Thursday, May 14, 2009

The NY Times needs better editors

From a New York Times article on the SPF values found on sunscreens (emphasis mine).
The difference in UVB protection between an SPF 100 and SPF 50 is marginal. Far from offering double the blockage, SPF 100 blocks 99 percent of UVB rays, while SPF 50 blocks 98 percent.
If SPF 100 blocks 99%, then 1% gets through.
If SPF 50 blocks 98%, then 2% gets through.

For those not so good with the math, 1% divided by 2% is one-half. Thus, SPF 100 has double the blockage of SPF 50.

Is it too much to ask that along the way to a degree in journalism at least one math class is taken?


Azura said...

If I ever found SPF 100, however misleading, I would buy it. When you think of 100, you think of total coverage. It's a bit of false advertising.

...I would still buy it.

Jane Dough said...

Hahaha. Awesome catch. I would have never noticed it. Maybe I should be an editor for NY Times.

Anonymous said...

this is crap... u r not comparing blockage. u have to use 98% and 99% to do that. just find some other way to show off in maths

Jason Harx said...

Looks like I have a NY Times editor reading my blog now...

Cameron said...

Oh boy - another math fight between me and Dave... But dude, I'm not buying the logic. I think I can easily agree it has half of the failure rate, but not double the blockage.

Let's take another word example to prove the point.

I make a mixture that is 90% rum, 10% coke.

I make a second mixture that is 95% rum, 5% coke.

The second mixture does NOT have double the rum. It just has half the coke.


Killer B said...

Sorry Harx, but I'm with Cameron on this...It's only double the blockage if you consider the rate of failure for this event.

By the way, I'll take either the 90% OR the 95% rum and coke, please.

Jason Harx said...

You guys are killing me.

Cameron, your first drink has precisely double the Coke as the second drink. That's what we're discussing here, comparative blockage not a quantity.

You pour your drink as a quantity (e.g. 1 ounce Coke, 9 ounces Rum) regardless of how you choose to measure it later, sunscreen works based on a percentage of UVB that interacts with it.

Try this, SPF 50 blocks 98% of UVB, so do the math, what would be the percentage that would give you double the blockage?


Cameron said...

Ah, but here's the dilemma sir.

If there are a FINITE number of UVB rays (let's say 100), and your sunscreen blocks 98% of them, then it is IMPOSSIBLE to block DOUBLE, because there are only 2 rays left and you would block 100%.

If there are an INFINITE number of UVB rays, and you are trying to find the ratio of number BLOCKED 98%x/99%x, then the limit as X approaches infinity would be 1/1 meaning it is almost zero difference, so still only a marginal blockage.

Though I will still concur that it does cut the failure rate in half :). Writers are artists in semantics, not math...

Jason Harx said...

Cameron, using your example.

- SPF 50 blocks 98 out of 100 UVB photons
- it then blocks the next 98 UVB photons
- it has now blocked 196 out of 198 photons, double the amount of physical photons

196/198 = 99%

Yes, I see where you are going with the semantics, but that sort of math only works in business school. In the real world you can only calculate a percentage after the total quantities are in.

Cameron said...

Nah - if it blocks 98 out of 100 photons, then it would only block 98 out of the next 100 photons - so 196/200 = 98%...

Jason Harx said...


Cameron said...

OK, now that we've chewed on this a couple of days, let's take a moment for me to agree with Dave, but switch my semantics and math around.

For starters, what is SPF? I will tell you - it is an estimated measurement of the average amount of time a person can spend outside without being sunburned.

That means that nominally, SPF 100 allows you to stay outside TWICE AS LONG as SPF 50 (double the protection).

SO, here's why Dave's convoluted math works: SPF is a measure of failure rate, not success.

So, if 2% of UVB passing through burns your skin in 600 minutes (SPF 50* 12 minutes - just a benchmark), then it would take 1% of UVB TWICE AS LONG (100*12 minutes = 1200 minutes) to burn you. So a mere shift from 98% effective to 99% effective DOES DOUBLE the amount of time theoretically that you could stand in the sun without turning to a lobster.

Funny part is, here's where the real world comes into play: sunscreen is generally only effective for 2 hours, so the length of time is not really relevant.

But, the part where the NYT gets it wrong is really in their definition of what SPF IS, which may have helped them with their poor mathematics and semantics.


Jason Harx said...

My point was only their failure to understand that 99% coverage really does provide "double the blockage" of 98% coverage.

Certainly that's just the theoretical value. From what I understand, an SPF rating of over 30 is extremely hard to confirm experimentally and may actually provide reduced coverage of UVA.

Either way, what kind of an idiot would actually stay out in the sun for 100 minutes without reapplying?

Seems like the common consensus is that sunblock advertising over SPF 30 is 98% marketing and only 2% science.