Overthinking Everything

Math Can Prove Some Amazing Things

Every company makes a bargain with you. They look like this:

Comics site:

We will provide you a comic that is hopefully funny!

McDonald’s:

We will sell you a burger that tastes exactly like you remember your last burger here tasting like!

FedEx:

We will deliver your package!

And so on: there’s no magic here, this is just what you expect a company to do for you. Let’s look at FedEx’s bargain a little more closely:

We will deliver your package!

is the pitch, but we know that sometimes businesses are closed, roads are difficult, etc. Not every package can be delivered, right? So let’s make that bargain more specific:

We will do our best to deliver your package!

Still a pretty good pitch, right? But we know that there’s limits: FedEx won’t try forever. So let’s bring numbers into it. And just for fun, let’s make it into a POP QUIZ: which of these do you think best captures FedEx’s value offering to you, the savvy package-having consumer?

a) We will make three attempts to deliver your package!

b) We will make at least one attempt to deliver your package!

c) We will make less than one attempt to deliver your package!

In a test situation, most of us would choose a), but some might say “Aha! c) is obviously the ridiculous choice, and b) TECHNICALLY includes a), so b) is the where the smart money is.” Well, we’re all wrong. Astoundingly, their new policy is c): less than one attempt. I know, it’s crazy. I know, it seems like it’s not even possible. But they found a way.

It’s all thanks to their new corporate policy, which is paraphrased like this: “FedEx will not to reattempt delivery if you live within 5kms of a FedEx location”. In other words, if the package is going somewhere close their home base - if the delivery is one of the EASY ones, not one that’s at the end of a fifteen-mile road to nowhere - they give up early. “We got the package most of the way,” they will say, “but now we’re tired. Look, you come here and finish our work for us. Please. Deliver it to yourself.”

Putting aside how awful this policy is to people who don’t own a car and thus might, you know, employ the services of a delivery company, this is still awful policy. With only one attempt - especially with drivers who are human and thus can be less than 100% reliable - any cut corner means packages don’t get delivered.

An example: I’m a cartoonist and I work from home, which means other delivery companies love me because I’m always there to accept packages. But last month there was construction on my street, and FedEx Delivery Dude (dude in the gender-neutral sense) decided to cheat on my package and was like, “Screw it, I’m just marking it as ‘attempted’ and moving on”. But this meant I didn’t get a notice saying “Hey where were you? Come get your package!” which meant the package sat around at FedEx for 10 days before being sent all the way back home. After I asked FedEx to look into this, two versions of what happened emerged.

My version: FedEx Delivery Dude said “Screw it” and lied, saying that I wasn’t home.

The FedEx version was a story that constantly evolved in response to what I’d say. Here’s how it started:

FedEx: “You weren’t home”.
Me: “I work from home, and I was home then.”
FedEx: “Oh. Hold on, let me check with the driver.”

next call:

FedEx: “…Okay, you WERE home, but you didn’t answer the door.”
Me: “I would’ve answered the door had the doorbell been rung.”
FedEx: “Oh. Hold on, let me check with the driver again.”

next call:

FedEx: “…Okay, so you were home, but the driver knocked instead of using the doorbell [editor’s note: because the driver is an insane person? who does this], and instead of putting the notice in the mailbox right beside the door, he stuck the notice on the door. Later, it blew away.”
Me: “Had there been a knock, my dog would’ve freaked out and alerted me.”
FedEx: “Oh. Hold on, let me check with the driver one more time.”

next call:

FedEx: “…The dog was real sleepy.”

In the end, it doesn’t matter whose version is the least credible: this system is designed so that one attempt is all you get, and this is with FedEx’s own admission that things can go wrong with their notices that just blow away and disappear.

But here’s the kicker: there were actually four packages being sent to me simultaneously, each with four separate tracking numbers. Let’s imagine you have some critical piece of information that you need delivered reliably to me: what’s the most reliable way to send it? (Assume email is out for some reason.) One package could get lost, but four packages means four separate attempts, which increases our odds that at least one of them will get through! Right?

It turns out that while FedEx will gladly offer to let you pay 4x over what you otherwise would, they’ll still group your separate packages together and make just one attempt. You’re literally paying extra money for nothing. And here’s where the magic happens: because the dude came to my door only once, these four separate packages had to share, and they got just a quarter of a delivery attempt each. And in talking to the FedEx manager, he said that the number of packages sent in parallel doesn’t matter: they’ll still get grouped together.

So 1 package gets 1 attempt. 2 packages get 1/2 an attempt each. 3 packages get a 1/3 of an attempt each. This allow us to construct an equation:

The number of delivery attempts FedEx makes per package is defined as

where x is the number of packages. This equation we can, in turn, graph:

In other words, the more packages you send at once, the shittier job FedEx does of delivering each of them, with each package getting less and less of a delivery attempt. And the limit actually approaches zero, which means that if you somehow send me infinity packages through FedEx, they will not even knock on my door. They will take the infinity dollars and run. I did honestly not intend today to use math to prove precisely how bad FedEx is at delivering packages, but, um, here we are?

Ironically, this equation also shows us that if we could somehow send fractional packages, FedEx would go ABSOLUTELY INSANE trying to deliver them. This is the “FedEx Zone of Impossibility” I noted in the graph, and it’s probably why everything is rounded up to at least one package to FedEx. Pretty sneaky!

I started by thinking that maybe this insane equation is an unintended consequence of their new “one attempt” delivery system combining poorly their desire to make things as efficient as possible. But after talking to their support and managers, I’m told it’s how things are supposed to go. Four separate packages don’t and won’t get a second delivery attempt if the first one failed. This is BY DESIGN.

I recommend you use other delivery companies in the future.

I don’t have proof, but judging from the shipping troubles I’ve been having with Barnes & Noble orders lately, I now suspect they use FedEx for their deliveries.