3/24/2009

03-24-09 - Cute but retarded

There's an article in last Sunday's New York Times called "Try, Try Again, Or Maybe Not" that I think is a great example. It's sort of cute, it comes across as smug, it interviews experts. And it's just completely wrong.

The core point goes like this : 22% of venture capitalists succeed. Those who have previously succeeded have a 34% success rate. Those who have previous failed have a 23% success rate. The conclusion is "you don't learn anything from failure, the success rate is basically the same".

Totally retarded. They completely miss the basic point that there are varying populations and the previous outcomes weight for the different populations. Furthermore the success rate of the group with experience is (0.22*34 + 0.78*23) which is clearly better.

Let's run some example numbers. Let's say the population is made up of good entrepreneurs and bad ones.


Initial population :

X good
(1-X) bad

success if good = P(G)
success if bad = P(B)

Initial success = X * P(G) + (1-X) * P(B) = 0.22

X * G + (1-X) * B = 0.22

In the successful group,

fraction successful Y = ( X * P(G) ) / 0.22

success rate = E + Y * P(G) + (1-Y) * P(B) = 0.34

E = additive benefit from experience

0.22 * E + ( X * P(G) ) * P(G) + (0.22 - ( X * P(G) )) * P(B) = 0.34 * 0.22

In the unsuccessful group :

fraction successful Z = ( X * (1 - P(G)) ) / 0.78

success rate = E + Z * P(G) + (1-Z) * P(B) = 0.23

0.78 * E + ( X * (1 - (G)) ) * (G) + (0.78 - ( X * (1 - (G)) )) * (B) = 0.23 * 0.78


This is three equations in 4 unknowns, so there is a variety of solutions.
X can be in [0,1]
For each X there is only one valid {G, B, E}

... meh I started to solve this but I got bored. The solution is something like G = 0.4, B = 0.1, E = 0.05.

Anyway it's absolutely clear that E is significantly greater than zero, and in fact the whole thesis of the article is wrong. Actually something the numbers are telling me that I think is perhaps more interesting is that the "Bad" population is *very* bad. The reason why the group that failed once is not too bad the second time is because there are still quite a few "Good" people in it that just got unlucky on their first roll, and everyone learned a bit from experience.

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