There are many reasons someone can fall in love with baseball: the excitement of a home run, the thrilling catch of a fly ball in the outfield, the mastery of a double play, and more. The bat-and-ball sport is very popular in the US, where the modern version first developed. Baseball is now played worldwide in countries such as Canada, Mexico, Japan, and more.

In the US, there is the Major League Baseball (MLB) season, which runs from late March/early April to late September/early October. With approximately 3 months left till the end of the season, we take a look at how math is used in baseball.

Ted Williams, an American professional baseball player, is considered to be one of the greatest hitters to ever pick up a bat. He is the only MLB player in the modern era to hold a batting average over .400 for an entire season. That sounds awesome, but what is batting average, and how do we determine it? Let’s take a look at some of the important calculations in baseball and how we can better understand them. This is Spark Math by VISPARK‘s newest blog series, Mathematics in Sports, so let’s play ball!

## Earned Run Average: ERA

A pitcher’s ERA represents the number of runs a pitcher allows per nine innings of play. Each pitcher gets measured by their earned run average and the lower the number the better. In modern baseball, Bob Gibson had a career ERA of 1.12. That means he only allowed about 1 run per game he pitched, which is incredible. But how do we calculate ERA and how can your little pitcher figure out their own ERA?

**Calculating ERA**

As the name implies, ERA will involve using the math concept of average. First, what is an earned run? An earned run is a run that is scored without any errors on the field while the pitcher is on the mound.

**Major League Baseball ERA **= (Earned Runs ÷ Total Innings Pitched) X 9

In this case, a standard MLB game is 9 innings long and thus we multiply the average runs by 9. If you want to help your child figure out their own ERA, you would change the 9 to the number of innings in a game at their age level (Little League games are typically 6 innings long).

## Batting Average

Batting average is one of the most crucial statistics for baseball fans and coaches. A poor batting average can lead to a ball player being sent to the minor leagues or cut all together. In 2022, the league-wide batting average was 0.243. That means the best players in the world were only getting a hit 1 out of every 4 at-bats. For Ted Williams, his batting average of 0.406 is almost double the current average of today. It’s not easy to land a hit in the Big Leagues, and this makes what Ted Williams did even more impressive.

**What is Batting Average**

Batting average is one of the oldest statistics in the game and is simply the number of player’s hits divided by his plate appearances. This number will be between 1 and 0 in the form of a decimal such as .243. However, when you read a batting average, you would say it as a number. Instead of .243, you would say 243.

**Batting Average **= Player’s Hits ÷ Plate Appearances

This statistic can be measured through a game, a season, or even an entire career. Keep in mind, this stat does not track reaching base due to a walk or being hit by a pitch. Do your little ball player a favour by keeping track of their at-bats and hits then have them calculate their batting average for fun.

## On-Base Plus Slugging: OPS

This is a more modern statistic for baseball but according to some of the top MLB players of today, they overwhelmingly voted this as the most important statistic. While stats like Batting Average and RBI (runs batted in) are still important, OPS can be a more reliable statistic for predicting success in a player.

With OPS we are taking two standalone statistics, on-base percentage and slugging percentage and adding them together. This involves more math but we are left with a fun and useful stat.

### On-Base Percentage

Unlike batting average, on-base percentage accounts for any time a player gets on base from an at-bat.

**On-Base Percentage **= (Hits + Walks + Hit By Pitch) ÷ (At-bats + Walks + Hit By Pitch + Sacrifice Fly)

Example: The American professional baseball outfielder for the New York Yankees, Aaron Judge, in 2022. (177 hits + 111 Walks + 6 Hit by Pitch) ÷ (570 At-bats + 111 Walks + 6 Hit by Pitch + 5 Sacrifice Flies). 294/692=~.425. On-base percentage.

Judge led the league last year with a .425 on-base percentage meaning he made it on base on nearly half of his at-bats!

### Slugging Percentage

Slugging percentage is the total number of bases a player records per plate appearance. Isn’t that just like batting average? Actually, it isn’t because not all hits are weighted equal with slugging percentage. A home run will be weighted higher than a single and unlike on-base percentage, walks or hit by pitches do not count. A single is considered 1 base, while a home run is considered 4.

Slugging Percentage = (Total Singles x 1) + (Total Doubles x 2) + (Total Triples x 3) + (Total Homeruns x 4) ÷ At-bats.

Example: Aaron Judge in 2022 (87 Singles x1) + (28 Doubles x 2) + (0 Triples) + (62 Homeruns x 4) = 391 bases earned ÷ 570 at-bats= .686 slugging percentage

**OBS for Aaron Judge**

On-base Percentage of .425 + slugging percentage of .686= 1.111 OBS

### Final Word

Now that is a lot of baseball math and it is only the tip of the iceberg on stats for this sport. Students who can do the core basics of math can try calculating their favourite player or their own stats. For more exciting insight into mathematics in sports, stay tuned to our blog for the next in the series. If you’re looking to help your child level up their math skills, stop by Spark Math so they can start improving today.