The Math of Unlimited

If one were to try to boil down what I say into a handful of specific sound-bites, one of those bites near the top would probably be, “Nobody needs unlimited anything.” Today, I’m going to explain why I say this by showing you the math behind unlimited mobile services, how finite they actually are, and how worthless that promise actually is.

Let’s start with the average monthly billing cycle of 30 days in your typical cellphone bill:

By: Simon Shek
By: Simon Shek

30 days = 720 hours = 43,200 minutes = 2,592,000 seconds

This assumes that you can stay awake 24/7/365. Feel free to check my math, by the way. Don’t just trust these numbers.

Of course, there’s a flaw with these numbers. We technically need to sleep for a third of our lives. So, let’s readjust those numbers to reflect the amount of time the average human can actually utilize these services any one month by subtracting a third from them:

20 days = 480 hours = 28,800 minutes = 1,728,000 seconds

Now that we’ve established roughly the amount of time we actually have available to utilize our miraculous global communications devices, let’s start crunching some numbers.

Minute Usage

If you have call waiting and conference calling, that’s basically operating two lines at once. This gives us a theoretical maximum usage of 57,600 minutes (960 hours) awake, or 86,400 minutes (1,440 hours) theoretical maximum phone call time any one person is capable of using within a 30 day cycle.

Texting Usage

The world record for total number of texts sent in one month is held by a Mr. Fred Lidgren, who sent 566,607 texts in one month back in 2012. This averages out to ~19.7 texts sent per minute, assuming the man slept and sat staring into his phone every waking minute.

There’s also a world record holder for the fastest complex message typing for a text held by a Mr. Gaurav Sharma in April of 2014, who was able to complete typing the phrase, “The razor-toothed piranhas of the genera Serrasalmus and Pygocentrus are the most ferocious freshwater fish in the world. In reality they seldom attack a human.” in 18.44 seconds. This means he could send out ~93,709 complex text messages in one month, assuming he slept as well, but did nothing else with his life.

Data Usage

Before diving into this one, first we need to understand how much data can be transferred at any one speed. Before we can do that, we need to understand a couple data measurements:

8 bits (b) = 1 byte (B)
1024 bytes (B) = 1KB (Kilobyte JEDEC standard) = 1KiB (Kibibyte IEC standard)
1024 Kilobytes (KB) = 1MB (Megabyte JEDEC standard) = 1MiB (Mebibyte IEC standard)
1024 Megabytes (MB) = 1GB (Gigabyte JEDEC standard) = 1GiB (Gibibyte IEC standard)

I won’t continue as I’m sure you get the idea. 1024 of the previous measure equals one of the next size up.

We also need to address the measurement bps, or bits per second. Pretty self explanatory once we unpack the acronym in relation to the above bits of information (no pun intended).

Now, let’s talk theoretical maximum data transfers based on each mobile data standard:

4G LTE: theoretical fastest connection is 299.6Mbps down 75.4Mbps up (375Mbps total)

375Mbps x 1,728,000 seconds = 648,000,000Mb = 81,000,000MB = 79,101.56GB = 77.25TB of total possible data usage in one month (awake)

375Mbps x 2,592,000 seconds = 972,000,000Mb = 121,500,000MB = 118,652.34GB = 115.87TB of total possible data usage in one month (theoretical max)

3G HSPA+: theoretical fastest connection is 168Mbps down 22Mbps up (190Mbps total)

190Mbps x 1,728,000 seconds = 328,320,000Mb = 41,040,000MB = 40,078.13GB = 39.14TB of total possible data usage in one month (awake)

190Mbps x 2,592,000 seconds = 492,480,000Mb = 61,560,000MB = 60117.19GB = 58.71TB of total possible data usage in one month (theoretical max)

100Kbps Throttled: average throttled data speed of “unlimited” data after hitting high speed cap with most carriers (0.09765625Mbps total)

~0.10Mbps x 1,728,000 seconds = 168,750Mb = 21,093.75MB = 20.60GB of total possible data usage in one month (awake)

~0.10Mbps x 2,592,000 seconds = 253,125Mb = 31,640.63MB = 30.90GB of total possible data usage in one month (theoretical max)

Now, let’s season these numbers with a little bit of data perspective:

The entirety of the English Wikipedia database, uncompressed as of February 2014 is approximately 44GB or 9.85GB compressed.

The average file size for the road maps of the entire United States as of 2014 is approximately 2.6GB, the entire planet is approximately 40GB compressed.

Netflix HD video streams at roughly 3GB/hour, or 1.41TB of video for 480 hours, or 2.11TB of video for 720 hours of around the clock video streaming.

National Averages for Mobile Usage

Now that we have the raw numbers, let’s look at the actual averages for mobile usage in the United States. The statistics are a little dated, but they certainly haven’t dramatically changed.

Minutes used: 1,300 (high end) 400 (low end) 650 (white people)

These statistics are from Nielsen (2010), but averages were on a downward usage pattern four years ago. Ethnicity appears to drive the biggest minute usage stats in the industry.

Texts sent: 3,417 (high end) 700 (moderately high average)

Average teenage texting user numbers in a month is around 3,417 (girls 3,952 – boys 2,815) or an average of ~7.1 messages an hour awake, again from Nielsen (2011). Teens are the market segment with the highest average texting numbers, so this classifies as the average for heavy texting usage.

Data used: about 2.5GB combined cellular + WiFi hotspot a month (870MB billed)

These numbers are from Fierce Wireless (2012), and have gone up some in recent years as screen sizes have increased, but average usage still appears to most likely be under the 2.5GB/month billed spot.

By: bixentro
By: bixentro

You should really pay attention to those linked marketing articles, by the way. Really soak in exactly how the mobile industry describes and views its users, the marketing efforts to increase dependence and usage, and the overall push for revenue generation. You are not a customer, you are a cow to them, and you exist solely for them to yank on your udders every month to extract a steady stream of cash. Moo.

Truth In Numbers

Reading numbers and doing math are always exercises in watching paint dry, but there is some valuable information there if you’ll only look.

What can we learn from all these numbers? Well, for one, the theoretical maximum usage is crazy insane high if you were to be plugged in all the time… but it’s not infinite. It’s very finite, and they are huge numbers: 960 hours of talk time, somewhere between 20GB to 77.25TB of data in a month depending on speeds (from the slowest to the fastest), and the human limits of somewhere between 94 to 565 thousand text messages. Advertisers know that when they push that unlimited button in your brain, these are the numbers you actually think about and imagine. Now that you’ve seen the numbers in black and white, however… be honest. Can you actually visualize using your phone this much? That’s crazytown bananapants, right?

Next, we know everyone’s average usage is considerably less than those numbers. You figure somewhere around 650-850 minutes, less than 1000 texts (unless you’re a teenager), and maybe 1.5GB of data. These are also numbers of people who have cord cut, and haven’t even tried to be conscious of their usage or make efforts to reduce costs. They are Joe Sixpack numbers for people who don’t try to tether to WiFi and constantly need to be entertained, have no VoIP service for home, or offload to other IM services to reduce texting usage. Basically, these are the numbers the marketing people have convinced you that you need to buy.

Finally, we know from experience that no mobile carrier in their right mind is going to give you anything approaching those numbers in reality when they promise you “unlimited” service of any stripe. “Unlimited” with these carriers could mean as low as 2000 minutes, 4000 text messages, and 2GB of unthrottled data most of the time before they blacklist you from their network. These are decidedly not numbers that even remotely approach theoretical real world unlimited usage numbers (which are still finite), and I’m not even sure you could get anything approaching those massive usage numbers through a post-paid carrier like Verizon or AT&T directly without paying dearly for it. Any provider who did mean these sorts of potential real numbers when they said “unlimited” at these sorts of sub $70/month prices would be bat guano insane and their bean counters would clearly be touched in the head, because doing so would put them out of business in months.

The truth is, nearly nobody needs anything even remotely approaching even the low-end MVNO definitions of “unlimited” service, and nobody is going to deliver much more on the promise of “unlimited” than a bit higher than national averages for what passes as heavy usage. This is why I’m so leery of the promise of “unlimited” without any definition or hard numbers of what constitutes abuse with most provider terms of service agreements, and why I laugh when I hear people tell me they need some sort of “unlimited” service with their mobile plan. I know what real unlimited monthly usage is, Jack… it’s why I have a nasty habit of putting the word in scare quotes when I write it in reference to phone service, and I can guarantee that you sure as crap can’t get that kind of usage for any stinking $9/month, $25/month, or even $60/month.

This is why I always advocate knowing what your actual usage numbers are before shopping around for alternative plans. It’s not that you couldn’t save money with heavier usage going into one of these “unlimited” plans, but most people probably don’t actually need even that much. This is especially true if you actually try to use your phone as a tool instead of a boredom alleviator or a poor planning crutch.

The truth is, the word Unlimited is nothing more than a marketing buzzword. The numbers expose it for what it is: at it’s best, it is nothing approaching what we mere mortals actually need; and at it’s worst, it is a worthless lie. When you shop for service, you ignore this fact at your own financial peril.

If you still believe in the “unlimited” service game at this point, I’ve got a great real estate opportunity that you might be interested in as well. There’s this bridge out in Brooklyn, see…


Until next time, faithful readers.

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