## Apple’s Fuzzy Math

I love Apple products. I have an iPhone and a Macbook Pro. I think that the iPhone 4 problems are overblown.

However, they may have just tried to pull a fast one on us with some funky math.

(CAVEAT: The Apple text says “<1 additional calls dropped per 100 calls compared to 3GS". If that means less than one additional call dropped per 100 calls DROPPED then that truly means less than 1% difference. If that number means less than one additional call dropped per 100 calls PLACED then my post below stands.)

I was watching the liveblog of the press conference on Engadget and saw Jobs flash up this slide:

They said that when you compare the number of dropped calls per 100 calls made between the 3GS and the 4, the difference is less than 1. Huh? Sounds like the difference is 1/100 or 1%, right? A trivial number?

Not necessarily. Lets break that math riddle down into a couple of scenarios where it’s easier to see the math in action. These are examples only, as I don’t have the actual dropped call data, since it’s AT&T proprietary:

3GS drops 1. Dropped calls = 1
iPhone 4 drops “less than one more than the 3GS”, say 0.9 (it’s an average). Dropped calls = 1.9

iPhone 4 rate 1.9 / 3GS rate of 1 = 1.9.
That means that the iPhone 4 drops 90% more calls than the 3GS in this example. Not a headline you’d want to report.

Try this one:

3GS drops 5. Dropped calls = 5
iPhone 4 drops “less than one more per hundred than the 3GS”, say 0.9. Dropped calls = 5.9

iPhone 4 rate 5.9 / 3GS rate of 5 = 1.18.
That means that the iPhone 4 drops 18% more calls than the 3GS in this example.

One more:

3GS drops 8. Dropped calls = 8
iPhone 4 drops “less than one more per hundred than the 3GS”, say 0.1. Dropped calls = 8.1

iPhone 4 rate 8.1 / 3GS rate of 8 = 1.0125.
That means that the iPhone 4 drops 1.25% more calls than the 3GS in this example.

Do you see where I’m going with this? They came up with a very mathematically vague way to report the additional dropped calls. It could be a case where the difference truly is only 1%, but they didn’t say 1%. They said less than 1 more out of 100. And that could be anything from 1% to %100’s of percent more than the 3GS, and still be mathematically true! How’s this for a mind-blower:

3GS drops 0.1 (or 1 out of 1000). Dropped calls = 0.1
iPhone 4 drops “less than one more per hundred than the 3GS”, say 0.8. Dropped calls = 0.9

iPhone 4 rate 0.9 / 3GS rate of 0.1 = 9.
That means that the iPhone 4 drops NINE TIMES as many more calls than the 3GS in this example.

And all of these examples fit within Apple’s “<1 out of 100" statement. Apparently, marketing IS Rocket Science…

### 2 Responses to “Apple’s Fuzzy Math”

1. Richard Says:

The relative comparisons are kind-of irrelevant for cases like this. I may like knowing that my food is 20% less poisonous than yours, but the important question is if my food is going to kill me or not. The brain likes comparisons more than absolutes, so statistics tie humans in knots too much.

Does the new phone drop an acceptably low number of calls? I guess the best answer Apple will give us is: if a phone that drops about 1 more call out of 100 than the 3GS is acceptable, then yes.

2. Prospectus Says:

Yeah, it’s overblown. The press is dumb. I just saw an infinitely valued equation presented in “1%” clothing and it irked me. The curse of an engineer I guess. I’m still going to buy an iPhone 4 either way. Because it is the best phone. I can download apps to it and it has the wi-fi’s. I want the one with the bigger gee bee’s.