The following shows the theoretical distributions of talent. It is based on estimates, some empirical data, and my intuition. I still have alot of work to do to prove and refine all this. For the moment, take this as being 10% completed.
Chart 1 - Follows the classical bell curve. Major league talent is not visible at the right-hand side
Chart 2 - Blowing up the red square of the above curve, and we see this shape among the 1500 best players in the world.
Chart 3 - The talent level follows an exponential pattern. I would suspect that such a pattern is true for all sports, and even all walks of life.
Chart 4 - Blowing up the red square of the above curve, and we see this shape among the 1500 best players in the world.
Chart 5 - The distribution of opportunities to perform in MLB follows the following pattern. There is an upper limit for PAs, while the lower limit is reached very fast for players on the bubble.
Looking at the last two graphs, we see that the talent level for the bubble MLB players, and the top minor league players is around .80.
If you multiply the above two graphs (talent level of MLB players, and the PAs of those players), you will get the average MLB talent level. In this case, the average is 1.00.
Chart 6 - This graph is a multiplication of the last graph (playing time per player, by talent level) and the second graph (number of players, by talent level). This produces the total playing time, among all players, by talent level. That is, how many PAs are handed out for each level of talent. As you can see, a rather typical distribution curve.
Conclusion
Next time you hear an analyst say that the talent distribution is not normal, but is actually the far end of the curve, you can respond back with, "That is true, but when you consider the number of opportunities each player gets, the total effective talent distribution is rather typical".
This just scratches the surface. More to come.