Calculating Baseball StatisticsUsing Algebraic Formulas

By E. W. Click the Baseball Bat to Begin

What you will be learning!

• You will be learning how to:• Calculate averages given two variables to the nearest thousandths• Calculate weighted averages given multiple variables to the nearest

thousandths place• You will also learn how to find and solve for missing variables when given the

averages or weighted averages.

Before hitting the field to play ball you need to make sure you know

how to get around

The baseball will be used to take you to the previous

screen

Home plate will take you to the home menu

The baseball bat will go to the next page

Definitions of Baseball Statistics

• Baseball is full of stats and all of them have a special abbreviation that you will need to get use to• The Lesson Includes the following

• Hit (H) – Times a player gets on baseball• At Bats (AB) – Number of times a player tries to get a hit• Single (1B) – A Hit where the batter reaches 1st base• Double (2B) – A Hit where the batter reaches 2nd base• Triple (3B) – A Hit where the batter reaches 3rd base• Home Run (HR) – Hit where the batter touches all three bases and home plate• Batting Average (BA) – percentage of hits per At Bats• Slugging Percentage (SLG) – Weighted average that takes total bases per At Bats

Example of a Baseball Card

Front of the baseball card just has the player’s picture, name, and team

The back of the card has the players basic information like height and weight along with season and career statistics.

Solving for SLG %

QUIZFinding missing variables

Solving for Batting average

Click the base you want to try first

Bases get more difficult as they go

Only take the quiz when finished with all 3 bases

What is Batting Average

•Batting average is one of the most basic, but main stats used in baseball when it comes to evaluating a player.•Batting average tells you the percentage of how many

hits a player has divided by the number of At Bats he has.

How to Solve for Batting Average

•Batting average, or BA, is displayed in decimal form and is rounded to the nearest thousandth• EX) .250 or .333

• The equation for batting average is:

Solve for Batting Average• If a player has 32 hit and 100 at bats, what is the correct way

to display his batting average

.32

32100.320

3.125

Incorrect

• Remember• Batting average is always in decimal form.• Batting average is always rounded to the thousandths place.• The equation for batting average is.

Go Back and try again

Correct!!

NICE JOB!

The correct way to say a batting average is to say it like this, three twenty.

Next we will solve batting average using

baseball cards

For batting average you are only interested in two categories. Hits (H) & At Bats (AB).

Examine this baseball card

Find the players batting average for 2008

.273

.234.252

.298

Incorrect

•Remember•When you are using a baseball card to find batting average

you only use the hits and the at bats.

• Also make sure you use the right year total row.

Go back and try It again

Correct!!

NICE JOB!The Player has 114 hits and 418 at bats in the year of 2008 so

Go back home and select a different base

What is Slugging Percentage

SLG % is a weighted average that takes into account how many total bases you reach and compares it to At Bats.SLG% differs from batting average because batting average only takes hits into account and not the value of each hit.

SLG % EquationThe general equation for SLG % is

SLG% is displayed in decimal form and rounded to the thousandths similar to batting average. However, it is possible for a player to have a slugging % than 1, unlike batting average

Total Bases?• Total bases is something we haven’t discusses, but that’s ok.

It is pretty easy to find.• Each hit has a value – single, double, triple, and Home Run• The value for each is:• Single = 1• Double = 2• Triple = 3• Home Run = 4

Total Bases?After you know how much each type of hit is worth, you just multiply the total amount per type and the value

If a player has 17 singles, 8 doubles, 1 triple, and 4 HRs then

And that would equal 52 total bases.

Solve for Total Bases• If a player has 84 singles, 23 doubles, 3 triples, and 19 HRs in

a season, how many total bases does he have?

129

250215

349

Incorrect

•Remember

• If you had them together without multiplying each value, you would just get hits

Go back and try It again

Correct!

That is right!

That equals 215

Solve for Slugging Percentage

• If a player has 119 singles, 48 doubles, 9 triples, and 5 Home Runs in 578 at bats, what is his SLG%

.307

.350.667

.453

Incorrect

•Remember• To find SLG % you have to find total bases first

• Then you divide by the number of At bats.

Go back and try It again

Correct!

That is right! Total bases is equal to 262 and that divided by 578

is .453

Getting information for SLG from baseball cards

• To Find SLG% from a baseball card, you have to use the information found in 2B, 3b, and HR.• Most baseball cards don’t give

you singles so you have to calculate that by

Find this players Slugging % in 2010

.307

.350.532

.453

Incorrect

•Remember• Focus on the 2B, 3B, HR, and calculate the 1B to find total bases• Make Sure you are using the correct year• Finally recall the equation is

Go back and try It again

Correct!

Looks like you are getting the hang of thisThe total bases = 295

So SLG% =

Go home and start working on the final base

Solving for a missing variable

For this section we are going to take what we have already been taught, and expand on it a little.

You will be given batting average or SLG%, but one part of the equation will be missing and you will learn how to find what the missing part is equal to

Solving for the missing variable in Batting Average

Finding the missing variable for batting average is simpler of the two because there are only 2 variables

The two variables are Hits and At bats

EX1) We know BA and Hits. Solve for AB

Step 1) take original equation and multiply both sides by AB

Now you have: (AB)BA = Hits

Step 2) divide by BA so you end up with

Tips!

• Remember that when solving for the missing variable you need the missing variable on one side of the equals sign and everything else on the other

• Also it is important to realize that for these problems you are finding an approximate answer since BA and SLG% are both rounded

Solving for hits• If the player has an average of .286 and he has 123 AB, how

many hits does he have?

35

3020

25

Incorrect

•RememberThe original equation was And since you are trying to find out how many hits he has you need to solve the equation so Hits is on one side

Go back and try It again

Correct!

Remember to just round to the nearest number

Solving for missing variables in SLG%

- This is a little more difficult because SLG% has 5 different variables to choose from

- It is simple to solve for AB so we will move on to a harder example

Solving for singles

Step 1) take the original equation and multiply AB

Step 2) Take the three variables you know and subtract

Hint- Since singles are multiplied by 1, you don’t have to go

any further

- If you solved for any of the other 3 then you would have to divide by the respective numbers like divide by 2 for doubles

Solving for the missing variable

• How many Home Runs did the player hit if he had a slugging percentage of .682, and he had 110 singles, 32 doubles, 1 triple, and had 632 AB

45 HR

64 HR53 HR

72 HR

Incorrect

First solve for HR

Next you just have to plug in your numbers

Go back and try It again

Correct!

If you were able to solve for the missing variable (HR) and got 64 Home Runs, then you are ready to take the final quiz.Go home and click on the quiz. Good Luck!

Quiz #1Player A has a total of 2297 hits and 8185 AB, and Player B has 5795 AB and 1645 Hits. Who has the higher average

Player A Player B

Incorrect-Make sure you are plugging the correct stat in the rights place of the equation

-Remember the equation for batting average is

Go back and try It again

Correct!

Player B has an average of .284 over his career, but Player A has an average of .281. It is close, but Player B has a higher average

#2Player A has 1267 singles, 386 doubles, 8 triples, 422 Home runs, and 8185 AB.Player B has 1136 singles, 332 doubles, 21 triples, 156 Home runs, and 5795 AB.Who has the higher SLG%

Player A Player B

Incorrect

-Notice that these are the same players as the previous problem and just because someone has a higher average does not mean he will have a higher SLG%-The formula i

Go back and try It again

Correct!

Player A’s SLG% = .499, while Player B only has a SLG% of .429

You should notice that Player A has hit a significant amount more Home Runs and how that affects it.

#3 Find the missing stat for batting average for 2006

556 492589528

Incorrect

Since the equation is , you have to solve for the missing variable which in this case is AB

Go back and try It again

Correct!

When you change the equation to solve for At Bats you will see

Just 2 more questions. Almost done

#4 Solve for the missing variable in SLG% in 2006

122 112136145

Incorrect- It may not be obvious what the missing variable is at first but you are solving for singles (1B)

You can do this two ways, and the first would be to solve the equation for 1B or simply just taking Hits-2B-3B-HR

Maybe you should try both to see if you get the same answer

Correct!

If you found that

Then you did more work than you needed.Hits-2B-3B-HR would have got you the same answer but it was

good practice

#5 Critical thinking

.325 .310.306.298

Find the Players Batting Average GivenAB = 533 Triples = 0 Singles = 111 SLG% = .489 Doubles = 22

Incorrect

Don’t feel bad, this problem take some thinking-To Find BA you need Hits and AB-Since you don’t have Hits you need to use H=1B+2B+3B+HR to find how many-Finally you don’t have HRs so you have to calculate it by changing the SLG% equation

Correct!

That was a hard problem and you should feel good that you got it right

1st 2nd H = 111 + 22 + 0 + 26 = 159

3rd

Congratulations!!!

• You have finished this lesson of finding averages, weighted averages, and solving for missing variables. You have passed the quiz by taking what you were taught and thinking critically. You may go home and review or exit the lesson using the ESC key.