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Comment by gizmo | Hacker News Reader

> It’s clear that a single investment would have a terrible expectation and huge variance, but how about five deals?

The author uses expectation in a different way than I usually do, I consider this the definition of the expectation:

    PAYOFFS = [ 0, 1, 3, 10, 20]
    PROBS = [0.50, 0.20, 0.15, 0.13, 0.02]
    PAYOFFS.zip(PROBS).inject(0.0){|s, i| i[0] * i[1] + s} => 2.35

So you're expected to double your money (and then some) for each investment.

Given that you have to be an accredited investor ($200k+ income or $1m+ net worth, iirc) to do an angel investment in the first place the investment shouldn't negatively affect your quality of life if it doesn't work out. So unless you can get a higher return than 2.35x somewhere else, the angel investment seems like a really good deal to me.

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I saw your original comment and started to respond, but in the edited version it is much more clear what you mean.

> So you're expected to double your money (and then some) for each investment.

Over time that is true. The average over time is what to look for. With a single investment and you can expect to lose your money.

But why does the average over time matter more than the expected result? Any single investment is (according to the numbers) going to make a significant expected contribution to the economy and to the investor. So why not go for it?

According to this logic it would be bad for 20 people (with a net worth of $1m+) to invest $100k each, but it would be good for one wealthy person to make 20 investments of $100k each. That doesn't compute.

>Any single investment is (according to the numbers) going to make a significant expected contribution to the economy and to the investor. So why not go for it?

Who's numbers? Yours or his? His simulation is saying that (as an individual angel) you have a 50% chance of losing all of your investment on your first deal. He's running 10,000 angels simultaneously doing deals and looking at the average performance across those angels.

Think of it like a piano with 10,000 keys. When you're in the money the key is up and when you're not its down. (I know the keys can go above 0 but I can't think of a better analogy.) After everyone does their first deal, a full 50% are completely down at 0. A few are way up. It takes four "turns" for 50% of the keys to be up above the starting point

"Average over time" is perhaps the wrong phrase for it. I should have said number of deals.

>According to this logic it would be bad for 20 people (with a net worth of $1m+) to invest $100k each, but it would be good for one wealthy person to make 20 investments of $100k each.

I don't see how that follows from the article.

I definitely agree, the article uses some messy statistics.

An additional concern is that if your argument is that 10 investments reduce variance, you want to keep in mind correlation effects. The probability of one investment failing is likely to be dependent on other investments from the same domain, due to the nature of booms and busts.

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