Above you can review an advertisement created by Sprint PCS, which was printed on page 207 of the May 23, 2004 edition of Forbes magazine. The primary thrust of the ad is that Sprint PCS’ network is 25% larger than AT&T Wireless’. At least, that is what I assume the ad is trying to convey. The ad actually says that you can “Get information in 25% more places on the Sprint high-speed wireless data network.”
Now, I will not go into the nuances of what that quote actually means, but because many of us understand that in a three dimensional world, even if Sprint PCS has only 1 cellular tower capable of high-speed wireless connectivity, they could factually make the following claim: “Get information in an infinite number of places on the Sprint high-speed wireless data network.” Why can they say “infinite?” Well, a single Sprint cellular tower, positioned on the surface of the Earth would roughly give a coverage area in the shape of the top half, or two-thirds, of a sphere (I say 2/3 because the tower is up in the air, after all and we have all seen The Terminator, so we understand what a sphere, a little up off the ground might look like – think of one of those around each tower – now cover your privates, to shield yourself from the radiation!) Now, this 3-D volume that is covered, of course, has an infinite number of physical locations within it, where you, the customer, could access the high speed network. This, of course, assumes that their network is working. But, I will concede that as a given for the rest of this discussion.
No – my concern is not with the text, but with the graphics that lead the advertisement before the text. Sprint has chosen the ubiquitous, classic iconic cityscape for the American city, in Blue and Red, to show graphically the actual size differential between AT&T and Sprint PCS (respectively). Now, the text claims “25% more places” than AT&T, and we know that they could have also written “Get information in infinitely more places on the Sprint high-speed wireless data network.” But, they chose to quantify it with 25%. I am cool with that.
We could go into a rather lengthy discussion of what this means. 25% more what? More towers? More bandwidth? Are there 25% more business and residential locations with Sprint’s network? So many variables factor into this, and I would assume that Sprint has gone through some lengthy calculations and then decided to back off the numbers a bit, just in case somebody was going to actually audit this information. So let’s further assume that Sprint does, in fact, have 25% more network capacity than AT&T. The article does, in fact, claim that Sprint “reaches over 245 million people” which must be garnered from taking the coverage area, and counting the number of people who live within it. It further states that the “Coverage claims are based on the Sprint Nationwide PCS Network and the AT&T Wireless GPRS/EDGE National Network excluding roaming areas.” Wow – that was a finger-full to type, but I am sure that you got all that – surely it somehow translates into Sprint having something 25% larger than AT&T.
OK – so this is all well and fine so far, I suppose – I mean, I am seeing some advertising license here, but hey – Wagner will have you believe that two waves of your hand with the new Wagner Power Sprayer from your sidewalk in front of your yard will paint the entire front of your whole house, and one wave will do a fence. My daughter really wants me to buy one, because “it will save you a lot of time Daddy, and we could change the color of our house every day.” What a Sweety-Pie. 5 years old and already mindful of the value of her Father’s precious time. Maybe she wants me to get my chores done more quickly, so that I will play with her more. . . so she could be devious yet . . . we’ll call the jury “still out” on that one.
If you are still reading, I am sure you are asking what the punch line is. Well, here it is: And, the vast majority of people in the world will never see the wool that Sprint is pulling over their eyes. In fact, probably over a dozen people handled this very ad and they obviously did not catch it, as the ad is, in fact, in print. The two icons, covering the upper third of the ad, are meant to convey just how much bigger Sprint is than AT&T (or what the fine print said it was to mean). However, the Sprint cityscape, which should then be 25% larger than the AT&T cityscape is not actually only 25% larger. In fact, it is 75.89% larger. This means that Sprint is graphically showing you that they are OVER three times larger than AT&T, than they really mean to! Further, the Sprint ad folks know that the graphics stick in your mind more than the text, which is why they ran them first, “front and center” so to speak. They also know that you like Red more than Blue, which is why they gave Blue to poor AT&T. Few people want to buy a brand spanking new Blue Corvette ZR-1, we all can agree on that. Heck – do they even make the Viper in Blue? I have never seen one . . . poor Pepsi, but I am not going to get into the cola wars today!
Anyhow, the size of the image is based on the area that the image takes up. I measured the height and width of both, with a digital caliper that is accurate to within 1/1000th of an inch. Anyone who knows me and my currency collection knows that I am good at measuring with a caliper. Thus, the height and width were multiplied and the areas were compared. Here are the measurements that I found:
AT&T – Width is 1.898 inches, Height is .878 inches
Sprint – Width is 2.529 inches, Height is 1.159 inches
So, AT&Ts representation of their network has a total volume of 1.666 square inches in this ad. Divide that out by the amount of cash they have spent on their network, and you are looking at some serious cost. Per square inch, I mean. AT&T cannot be happy about the insinuated cost of their network here. Sprint PCS’ area is a whopping 2.931 square inches, representing their “25% larger network” than that of AT&T. Well, it is, in fact, being represented as being 75.890% larger. (Better keep three digits of accuracy going here, eh?)
Now, I have seen this mistake made in print before – both in other ads and in the newspaper (you can thank USA Today for the prevalence of these graphics in print media today – it is truly a double-edged sword – nice to have color graphics to convey a quick point, but bad to have them done improperly, so the public walks away with the wrong ideas). And let’s be honest here – advertisement folks (and those in the general print media) are not typically known for their strong math and science skills, if you know what I mean. Also, being primarily of the Democratic persuasion, they are also not too interested in facts, or thinking long term. No, they are more interested in pulling the wool over people’s eyes by slight of print, speech, text and/or hand. So, at this time, I would normally point out how adding 25% to both the height and width of AT&Ts Blue cityscape would not be correct. In fact, that would yield a Width of 2.373 and a Height of 1.098 for Sprint PCS’ cityscape, for a total area of 2.604 square inches, which would still be a whooping 56.250% larger than AT&T. Twice the textual claim.
No, as I can attest, and will go on to prove now, utilizing my Mathematics degree (and I thought that it would never help me in life!), is that to correctly compare these two cityscape icons, Sprint PCS should have added 12.328% to the Width, and 11.282% to the Height, for values of 2.132 inches for the Width, and .977 inches for the Height, which would have given them a cityscape area of 2.083 square inches, almost exactly 25% larger than their competitor, AT&T.
But, here is where it gets REALLY good:
[The following account is merely a conjecture on my part of the events as they may have unfolded. No facts were used in determining this representation of the possible chain of events, and any similarity to any real facts or real persons is entirely coincidental:]
Sprint, not wanting to have a “small” network (certainly not smaller than AT&Ts!), guaranteeing to be shunned by all the girls in Junior High, have taken, what we call in Mathematics, a “little multiplicative liberty.” (Okay, I made that phrase up, but I am calling Pat Riley to find out how to trademark it now.) So, I am sure that this is how it started:
No, what went to print was an AT&T cityscape of Width 1.898 inches and Height of .878 inches, with the Sprint PCS cityscape being 2.529 inches by 1.159 inches. You see, these measurements are fully 33.246% wider, and 32.005% taller than AT&T’s.
In text, Sprint claims to be 25% larger, in graphical form, they claim to be 75% larger (76% if you are rounding to the nearest percent), but no matter how you cut the cake, they definitely purposely exaggerated the size of their cityscape. Just no question about it.
“Truth in Advertising” right, Junior Ad Man?