The start of the school year is upon or soon upon us. According to the National Summer Learning Association, research spanning 100 years shows that students typically score lower on standardized tests at the end of summer vacation than they do on the same tests at the beginning of the summer. Further, most students lose about two months of grade level equivalency in mathematical computation skills over the summer months. What to do? Try money -- moneyball, that is.
If your child has learned fractions, you can dive into some of the math behind the 2011 film Moneyball and the 2003 book by the same name. The story details the use of data analysis by the Oakland A's baseball team and its general manager Billy Beane. With a much smaller budget than many other teams, the A's emerged as a World Series contender by being really good - at math.
In the film, the character of Peter Brand informs Billy Beane that the team needs to win at least 99 games to guarantee a playoff spot. How can fractions help us figure out how to win 99 games in a season? We turn to a statistic developed by Bill James, who is behind many of the techniques detailed in Moneyball. James discovered a relationship, called the Pythagorean expectation, between the total number of runs a team scores and allows. The resulting fraction estimates the percentage of games a team will win. The numerator equals the square of the number of runs scored by a team. The denominator equals sum of the square of the number of runs scored by a team and the square of the number of runs allowed by that team.
To see this in action, let's look at the 2002 A's. The team scored 800 runs and allowed 654 runs during the regular season. So, the A's were expected to win (800)^2/(800^2 + 654^2) = 160,000/266,929 which equals 0.5994 or 59.94 percent of their games. Since there are 162 games in a season, the A's were expected to win 97.1 games. It's interesting that the Pythagorean expectation did not reach the 99 win threshold. However, the team did win 103 games. Teams, like the A's that win more games than the Pythagorean expectation calculates, are sometimes called lucky.
Using other statistics such as Bill James' Runs Created, the A's cobbled together their roster. Rather than think about managing a team, let's use the Pythagorean expectation to gain insight on this year's season of MLB. Let's look at the tightest contest as of August 16, the American League West, where the Texas Rangers lead the Oakland A's by half a game.
First, we need to know the number of runs scored and allowed by each team. You can find this on ESPN or, to keep with our mathematical theme, using the free computational search engine WolframAlpha and visit their page for the Texas Rangers. (You will need to search the menu options for hitting to see the data on runs.)
Now, the Rangers have scored 526 runs and allowed 482 in 122 games. The A's have scored 536 and allowed 465 in 121 games. Using the Pythagorean expectation, the Rangers were expected to win 66.67 games, whereas the A's were expected to win 69.04.
From this data, we see that the A's are playing as expected. On the other hand, the Rangers are a "lucky" team. Could their luck run out? Clearly, it depends on a number of factors, many beyond the analysis. For example, how healthy their players stay? In time, we'll find out which legends are born in October. For now, compute the numbers, curb summer learning loss, and enjoy some baseball.