yes there are points under the curve out at 10X the mean but they are very, very rare. The normal distribution falls off a cliff. I don't have the reference in front of me but something like 99.6% of the population will fall within 2 standard deviations of the mean. This same issue comes up when people try and predict something like the daily fluctuation of the Dow Jones Industrial average using a normal curve. They think that there are random swings up and down but that large swings of 500 points are more are very unlikely. Then those large swings come along and show everybody that it isn't smart to use the normal distribution to try and model the absolute change in the closing price.
The main point here is that programmers who are 10X more productive than the average coder seem to be not so rare. Many people have stories about having worked with guys like this. Therefore I don't think you should use the normal distribution to model the distribution of productivity in programmers. I think there are many guys at the low end of the scale and it drops off slowly as you move into the higher productivity. And NO you can't include the negative x-axis to get a symmetric, "normal-like" distribution. In this model the negative values on the x-axis don't mean anything.
I would have to disagree on two counts. The first point is pedantic, but, in the standard normal distribution, half the curve is over ten times greater than the mean. Of course, that's cheating, since the mean is zero, but it's not impossible for the relationship between the mean programmer productivity and the standard deviation to allow for large number of programmers with 10x the mean productivity.
The catch is that any normal distribution which allows for large numbers of 10x programmers requires large numbers of programmers with negative productivity. However, I disagree that those values are meaningless. Rather, it simply indicates a programmer who makes code worse. I would readily argue that, for every 10x programmer, there's at least two who create more bugs than they solve.
Ok, I spent way more time thinking about this than I should have :)
When we measure human attributes they are almost always normal distributions, I see no reason that programming ability is any different. But, maybe tools allow good programmers to magnify their ability more than poor programmers. If that's the case then we'll have a lopsided normal curve, and that sounds plausible. But, I'm highly skeptical of the idea of "productivity" being a simple metric and that 10x means much of anything.
However, I'm quite certain it's not a power law :)
The main point here is that programmers who are 10X more productive than the average coder seem to be not so rare. Many people have stories about having worked with guys like this. Therefore I don't think you should use the normal distribution to model the distribution of productivity in programmers. I think there are many guys at the low end of the scale and it drops off slowly as you move into the higher productivity. And NO you can't include the negative x-axis to get a symmetric, "normal-like" distribution. In this model the negative values on the x-axis don't mean anything.