Is a draft pick worth the mean or median value?

A topic that has long be gnawing on me is whether or not it makes sense to value draft picks as many who connect a dollar sign to picks do.  To me there is an argument between using the mean (which is common) versus using median (which I have not seen).  Both are ways to measure central tendency.  Mean is often the best to use in order to either describe the population as a whole or to determine typical value if value are normally distributed.  Medians are used often when you want to determine what is a typical result when the population is distributed asymmetrically.

The following graph shows the difference between how we assign draft picks value either by mean or median.

click to make larger

In the first 30 selections from 1991-2000, there were only four instances where the median was higher than the mean.  Seventeen median values within the 30 picks were worth zero WAR or less.  In other words, a team is not likely to receive mean value for a pick.  Picks tend to be overvalued because a few individuals increase the worth of the pick within the population.

What is interesting here is how do you exactly come to a specific value for a pick?  Does a 33% chance of getting a useful MLB player mean that it is permissible to overvalue the population as a whole?  It is easy to see how many MLB teams deplore spending money in the draft because much of the money spent on individuals is wasted.  The question is whether or not the money spent on the entire portfolio is beneficial to the team.  I would say that if you are evaluating a single player, the median makes sense.  If you are evaluating the population, then the mean makes sense.  To look at it differently, it is like a lottery that benefits the buyer of the tickets.  Most likely, most of your tickets are worthless, but a couple might wind up bringing back a great deal of value.