It's a fallacy (though a very commonly held one) that if x% of people succeed at some task, the chances you will succeed are x%. That's only true for tasks where aptitude is not a factor.
Truly, we don't get where we get because of our capacity or our ability (in most cases). We get lucky, a lot, and we can't really change that.
Much of the remaining "luck" comes from our choices. Think of it this way: how many people choose to work a steady job for all of their life. They will never be a billionaire, regardless of how lucky they get, and so their contribution to the average is zero. Actually, I suspect this invalidates your math: more than 1 in 2 people have probability zero of being a billionaire simply by virtue of not taking the chance of being one, and therefore of the people who take the chance, the odds are significantly better than 0.0001%.
People who actually care about these odds (in the sense of betting on them) are founders and investors. Neither, in their decision making process, gets to (or wants to!) uniformly sample all companies.
PG's numbers are thus much more useful to anyone actually trying to make a decision about a pool of investments: assuming the distribution of YC startups is fixed over time, and you are someone like Start Fund who will bet on the pool (i.e. equivalent to a repeated uniform sampling in expected value), the 0.5% is actionable information and the 0.00006% is not.
For example, if the prior on "making a successful company" (defined however you want) were a vastly higher 40%, then I'd imagine a lot more laypeople would take the plunge. Reading sites like TechCrunch makes it seem to the layperson that building a successful company is much easier than it really is. So yes, knowing that "mega success" is a massive outlier (to the tune of 1:1,000,000) is indeed actionable information to a layperson thinking about starting a company without any additional evidence.
As the source article notes: The goal of the entrepreneur is to learn as much as they can, thereby increasing their own odds of success (or minimizing their odds of failure). Obviously, getting into YC massively improves your odds and would probably be a good decision! As a YC alum, my advise would jive with this observation. ;)
That depends on how, exactly, you define "luck". I posit that a lot of what people call "luck" can be manufactured, or at least cultivated through directed action.
Remember the article that showed up here a while back about "How to date a supermodel"? The premise was that if you want to date a supermodel, you have to move to a city where there are lots of supermodels, and hang out at the places where supermodels shop, work out, dine, etc., and you have to start conversations with supermodels, blah, blah..
So if one of you buddies shows up next year dating a supermodel, everybody is probably going to go "Dude, that's amazing, you are SO lucky!" And this will completely ignore the fact that he did a lot of things to create the opportunity.
It's SUCH a cliche, but I guess cliches exist for a reason, so I'll just come back to:
Luck = Preparation + Opportunity
Likewise, if you don't want to date anyone at all, you move to silicon valley and work on a startup!
(Kidding! sort of...)
To date one you would need to be compatible with her lifestyle. That means highly successful or at least part of a similar industry like fashion or music. It means that you have to be somebody that can be announced in gossip columns as dating her. It has to be a good career move for her.
Naomi Cambel once walked past me while I was hanging out backstage at New York fashion week. Even if I had said hi there are still significant reasons why I am not now dating her.
And so it is with startups. Pedigree matters, the pedigree of your investors matters. Press matters and is heavily influenced by your position in the network. People in the game are deciding who the winners and losers are. Public perception is influenced by that.
FWIW, I really dislike it when people perpetuate the myth that 50% of marriages end in divorce. We actually have no idea what the true percentage is, and I think they myth got started because people compare the annual marriage rate with the annual divorce rage.
http://en.wikipedia.org/wiki/Divorce_demography
But I was just being illustrative; my point applies even if it's 20% or 80%.
Not necessarily, because people are notoriously bad at evaluating themselves, and often tend to assume that statistics (especially troubling ones) don't apply to them for whatever reason. For the divorce statistic (which I understand is not necessarily accurate, but let's pretend it really is 50%), how many of the divorced couples previously thought the statistic was irrelevant for them, because they're "truly in love" or some other reason?
That's like saying that I should expect to live to 120, because it's been done before. And, I should ignore the expected lifespan number.
Maybe healthy lifestyle choices will increase my lifespan. But, to expect that I should be a statistical outlier seems risky.
The article makes some really great points about solving meaningful problems vs starting a startup for it's own sake. It further makes great points about eliminating luck in the process and offers actionable advice on how to do that. I think that would be the subject of a much better conversation.
And what if you calculated the chance of starting a billion dollar company in Bentonville Ark (Walmart) which has a population of 38k (which no doubt was way less when Sam Walton decided to locate there). Not bad "odds".
if i have 10 coins, 9 of which have 44.4% chance of heads and 1 has 100% chance, choosing a coin at random and flipping it has 50% chance of heads overall. sure, there is one outstanding coin.
the "fallacy" is true when you look at the whole rather than the individual factors, which include aptitude in some cases so i guess you're correct on the last point.
P(getting into YC | sold a startup, graduated from Stanford/MIT, worked on/built something awesome, etc)
Or the chance of building a $1B company:
P($1B company | you're in SV, $100MM in funding, etc)
This also comes up all the time in data-science and A/B testing of products. Frequently you'll end up with results like "This change decreased revenue by 3%." Sounds bad, right? Except then you drill into your results and find out that there was a bug in the implementation of the change in IE6, which decreased revenue by 100% on that one browser which happens to be 5% of traffic, and find that your change actually increased revenue by a percent or two, but that one slice cost you all the benefit and more. You fix the bug and happily start making more money.
Always slice your population. Many times blanket probabilities tell you nothing unless you know what's causing them.