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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

Ballpark Mathematics

Like the dawn of a new day, the start of the baseball season carries with it tremendous promise. These first few weeks provide a reprieve from the breakneck pace of March Madness, where every team is burdened with the knowledge that one loss is all it takes to prevent it from total victory. Instead, the major leagues are a product of the season in which they begin, and just as the warming weather invites us to spend weekend afternoons on grassy knolls looking for shapes in the clouds, so too do the opening games of the baseball season encourage us to let our hair down and reacquaint ourselves with this traditional American pastime.

The American Dream personified?

However, eventually Spring must give way to Summer, and Summer must give way to Fall. As the days grow shorter, so does the window of opportunity for a team to make it into . . . → Read More: Ballpark Mathematics

The Math of March Madness

With the NCAA college basketball tournament now well under way, no doubt many of you are following the games closely, and vying for your teams to make it to that sacred promised land known as the Final Four. Even the President’s caught some of the madness.

When filling out a bracket, of course you would like to predict as many games correctly as possible. No doubt a thorough understanding of the teams can help in this endeavor, as well as a careful analysis of their performance throughout the season. But none of us is perfect, and we are bound to make some incorrect predictions.

Even if you are quite skilled when it comes to picking winners, and can pick correctly 75% of the time, the odds of you selecting the correct winner for each game of the tournament are about 1 in 74,325,939. Roughly speaking, this means that even if . . . → Read More: The Math of March Madness

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