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Archive for February, 2016

“I tried to start a business, but it failed. It must be Obama’s fault.”

People make this sort of argument all the time. They use their own experience (i.e. one data point) to make some generalization about POTUS or Congress or the governor or whatever. But such arguments are, most of the time, completely bullshit.

I’ll go out on a limb: if your business failed, it’s probably your fault.

The fact of the matter is, it’s hard to succeed in business. After about six years or so, over 50% of new businesses have failed. [See here to see where I got my hard numbers, most of which come from the U.S. Bureau of Labor Statistics.] How do you know, if your business failed, that it was x, y, or z’s fault and not your own? Would your business have really survived, even under a perfect utopia of your imagining?

First of all, the consistency of the “current administration” (and by that I mean POTUS and Congress and the governor and your local city council and so on) doesn’t really matter jack squat when it comes to business survival rates. Check out this graph:

jobs

There’s no noticeable difference between Clinton, Bush, and Obama here. 20% to 25% of all new businesses fail in their first year, no matter who’s in charge. (This is a little hard to see from the graph directly, as the x-axis is shifted in a strange way.  I used the hard data here.)  After a decade, roughly two-thirds have failed. You can blame POTUS if you like, or alternatively, blame whoever is controlling Congress, but either way you’re slipping into the No True Scotsman fallacy: “Sure, 25% of businesses fail in their first year, but I am different… I would have succeeded had it not been for x, y, or z. I am not bad at business; I would have succeeded if only…” You get the idea. (By the way, and anecdotally, if I were playing a blame game, I’d be more likely to blame a governor, because in my experience state policies tend to effect businesses more than federal policies.)

Now, I’ll admit that certain laws (passed by Congress) or policies (enacted by POTUS) can hurt businesses in specific instances. If you start the Acme Widget corporation, and there’s a huge Widget Tax enacted, your business might fail, and you wouldn’t be remiss in blaming Congress or POTUS. But I’m more interested in generalizations: given that your business failed, can we estimate (if at all?) whether or not it was your fault, or someone else’s fault?

Here’s where Bayes’ Theorem comes to the rescue. First, let’s make some definitions. Let

P(good) = Probability that a random person is good at business;

P(suck) = Probability that a random person sucks at business;

P(fail|good) = Probability that your business fails in year 1, given that you’re good at business;

P(fail|suck) = Probability that your business fails in year 1, given that you suck at business;

P(suck|fail) = Probability that you suck at business, given that your business failed in year 1.

Bayes’ Theorem can help us calculate that final quantity, given assumptions about the previous four. Let’s start with a pretty arbitrary guess:

P(good) = 20%

P(suck) = 80%

What’s my justification for saying that 4/5 people suck at business? Well, the graph above seems to be approaching 20% asymptotically. Only 20% of businesses survive “for the long haul”. And 20% “feels” right: most people aren’t good at business, but there’re still millions of people who are.

Now, let’s say 1000 people start a business. Based on the assumptions above, 800 of them suck at business, whereas 200 of them are good at it. We’ve already mentioned that (say) 75% of the businesses will survive their first year, and 25% will fail: 750 vs. 250. Let’s further assume that

P(fail|suck) = 30%.

I pulled that percent out of a hat, but it seems reasonable to assume if 25% of all businesses fail in their first year, then more than 25% of businesses run by sucky managers will fail. But not too much more: 75% of businesses still succeed in their first year, no matter who is running the show. With P(fail|suck) fixed, we’re forced to concede that

P(fail|good) = 5%.

Bad luck, that. Some 5% of businesses run by good managers will still fail in their first year. These are the people who can rightly blame the administration. (Where did the 5% come from? Well, 30% * 800 + 5% * 200 = 250 failed businesses.)

Now: on to Bayes’ Theorem! (For a discussion of how to use this handy tool, see here). We find that

P(suck|fail) = [P(fail|suck) P(suck)]/[ P(fail|suck) P(suck) + P(fail|good) P(good)]

P(suck|fail) = [(0.3) (0.8)]/[ (0.3) (0.8) + (0.05) (0.2)] = 0.96

Translated into English, this means that if your business fails in its first year, we can conclude that it was probably your fault. There’s about a 96% chance that you suck at business.

This is a fascinating result…and you’ll get similar results no matter what assumptions you make, as long as they are reasonable and consistent. For one thing, you’ll always get that P(suck|fail) > P(suck). If I take a person off the street, they have about an 80% chance of sucking at business. But if I take a failed business owner, someone whose business failed in its first year, then I have some extra data, and their chance of sucking at business has gone up to 96%. (There’s a 4% chance that they are good at business but got unlucky.)  A person whose business fails has no right to complain about their failure. It was probably their fault.

There are two lessons here. One, stop whining. Two, remember Bayes’ Theorem!

Thomas_Bayes

I suck at business, too.

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