Super Safi’s Monday Morning Math Mayhem 13 – Bat Math Part 1: Batting Average

Morning Mathematical Monsters & Maniacs!

(Today’s post is sponsored by the letter “M”)

Hi, I’m Super Safi and you may remember me from such stats and strategy posts as Kwik-E-Mart Farming and the advanced losing-to-win Superheroes battle strategy.

Over the past 600+ episodes, The Simpsons has taken us on an amazing mathematical journey involving fractions, probability, Fermat’s last theorem, and hundreds of other aspects from the wonderful world off mathematics.

And what better way to start your week, then by discussing math Monday morning?

With baseball season officially underway, this month we’re going to explore one of my favourite branches of math – sabermetrics. After all, as Prof Frink so aptly said, “baseball is a game played by the dexterous, but only understood by the poin-dextrous.”

Sabermetrics

Sabermetrics is the empirical analysis of baseball, especially baseball statistics that measure in-game activity. The term is derived from the acronym SABR, which stands for the Society for American Baseball Research, founded in 1971. The term sabermetrics was coined by Bill James, who is one of its pioneers and is often considered its most prominent advocate and public face. We’ll discuss him a little more next week. However, baseball statistics long pre-dates Bill James and SABR.

English-born, American sportswriter Henry Chadwick (pictured below) was influential in baseball statistical analysis. Born in England in 1824, he was an avid cricket player. After moving to Brooklyn, New York, he became the cricket sportswriter for the New York Times (Yes, the New York Times used to have a cricket sportswriter on staff). However, his attention shifted to baseball when he was hired as a sportswriter by the now defunct New York Clipper.

Chadwick was paramount in the rise of baseball to its popularity at the turn of the 20th century. As a keen amateur statistician and professional sportswriter, he helped sculpt the public perception of the game. He provided the basis for the records of teams’ and players’ achievements in the form of baseball statistics. He also served on baseball rules committees and influenced the game itself, eliminating the ‘bound rule’, where batters would be out if a defensive player caught a hit on one bounce. He is sometimes referred to as “the Father of Baseball” because he facilitated the popularity of the sport in its early days.

For all his contributions to the game, Henry Chadwick was posthumously inducted into Cooperstown, the National Baseball Hall of Fame, in 1938. In 2009, the Society for American Baseball Research (SABR) established the Henry Chadwick Award to honor the outstanding contributions of baseball researchers.

From a statistical standpoint, his many contributions include devising the baseball box score, establishing metrics such as batting average (AVG.) and earned run average (ERA), and assigning the abbreviation K for strikeout.

Batting Average

Let’s take a look at one of Chadwick’s statistical tools – batting average.

In MoneyBART (Season 22, Episode 03), in an effort to broaden her extracurricular horizons, Lisa plans to manage Bart’s little league team. However, knowing very little about baseball, she approaches Prof Frink, Benjamin, Gary, and Doug who introduce her to the works of the aforementioned Bill James.

With the use of statistics and probabilities, Lisa leads the team to an incredible winning streak. The Isotots go from the league cellar dwellers in 12th place to the top of the standings. All the while, Lisa is seen studying various statistics. At one point, she is reviewing the stats of an opposing player by the name of Melvin Trueblood.

We see that Melvin Trueblood is a left-handed second baseman, who can alternatively play center field. We also see the following statistical line:

AVG. is the abbreviation for the statistic of batting average that was developed by Chadwick.

The other statistical categories recorded on Trueblood show that he has taken 46 at bats (AB) and gotten 19 hits (H) in those 46 at bats. Of those 19 hits, 4 have been home runs (HR). He also has 7 runs batted in (RBI) and scored 8 runs (often abbreviated R). In the field, he has defensively committed 2 errors while playing second base or center field. And lastly in his 46 at bats, 13 times he has struck out (SO).

[Note: The K abbreviation of strike out assigned by Chadwick is used in pitching for when a pitcher strikes out a batter. The SO abbreviation of strike out is used in hitting for when a batter is struck out by a pitcher.]

So how do we calculate Melvin Trueblood’s batting average? How did Lisa calculate .413?

Chadwick adapted the concept behind the cricket batting average to devise a similar statistic for baseball. Rather than simply copy cricket’s formulation of runs scored divided by outs, he realized that hits divided by at bats would provide a better measure of individual batting ability.

AVG. = H ÷ AB

So if we take Trueblood’s 19 hits and 46 at bats, we can calculate his batting average.

AVG. = H ÷ AB = 19 ÷ 46 = .413

Batting average can range anywhere from .000 (for someone who has no hits in any at bat) to 1.000 (for someone who always gets a hit in every at bat). In modern times, a season batting average higher than .300 is considered to be excellent, and an average higher than .400 a nearly unattainable goal.

The last player to hit over .400 in a single season was Ted Williams of the Boston Red Sox who hit .406 in 1941. Ty Cobb holds the record for highest career batting average with .366 while playing for the Detroit Tigers from 1905 to 1926 and the Philadelphia Athletics from 1927 to 1928.

On a few rare occasions, a handful of players have had only one or two major league at bats and gotten a hit in those at bats, resulting in a career batting average of 1.000. One such player is former Dominican born pitcher Estaban Yan who hit a home run in his first major league at bat, on the first pitch on June 4th, 2000. He also had a single in his next at bat, the only other of his career, giving him a 1.000 batting average with 2 hits in 2 at bats.

AVG. = H ÷ AB = 2 ÷ 2 = 1.000

If that name Estaban Yan sounds familiar, it’s because in C.E.D’oh (Season 14, Episode 15), the name makes an appearance. While playing baseball, Bart says “Look at me! I’m Tomokazu Ohka of the Montreal Expos!”, to which Milhouse replies “Well, I’m Esteban Yan of the Tampa Bay Devil Rays!”.

While Ohka acheived most of his success with the Montreal Expos, I would be remiss to point out that Ohka was a former Toronto Blue Jay as well.

In Regarding Margie (S17, E20), Bart, Milhouse, and Nelson go around town spray-painting people’s addresses on their curbs and making them pay ten dollars for it. After they already add the “7” and the “4” to the Simpsons’ curb, Homer tells them that he won’t pay, so they leave without finishing. Homer completes it by painting “’74 Oakland A’s – Best Team Ever” on his curb.

Lisa: “Dad, all you had to do was paint one number, now no one is going to be able to find our house!”
Homer: “But sweetie, I just wanted to tell the ’74 Oakland A’s how I felt about them.”
(The 1974 A’s roll up in a convertible)
Sal Bando of the A’s: “Look, that guy remembers us!”
Gene Tenace of the A’s: “Hey Sal Bando, give him a ’74 A’s thank you honk!”
(Sal Bando honks horn and drives off)
Homer: “My work here is done.”

In addition to playing for the ’74 Oakland Athletics (shortened to Oakland A’s), Gene Tenace was the bench coach for the Toronto Blue Jays when they won the World Series in 1992 and again repeated in 1993. He also won 4 World Series as a player with the Oakland Athletics in 1972, 1973, 1974 and with the St. Louis Cardinals in 1982.

As a player, in 15 regular seasons, he accumulated 1,060 hits in 4,390 at bats for a career regular season batting average of .241.

AVG. = H ÷ AB = 1,060 ÷ 4,390 = .241

Sal Bando also has a slight indirect connection to the Toronto Blue Jays, as he was the GM of the Milwaukee Brewers who did not re-sign Paul Molitor and failed to take him to arbitration, despite Molitor’s interest in remaining a Brewer. He referred to Molitor as “only a DH”. Molitor signed with the Toronto Blue Jays as a free agent and became the 1993 World Series MVP and runner up for American League MVP with Gene Tenace as his bench coach.

Now that we’ve got a better understanding of batting average and calculated the batting averages of Melvin Trueblood, Esteban Yan, and Gene Tenace, are you ready to learn more baseball stats next week? Are you ready to play some baseball? Did you remember these episodes? Were you familiar with batting average? Have you heard of sabermetrics before? Do you enjoy calculating sport stats as much as I do? Sound off in the comments below. You know we love hearing from you.