl, like many of my fellow Americans, I participated in the great tradition of the football pool. This method of betting on a football game is quite simple. For those of you who have never partaken in this activity, here’s how it works: You begin with a 10 x 10 grid of empty squares, which you auction off at a certain price ($1 per square, say). When someone buys a square, they put their initials in that square. Once all the squares have been purchased, each row and each column in the grid is randomly assigned a digit from 0 through 9. This means that each box will correspond to a unique pair of digits, from the 0-0 square through the 9-9 square. Since the assignment is . . . → Read More: A Variant of the Traditional Football Pool

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