Math for SpoJos

(& other numerically challenged COM

majors)

Comparing apples and oranges

• Rates (percent)

• Index numbers (CPI)

• Percentile rankings (SAT v. ACT)

• Standardized scores (standard deviation units)

Percent is a rate per hundred

• First, convert the fraction to a decimal by division.

• ¾ = .75• To get a rate per hundred, multiply by

100• .75 * 100 = 75• Another word for “rate per hundred” is

“percent.”

Other rates

• To get a rate per thousand, multiply by 1,000.

• .75 * 1000 = 750

• To get a rate per hundred thousand, multiply by 100,000

• .75 * 100,000 = 75,000

Furman’s sports teams have 693 athletes, or 5 percent more than it had last year. How many did it have last year?

What number when multiplied by 1.05 yields 693?

Answer: 693/1.05 >> 660

Order-of-magnitude checks

The Jacksonville State football coach expressed concern that.05% of his team failed a drug screening. Should he be concerned?

Drug use by athletes

What the numbers mean:

5 percent = 5 out of 100 or 1 in 20

.5 percent = 5 out of 1,000 or 1 in 200

.05 percent = 5 out of 10,000 or 1 in 2,000

Anything wrong here?

Average price of aUGA football ticketlikely to surpass $45 toset a new record

True or false?

The record is …

In nominal dollars, the record is $40.50

But in constant dollars: $56.50

So, no, the record will not be broken in a way that matters.

National League revs

Ticket revs for the American League for the 2015 season: $384.1 million. Is this a record?

In 1939, revs totaled $199 million. So it looks like a record, but what’s $199 million in constant dollars? Did 2015 in fact break the record?

Consumer Price Index

• 1939 = 13.9

• 2014 = 235.8

13.9 = $199 million

235.8 x

X = (235.8 * 199m) / 13.9

http://www.bls.gov/cpi/home.htm

$199 million in 1939 had the same buying power as $3.4 billion in 2014.

NL’s revs are NOT a record. Not even the same monetary universe.

How to write with numbers

First rule:

no more than two numbers in a paragraph

Example• Escobar hit .292 in the playoffs overall, but

his batting average for the series against Toronto was .400, with a 1-for-4 performance in Wednesday’s loss that left the Royals’ lead in the series at 3-2. If you combine the two years, Escobar’s .333 batting average is the best among Royals regulars, and his regular-season average in that span is .270.

Whaaaaa?!?!

Second rule:

if you use two numbers in a paragraph, it’s better if they can be compared with each other.

How to write with numbers

Example

As of Tuesday, Boston had a team OPS of .767. Division winner Toronto topped the league at .989.

--USA TODAY

Third rule: don’t use more significant digits than you need.

• If 22.34% of the public believes the Royals can upset the Mets in this year’s Series.

• No. Either report it as 22% or, better yet, use “roughly one in five.”

• Remember: Polls are never actually accurate to fractions of a percentage point, so presenting to much in this context is to mislead about accuracy.

How to write with numbers

On the other hand …

A baseball batting title sometimes comes down to a thousandth of a percentage point, so give all of the data you need to provide clarity.

2015 batting averages:

6. Yunel Escobar, .314

7. Joey Votto, .314

Writing with numbers

• Express the concept in words first.

• Then back it up with the numbers.

• Show the numbers as part of a system.

Example

A new study finds what may seem obvious to even casual observers: Many National Football League players are obese.

--USA TODAY

Five paragraphs later …

• Approximately 56% of players qualify as obese, which is roughly 30 or more pounds over a healthy weight.

• About 26% of football players qualify as severely obese, and 3% are morbidly obese.

Writing with numbers

• Choose your typical value carefully

• Mean = the value each case would have if each case were the same (and the total was constant). Much like an average.

• Median = the value of the middle case.

• Mode = the most frequent value.

Outliers: Graduates of what UNC academic department had

the highest mean salary in 1986?

• School of medicine

• School of journalism

• School of law

• Geography department

• School of business administration

Michael Jordan, who graduated from UNC in 1986, majored in geography!

• The Chicago Blackhawks (NHL) scored 229 goals in the 2014-15 season and allowed 189 goals scored against them. What were the team’s per game averages?

The New York Giants punt the ball from their own 35-yard line. The ball is caught at the Dallas 18-yard line and returned nine yards. How far did the ball travel, and what was the net change in field position?

Jordan Spieth drives off the tee 325 yards. He then hits a 3-wood 175 yards into a bunker. His third shot goes 24 yards, leaving him three feet from the cup. He puts out. What is his score, and how long is the hole?

The Pittsburgh Pirates paid Honus Wagner $10,000 in 1912. How much would that salary be worth today in constant dollars?

Yoenis Cespedes had 77 at-bats for the Mets with runners in scoring position. He got a hit in 24 of those at-bats. What’s his batting average for that situation?

Knuckleballer R.A. Dickey pitched 186 innings in 37 games, giving up 47 earned runs. What is his ERA?

Todd Gurley has gained 812 yards rushing in the first six games of the season. If he continues at this pace, in what game will he break the Rams’ rookie rushing record of 1,406 yards?

How large a role should statistics play in how a reporter covers a story?

How should we use statistics to better interpret or understand a game?

Math for SpoJos

(& other numerically challenged

COM majors)