Amateur Portfolio Example

In a previous article, I wrote on how I start to think about risk for domestic and international amateur classes, and how decisions in one can affect the other and what makes for the best porfolio. That is linked below. In this article, I want to run through a hypothetical scenario to illustrate what the distributions of two portfolios would look like given certain parameters for what a safe and risky player is for domestic and international players.

To start, I want to define the outcome space for a player. Here, I am saying that a player can either produce 0, 1, or 2 WAR per year, and there is a set of probabilities of being each WAR type given the player type you are. The four player types are "Risky-International", "Risky-Domestic", "Safe-International", "Safe-Domestic." I attached a picture of the probabilities and the corresponding expected values for each player type below. Note the premiums for risky portfolios. Since the risky portfolio is risky, I want there to be a premium for choosing it. Here I chose 10%. Then for the player level, I divided it up equally for each player, and found probabilities that lead to the desired expected value per player.

The next step was choosing portfolio types to sim through. For this example, I wanted to compare a "safe-safe" portfolio and a "risky-risky" portfolio. This means that we should expect to have a mean average WAR of 10% more with the risky portfolio than the safe, but we may prefer the safe one if it provides us with more depth pieces/1 WAR types. This is what the distributional outlay looks like:

This is about what we expected. In 10,000 simulations, the safe portfolio has a slight edge in avoiding outcomes with 0 WAR, and also provides more instances of 1, 2, and 3 WAR, but doesn't provide as many whale portfolios with 4+ WAR as the risky one does.

It's important to note that these are fictionalized distribution probabilities and that we can't draw any real life conclusions from them. I chose to do a toy model instead because I do not have the proper data to make international predictions, and opted for simplicity with the domestic side. In the next article, I will give a more in depth analysis of this example and examine when you may prefer one over the other.

Previous article:

https://davidgerth.blogspot.com/2022/06/setting-up-international-free-agency.html