I privately received a couple of interesting comments on my diversification post:

One of RSCM‘s angel advisors wrote, “I would think most smart people get it intellectually, but many are stuck in the mindset that they have a particular talent to pick winners.”

One of my Facebook friends commented, “VC seems to be a game of getting a reputation as a professional die thrower.”

I pretty much agree with both of these statements. However, even if you believe someone has mad skillz at die-rolling, you may still be better off backing an unskilled roller. Diversification is that powerful! To illustrate, consider another question:

*Suppose I offered you a choice between the following two options:*

*(a) You give me $1M today and I give you somewhere between $3M and $3.67M with 99.99% certainty in 4 years.*

*(b) You give me $1M today and a “professional” rolls a standard six-sided die. If it comes up a 6, I give you $20M in 4 years. Otherwise, you lose the $1M. But this guy is so good, he never rolls a 1 or 2.*

The professional’s chance of rolling a 6 is 25% because of his skill at avoiding 1s and 2s. So option (b) has an expected value of $5M. Option (a) only has an expected value of $3.33M. Therefore, the professional has a 50% edge. But he still has a 75% chance of losing all your money.

I’m pretty sure that if half their wealth were on the line, even the richest players would chose (a). Those of you who read the original post probably realize that option (a) is actually an unskilled roller making 10,000 rolls. Therefore:

* Diversifying across unskilled rolls can be more attractive than betting once on a skilled roller*.

Of course, 1 roll versus 10,000 hardly seems fair. I just wanted to establish the fact that diversification can be more attractive than skill in principle. Now we can move on to understanding the tradeoff.

To visualize diversification versus skill, I’ve prepared two graphs (using an enhanced version of my diversification spreadsheet). Each graph presents three scenarios: (1) an unskilled roller with a standard 1 in 6 chance of rolling a 6, (2) a somewhat skilled roller who can avoid 1s so has a 1 in 5 chance of rolling a 6, and (3) our very skilled roller who can avoid 1s and 2s so has a 1 in 4 chance of rolling a 6.

First, let’s look at how the chance of at least getting your money back varies by the number of rolls and the skill of the roller:

The way to interpret this chart is to focus on one of the horizontal gray lines representing a particular probability of winning your money back and see how fast the three curves shift right. So at the 0.9 “confidence level”, the very skilled roller has to make 8 rolls, the somewhat skilled roller has to make 11, and the unskilled roller has to make 13.

From the perspective of getting your money back, being very skilled “saves” you about 5 rolls at the 0.9 confidence level. Furthermore, I’m quite confident that most people would strongly prefer a 97% chance of at least getting their money back with an unskilled roller making 20 rolls to the 44% chance of getting their money back with a very skilled roller making 2 rolls, even though their expected value is higher with the skilled roller.

Now let’s look at the chance of winning 2.5X your money:

The sawtooth pattern stems from the fact that each win provides a 20X quantum of payoff. So as the number of rolls increases, it periodically reaches a threshold where you need one more win, which drops the probability down suddenly.

Let’s look at the 0.8 confidence level. The somewhat skilled roller has a 2 to 5 roll advantage over the unskilled roller, depending on which sawtooth we pick. The very skilled roller has a 3 roll advantage over the unskilled roller initially, then completely dominates after 12 rolls. Similarly, the very skilled roller has a 2 to 5 roll advantage over the somewhat skilled roller, dominating after about 30 rolls.

Even here, I think a lot of people would prefer the 76% chance of achieving a 2.5X return resulting from the unskilled roller making 30 rolls to the 58% chance resulting from the very skilled roller making 3 rolls.

But how does this toy model generalize to startup investing? Here’s my scorecard comparison:

**Number of Investments**. When Rob Wiltbank gathered the AIPP data set on angel investing, he reported that 121 angel investors made 1,038 investments. So the mean number of investments in an angel’s portfolio was between 8 and 9. This sample is probably skewed high due to the fact that it was mostly from angels in groups, who tend to be more active (at least before the advent of tools like AngelList). Therefore, looking at 1 to 30 trials seems about right.**“Win” Probability**. When I analyzed the subset of AIPP investments that appeared to be seed-stage, capital-efficient technology companies (a sample I generated using the methodology described in this post), I found that the top 5% of outcomes accounted for 57% of the payout. That’s substantially more skewed than a 1 in 6 chance of winning 20X. My public analysis of simulated angel investment and an internal resampling analysis of AIPP investments bear this out. You want 100s of investments to achieve reasonable confidence levels. Therefore, our toy model probably underestimates the power of diversification in this context.**Degree of Skill**. Now, you may think that there are so many inexperienced angels out there that someone could get a 50% edge. But remember that the angels who do well are the ones that will keep investing and angels who make lots of investments will be more organized. So there will be a selection effect towards experienced angels. Also, remember that we’re talking about the seed stage where the uncertainty is the highest. I’ve written before about how it’s unlikely one could have much skill here. If you don’t believe me, just read chapters 21 and 22 of Kahneman’s Thinking Fast and Slow. Seed stage investment is precisely the kind of environment where expert judgement does poorly. At best, I could believe a 20% edge, which corresponds to our somewhat skilled roller.

The conclusion I think you should draw is that even if you think you or someone you know has some skill in picking seed stage technology investments, you’re probably still better at focusing on diversification first. Then try to figure out how to scale up the application of skill.

And be warned, just because someone has a bunch of successful angel investments, don’t be too sure he has the magic touch. According to the Center for Venture Research, there were 318,000 active angels in the US last year. If that many people rolled a die 10 times, you’d expect over 2,000 to achieve at least a 50% hit rate **purely due to chance**! And you can bet that those will be the people you hear about, not the 50,000 with a 0% hit rate, also purely due to chance.