# Broker Math

Disclosure – I have investments with both Vanguard and Schwab, they are both good companies. I don’t blame Schwab for this ad, odds are good that they used an outside firm. One that should be fired.

Do you see where they went wrong? .03 is 80% less than .15. But the reverse isn’t true, .15 is five times .03, not “Nearly 80% more.”

Say, we have 2 dogs. Mine is 10 lbs, yours is 20 lbs. Mine is 50% the size of yours, but yours is not then 50% larger. He’s twice the size. This is math we expect our kids to learn in grade school, well before high school.

And for the record, Vanguard charges me .02% for the S&P fund in my 401(k) retirement account. The ticker is VIIIX, look it up.

# Gold Seller doesn’t know percentages

The Globe ad was just one example of how ad writers can be clueless. Here’s another example. I scanned this from an advertisement from a company trying to sell you gold coins. Set aside the timeframe of this ad, by the end of 2016 the S&P had recovered so that 2000-2016 would have shown growth to \$21,000, otherwise known as +110%.

Look at the percent growth the ad shows for Real Estate and Gold. \$10,000 to \$26,065 is “Up \$16,065” which, from a starting point of \$10,000 is +161% (rounding up). Not +260%. If gold was worth just \$11000, would they have advertised “Up 110%”?

I can’t help but wonder what the qualifications are for ad writer at these companies.

# The Mother of All Math Errors

First, a disclaimer. War is awful. As is people dying. I won’t get into the politics of recent events, just the math.

It’s time to call out USA Today for what it is. Not quite fake news, the right words might just be “a mathematical abomination.”

The graphic might be visually pleasing to some. “Hey, the bomb was 5 times the height of a man.” Ok. Then, the comparison to the bomb the US dropped on Hiroshima. The text suggests this bomb was more than 2/3 as powerful as the Hiroshima bomb. And that text made it past a number of employees at USA Today. But not one of them had the mathematical gut to realize something was wrong. The Hiroshima bomb was an atom bomb. Its blast was equal to not 15 tons of TNT, but 15 kilotons, or 15,000 tons. The Atom bomb was more than 1300 times as powerful as the bomb just dropped in Afghanistan.

USA Today deserves their own category for innumeracy. This is typical for the paper.

# 90% off!

This speaks for itself. “Was \$235” and “90% off” makes the math easy. 10% is left. \$23.50. If they rounded to \$24, I’d cut them some slack. \$29 is, well, 87.66% off.

# 2016 12 08

Ha! That’s today’s date. My daughter tells me this is not remarkable. That I seem to come up with an observation like this pretty often. Well, to be fair, I was pretty excited when it was 3/14/15 especially the two times the clock showed 9:26:53. But that was a year and a half ago.

Let’s see when my next date of interest will be. Stay tuned.

# Supermarket Math

The grapes were on sale, \$1.99. But, with a \$25 purchase and coupon from my store flyer, \$0.97 per pound. When I went to buy the other items, the chicken I wanted was out of stock. I got a raincheck, and at the same time, asked the customer service person if they’d honor the grape sale even though my order was under \$25. They agreed, but good luck trying to override anything on a cash register. The cashier couldn’t figure it out and the manager finally came over and couldn’t do it either. Finally, he said he’d just enter a credit. Now, \$1.03/lb discount times 4.52 lbs might be tough to do in your head. \$1 times 4.5 is \$4.50. The extra .03/lb gets us to \$4.63. I’d have been happy with \$4.50, I just wanted to leave. \$5.56 is what he entered as a discount. Final cost \$3.43 for 4.52 lbs. We need smarter cashiers or Siri-enabled registers.

# Don’t ignore scale

I read a question on the Skeptics StackExchange site titled Does this map show every car bomb explosion in Baghdad since 2003? along with this image –

As I looked at it, three things occurred to me. First, violence is awful, the ideal number of violent deaths per year is zero. Second, the image is a time-lapse, accumulated over 13 years. And last, the size of the red dots are misleading. zoom out much further and the image is a solid red blur. Zoom in, just a bit more, and you’ll have some sanity –

The answer to the original question is “no,” these were total deaths, not just car bombs. But the important issue, that the map’s scale implied far worse than reality, was something the members of Skeptics weren’t interested in. When I found the data source, and rescaled the image, my answer was closed as “original research.” Suffice it to say, the US city of Detroit averages 300 homicides per year, so nearly 4000 over the same 13 year period.

You can look at this and decide whether the original image was fair or misleading. My only point today is that scale can’t be ignored.

# Discounts on My Sunday Paper

“Others pay twice as much.” And yet, I’m saving 75% if I take this deal. The deal is better than the copy reads, but still, the math is just awful.

Do you have any examples like this? Please click above to submit or forward to me at badmath at b-1.org.

# Growth and Decay

This is an ad I set aside some time back. It took a few seconds to see what I found so wrong with this ad. Was it that this chart had no vertical axis, showing investment return over time? No.

It was the failure of the marketing department to catch the simplest of math errors. When we see a price rise from \$10,000 to \$14,197, it’s 5th grade math that will tell us the percent growth. 10000/14197 = 1.4197 or a 42% rise. Similarly, The \$10,000 rise to \$26,065 isn’t “Up 260%”, it’s actually up 161%. They can have their 1% extra due to rounding.

In the US, there’s a TV program called “Are You Smarter than a 5th Grader?” In the case of whoever edited this copy, I believe we have our answer.

# A False Correlation

Some time ago, a bit of news came out, “Coffee drinkers have a higher cancer rate than non coffee drinkers.” My immediate response was “false correlation.” My wife asked me why professionals would issue a report that was not only flawed, but flawed so badly that it took me seconds to reach that conclusion. That’s actually the tough part of this. Let me explain the easy part, how false corrections can easily produce bad results.

I’ll use a population of 10,000 random coffee drinkers. They are surveyed and discovered to have a cancer rate of 5%. Those conducting this experiment find a 3.3% rate of cancer in the general population, and even with margins of error (I’ll pass on that math for this article) the 5% rate they see is significant, 50% more instances of cancer than expected.

Let’s look at the data that might have revealed the error made.

• Cigarette smokers show a 10% rate of cancer
• Non-smokers show a 1% rate of cancer
• Random population shows 25% smokers

You can already see where this is going. The study was conducted to understand if coffee drinkers had a higher rate of cancer. So far, I’ve jumped to data regarding smoking. To continue –

• Coffee drinkers reveal a 50% rate of smoking (Not likely the case, I exaggerate a bit to make a point)

Now, in a population of 10,000 coffee drinkers, the 5,000 smokers would be expected to have 500 cancer instances and 5000 non-smokers, another 50. When this is taken into account, the resulting 500 cancer results are actually a bit lower than expected. New headline? “Coffee may reduce cancer rates for smokers.”

The above is a bit of an exaggeration.The truth is, press releases rarely offer the data behind the conclusion, leaving the reader to decide whether the headline is worth researching or giving any credence at all. It was only a few month later that I read new reports that reached the same conclusion I did. That coffee drinkers tended to have more smokers that non-drinkers. In the end, even the so-called pros make mistakes.

Do you have any examples of similar error in data analysis and false correlation? Send me a note, I’d be happy to print it.