Making Math Fun… with Trading Cards!

I hated math. I still do, which is probably why I write. I just could never grasp certain concepts, and the more I studied, the more frustrated I would become. But I loved sports (I still do). And as a kid I collected sports trading cards–baseball, basketball, football, hockey. If it came in a pack, I bought it. Of course, collecting cards was a hobby…but I also discovered something extraordinary as I studied my favorite players–I was learning math. And I enjoyed it! Little did I realize at that time that math plays a huge role in every sport, especially when it comes down to evaluating players. How?

The statistics of sports (fun fact…it’s ALL math).

Every sport keeps its own statistics, numbers that more or less dictate how well (or poorly) an athlete is performing. And these statistics are more than mere numbers you just keep adding up, such as home runs, runs batted in (RBIs), touchdowns scored, goals scored, etc. Every average and statistic requires some type of math.

For baseball, you have tons of statistics and analytics that team executives use to scout and evaluate players. Some go way beyond my scope of knowledge, but others are much easier to calculate, including:

• Batting average
• Slugging percentage
• On-base percentage
• OPS (on-base + slugging)
• ERA
• WHIP (walks plus hits per inning pitched)

In football and basketball, many statistical categories involve per-game averages, such as:

• Points per game
• Rebounds per game
• Passing yards per game
• Rushing yards per game
• Assists per game

As adults, we can look at these categories and brush them off as basic math skills that are pretty easy to do with a calculator. And that’s true. But not to a young elementary school student who is struggling with multiplication tables and long division. Or who is having trouble following along with a word problem.

That’s when it’s time to appeal to their interests and break the math down in terms that they understand and want to learn. If you have a young sports fan in the house, it’s as easy as digging up some of your old sports trading cards or grabbing a pack at the local supermarket or convenience store. Then the fun begins.

The back of the card and how to analyze it.

OK, you grabbed a pack of baseball cards and you’re ready to share it with your child and teach him or her some basic math. Let’s take a look:

SWEET! You pulled a Mike Trout! Hang onto this one and keep it safe! Anyway, let’s dig into AVG (batting average). You can see Mike Trout’s yearly batting average and his career number as well. So, here’s where some division comes into play.

You’ll need to explain to your child that averages (in this case, batting average) require division, and you need to figure out which numbers to use. In the case of batting average, you’re determining the rate at which Mike Trout gets a base hit (H) per his number of at-bats (AB). So, for his ridiculous 2012 season, your child would note that Trout had 182 hits in 559 at-bats. To find the average, we need to divide 182 by 559. The result? An amazing .326 batting average! (It actually comes out to .3255, which would be rounded up to .326…another lesson built in!)

Now let’s look at some more complicated math…slugging percentage.

NICE! A Bryce Harper card…also a keeper! Anyway, let’s look at his league-leading slugging percentage from the 2015 season. In order to do the math, we need to understand how to calculate slugging percentage. Why do we need to do that? Well, we don’t…no one really does. But it’s good math practice that involves multiple calculations to come up with the final answer–think word problems. It gives kids something to concentrate on and plenty of practice with addition, subtraction, multiplication, AND division!

OK, slugging percentage is the number of total bases a player has, divided by the number of at-bats he has. So, how do we figure out total bases? Glad you asked!

In baseball, a single is one base, a double (2B) is two, a triple (3B) is three, and a home run (HR) is four. Makes sense, right? Let’s look at Bryce Harper’s numbers then. In 2015, he had:

• 38 doubles
• 1 triple
• 42 home runs

Let’s figure out the total bases:

1. 38 doubles x 2 = 76 total bases
2. 1 triple x 3 = 3 total bases
3. 42 home runs x 4 = 168 total bases
4. 76 + 3 + 168 = 247 total bases

What about singles? Ack! They’re not listed on the baseball card! So, now we need to figure out how many singles Harper had. Easy enough. Let’s find his total number of hits (H)…172. So, in order to determine how many singles Bryce Harper hit in 2015, we’ll need to add up his extra base hits (doubles, triples, and home runs), then subtract that number from 172 (total number of hits)!

38 (doubles) + 1 (triple) + 42 (home runs) = 81 extra base hits

172 – 81 = 91. So, Bryce hit 91 singles that season. Since a single counts as one base, we’ll add 91 to the 247 total bases he got from extra base hits.

247 + 91 = 338

Harper had 338 total bases in 2015. That’s one big part of the equation finished! Next, we divide his total bases by the number of at-bats (AB). Looking at his card, he had 521 at-bats in 2015. So…

338 ÷ 521 = .64875. Rounded up, that gives you a .649 slugging percentage…which went a long way in helping Bryce Harper win that season’s Most Valuable Player (MVP) award!

Didn’t that make a complicated math problem much more fun?

How about pitchers?

OK, let’s take a quick look at a couple of pitching statistics. Let’s see who you got in the pack…

Walker Buehler! You’ve got some great luck!

Let’s take a look at multi-step calculations to get both ERA (earned run average) and WHIP (walks plus hits per inning pitched) stats.

First, ERA. To calculate this, you’ll need to find the total number of earned runs (ER), then divide that by the number of innings pitched (IP)…then multiply that number by 9. Why 9? Because baseball games are 9 innings long, and any “per-game” type of pitching stat is kept with 9 innings in mind. How do we find Buehler’s ERA from 2019?

• 66 earned runs (ER)
• 182.1 innings pitched (IP)

66 ÷ 182.1 = 0.36243

Don’t forget, we have to multiply that by 9!

0.36243 x 9 = 3.26187 (baseball stats round to the nearest hundredth, so 3.26 was Walker Buehler’s ERA in 2019!

Let’s move on to WHIP. Remember, this is walks (BB–bases on balls) plus hits (H) per inning pitched. Looking at Buehler’s card, he had:

• 37 walks (BB)
• 153 hits allowed (H)

We add these up: 37 + 153 = 190

Buehler pitched 182.1 innings in 2019, and we want to find out how many walks + hits per inning he allowed. So, we divide:

190 ÷ 182.1 = 1.0433, or a 1.04 WHIP…which is really, really good!

Some simpler stats.

Those multi-step problems can be challenging, but there are also plenty of basic equations that are easy enough to figure out with some simple math.

Say you want to figure out how many rebounds and assists Michael Jordan averaged per game in the 1989-90 NBA season.

This is a pretty straightforward equation. Jordan grabbed 565 rebounds (REB) and dished out 519 assists (AST) in 82 games. So, to find both figures, simply divide the rebound and assist totals by 82.

565 ÷ 82 = 6.89 rebounds per game

519 ÷ 82 = 6.33 assists per game

Easy, right? And fun!

Math doesn’t have to equal misery.

Of course, not everyone feels this way about math. But it can definitely be challenging. That’s why it’s important to inject some fun into it, and sports cards supply all of the information for you–which beats inventing your own word/math problems, right? From basic equations to more complex calculations, the back of a trading card can be quite the educational tool–and a wise investment, which means that Today’s Lesson can be making math fun!