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Chess reduces the chance of getting Alzheimers by 60 to 75 Percent

Where does the figure that chess reduces the chance of getting Alzheimer’s by 60-75% come from?

By Coach Patrick

It comes from the article written by the Associated Press (below in it’s entirety) that says that, “Adults with hobbies that exercise their brains — such as reading, jigsaw puzzles or chess — are 2.50 times less likely to have Alzheimer's disease, while leisure limited to TV watching may increase the risk, a study says.”

I looked at the figure given and it made no sense to me. “2.50 time less likely?” What percentage would that be? Not being a mathematician I searched online for help and found a “Mr. Math” who helped people with math problems and he confirmed my suspicion that it meant “60-75%” and he gave me the math to show it. (E-mail below) If you have any other information to verify or disprove this, please let me know.

Sincerely
Patrick Ellis
(Coach Patrick)

THE ARTICLE

http://www.usatoday.com/news/health/2001-03-05-alzheimers-hobbies.htm

This article says that chess may reduce your chances of getting Alzheimer's by 75 percent:

http://www...preventalzheimersdisease

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THE EMAIL

As Patrick wrote to Dr. Math
On 08/28/2007 at 00:37:25 (Eastern Time),

[Question]
If someone says "Research shows that people who play chess are 2.50 times less likely to get Alzheimer's disease than those who just watch TV.”

How can that be expressed in a percentage? I think the answer is that chess players are "60-75 percent less likely" to get Alzheimer's than those who just watch TV, but I'm not sure why. Am I correct? Can you show the math involved?

Thanks! Coach Patrick

[Answer]

Dear Patrick,
I think we have to be careful here; the phrase is something of an diom in English. If I took the phrase "2.5 times less likely" piece by piece, I'd say that 2.5 is the same as 250%, so it should mean the same as "250% less likely." The way we would calculate this is to take 250% of (or 2.5 times) the base number (the likelihood of getting Alzheimer's if you "just watch TV") and subtract this from the base number. However, if you do that, you get a negative likelihood, which makes no sense!

What you tried instead, if I follow your thoughts correctly, is to take "2.5 times less likely" to mean "1/2.5 times as likely." I think this is correct; it's what people mean by the expression.

Here is the logic, as far as I can see it: when they say "2.5 times less likely", they mean "less likely by a factor of 2.5". If you want to REDUCE a number in a multiplicative fashion, you need to DIVIDE by the factor rather than multiply. (Since the given factor is greater than 1, multiplying by it would increase the number rather than reducing it.) Thus the intent is to divide by 2.5, or equivalently, to multiply by the reciprocal of 2.5. Thus you express 1/2.5 as a percentage:

1 x
--- = --- ==> x = 100/2.5 = 40
2.5 100
I would suggest stopping here and saying that chess players are "40% as likely" to get Alzheimer's. But you want, I suppose, to get it back into the format of "... less likely", even though the meaning of the word "less" is significantly different in the new context. (It means to subtract, not to divide.) Given that this is what you want to do, you are correct that "40% as likely" is equivalent to "60 to 75% less likely."

Does this make sense?