Originally Posted by Fat petrie911
Strictly speaking, wouldn't it be better to simply do a least-squares fit to the data to find lambda? ie, instead of using the 5/6 method on the cumulative distribution function, do an exponential fit to the probability distribution function (or a linear fit to the logarithm of said function). That should give better values for lambda. It can also give you an idea of how good the exponential fit is.
Additionally, I wonder what the fact that usage distributions are nearly always exponential tells us about how people choose Pokemon for their teams.
Yes, you could do that. You could also reduce the cumulative frequency distribution equation to linear form and apply linear regression. These would probably find a better value for lambda, but the method to find lambda from the diversity has the merit of being much quicker and, more importantly, shows that diversity and lambda are inversely proportional.