Super Safi’s Monday Morning Math Mayhem 15 – Bat Math Part 3: On-Base Percentage

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

As we discussed two weeks ago and last week, Sabermetrics is the empirical analysis of baseball, especially baseball statistics that measure in-game activity. We also mentioned that 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. While we discussed the recent work of Bill James last week and the pioneer work of Henry Chadwick two weeks ago, this week we are going to look at another influential figure in baseball statistics, Baseball Hall of Fame General Manager Branch Rickey.

Branch Rickey (pictured below) was born in Ohio on December 20, 1881. He joined the Major Leagues playing for the St. Louis Browns and New York Highlanders from 1905 through 1907. After a less than stellar playing career, Branch returned to the Majors as a manager for the St. Louis Browns from 1913 to 1915 before World War I and St. Louis Cardinals from 1919 to 1925 after the War. Along with managing, he became the General Manager of the St. Louis Cardinals from 1919 to 1942, where he established the concept of the farm system in the Minor Leagues.

From 1943 to 1950, Branch became the General Manager of the Brooklyn Dodgers. As GM of the Dodgers, Branch established the first spring training facility and was the first to invest in equipment such as batting cages, pitching machines, and batting helmets. However, his innovations extended beyond this, and into the world of baseball statistics. He hired statistician Allan Roth and upon reviewing Roth’s data, shifted focus from batting average (which we discussed two weeks ago) to on-base percentage.

Branch served a few more years as GM of the Pittsburgh Pirates from 1950 to 1955, before retiring. Branch died in 1965 at the age of 83 and was posthumously enshrined in Cooperstown in the Baseball Hall of Fame two years later in 1967.

While all of the above were notable achievements, what he is most remembered for (especially this Monday April 15th) is perhaps for breaking Major League Baseball’s color barriers by signing black player Jackie Robinson (pictured below).

Jackie Robinson was born on January 31, 1919. After playing for the Kansas City Monarchs of the Negro League, Jackie signed a contract with Branch Rickey and the Brooklyn Dodgers on November 1, 1945. Jackie started his professional career in Canada playing for the Montreal Royals, a minor league affiliate of the Brooklyn Dodgers.

72 years ago today, on April 15, 1947, Jackie Robinson broke the Major Leagues colour barrier when he played for the Brooklyn Dodgers. Robinson had an exceptional 10-year MLB career in which he was the 1947 Rookie of the Year, was an All-Star for six consecutive seasons from 1949 through 1954, and won the National League Most Valuable Player Award in 1949. Robinson played in six World Series and contributed to the Dodgers’ 1955 World Series championship. Robinson was inducted into the Baseball Hall of Fame in 1962, five years before Branch.

In 1997, MLB retired his uniform number 42 across all major league teams; he was the first pro athlete in any sport to be so honored. MLB also adopted a new annual tradition, “Jackie Robinson Day”, for the first time on April 15, 2004, on which every player on every team wears # 42. So when you watch any major league baseball game today, or the highlights tomorrow, it is in honour of Jackie Robinson that everyone is wearing 42.

And it was Branch Rickey who signed Jackie Robinson, following a three hour infamous meeting. [To learn more about that meeting and Jackie, I highly recommend you watch the 2013 movie 42, starring Black Panther Chadwick Boseman (not the father of modern baseball Henry Chadwick) as Jackie Robinson and Harrison Ford as Branch Rickey, and Branch Rickey’s great-granddaughter, actress Kelley Jakle from the Pitch Perfect trilogy, making an appearance.] So let’s take a look at one of Branch Rickey’s contributions to sabermetrics – on-base percentage.

On-Base Percentage

On-base percentage is a statistic generally measuring how frequently a batter reaches base. Unlike batting average, which Henry Chadwick calculated by just looking at hits and at bats, on-base percentage looks at many other ways of getting on-base.

AVG. = H ÷ AB

OBP. = [H + BB + HBP] ÷ [AB + BB + HBP + SF]

Henry Chadwick calculated batting average (AVG.) as hits (H) divided by at bats (AB). The on-base percentage (OBP) that Branch Rickey and Allan Roth developed took into account other ways of getting on base such as being walked (BB, for base on balls) or being hit by a pitch (HBP), as well as taking into account hitting a sacrifice fly.

Some people erroneously consider the denominator as the number of plate appearances (PA). However, plate appearances would also include certain infrequent events that will slightly lower the calculated OBP., such as catcher’s interference and sacrifice bunts.

In Homer at the Bat (Season 03, Episode 17), with Homer leading the Springfield Nuclear Power Plant team to the championship game versus Shelbyville, Mr. Burns decides to set up a one million dollar bet with Aristotle Amandopolis on who’s team will win. In order to win, Mr. Burns decides to cheat and recruit professionals on his team.

Mr. Burns: “No, Smithers, I’ve decided to bring in a few ringers. Professional baseballers. We’ll give them token jobs at the plant and have them play on our softball team. Honus Wagner, Cap Anson, Mordecai ‘3-Finger’ Brown…”
Smithers: “Sir?”
Mr. Burns: “What is it, Smithers?”
Smithers: “I’m afraid all those players have retired and… passed on. In fact, your right fielder has been dead for 130 years.”
Mr. Burns: “Damnation! Alright, find me some good players. LIVING players! Scour the professional ranks. The American League, the National League, the Negro League!”

Mr. Burn’s dream team was composed of pitcher Mordecai ‘3-fingers’ Brown, catcher Gabby Street, first baseman Cap Anson, second baseman Nap Lajoie, third baseman Pie Traynor, short stop Honus Wagner, right fielder Jim Creighton, center fielder Harry Hooper, and left fielder ‘Shoeless’ Joe Jackson.

Looking at Mr. Burns’ roster, we can see he too valued some of the same criteria Branch Rickey did as GM of the Brooklyn Dodgers.

Jim Creighton, who as Smithers’ so aptly pointed out died over 130 years ago in 1992, played in an era before Henry Chadwick created the baseball box score. So we don’t have all the numbers required to calculate his on-base percentage. However, ‘Shoeless’ Joe Jackson retired with one of the highest on-base percentages in history, and still the 17th highest of all time as of the start of the 2019 season. Likewise Cap Anson and Honus Wagner also were amongst the best in their era and currently rank 82nd and 97th of all time, respectively.

So let’s calculate ‘Shoeless’ Joe Jackson’s on-base percentages:

OBP.  =  [H + BB + HBP] ÷ [AB + BB + HBP + SF]  =  [1,772 + 519 + 59] ÷ [4,981 + 519 + 59 + 0]  =  2,350 ÷ 5,559  = .423

So ‘Shoeless’ Joe Jackson  has a career on-base percentage of .423. That is to say that he got on base 42.3% of the time he came up to bat. The only active player with a higher on-base percentage than ‘Shoeless’ Joe is Canadian Joey Votto of the Cincinnati Reds with an on-base percentage of .427 as of the start of this season. The all time career on-base percentage record is held by Ted Williams at .482, followed by Babe Ruth at .474. Jackie Robinson is currently 37th all time at .409.

As was mentioned last week, in Homer at the Bat, we saw Homer come to the plate 4 times in games. In those 4 at bats, he hit 3 home runs and infamously was hit by a pitch to win the championship.

So let’s calculate Homer’s on-base percentages base on what action we saw:

OBP.  =  [H + BB + HBP] ÷ [AB + BB + HBP + SF]  =  [3 + 0 + 1] ÷ [3 + 0 + 1 + 0]  =  4 ÷ 4  =  1.000

So Homer has a perfect on-base percentage of 1.000. No wonder he was induced into Cooperstown in the Baseball Hall of Fame last year.

Now that we’ve got a better understanding of on-base percentage, are you looking forward to see who get’s on base today? Excited to see everyone wearing #42 today? Were you already familiar with on-base percentage? Sound off in the comments below. You know we love hearing from you.