You're a Cap Analyst. The GM is forecasting potential roster changes and needs to understand how much cap space he will have for the next season.
In this hypothetical, the NHL and NHLPA have amended the CBA to allow performance-based incentives in standard player contracts. When a player hits an incentive, the bonus is deducted from their team's cap the following season. The GM asks for you how likely it is that one of the team's forwards will hit their 20-goal incentive this season , so they can start roster planning for the following season.
Information is revealed across five rounds. You set a probability after each one as you proivde status updates to the GM. At the end, you can compare your thought process to a simple bayesian model.
Note: A random player is selected each time the game starts, so you can play many times!
This game is an exercise in Bayesian thinking. It begins with a base rate that sets your initial probability. As you progress through each round, new evidence is presented. You should use that evidence to continually update the probability you assigned in the prior round. The rate at which you update that probability should be proportional to the strength of the evidence. A small, or noisy, piece of evidence should slightly nudge your prior belief, while a large, or direct, piece of evidence should more drastically change your prior belief.
This method of thought may sound obvious, but we often fall into traps that pull us away from Bayesian thinking. We tend to overweight the most recent piece of evidence or completely abandon our prior beliefs in light of new information. For example, if a forward is on pace for 15 goals through 10 games, but was a late draft pick who has had a long career of sub-20-goal seasons, we shouldn’t throw away years of historical data and base rates just because of a hot streak at the beginning of a single season.
By forcing yourself to pause and quantify a probability after every piece of data, this game trains your brain to make more intentional decisions under uncertainty. Similarly, it allows you to see the thought process utilized to refine your prediction as you build greater confidence in your belief of whether or not the performance payout will be required. A simple Bayesian model evaluates the exact same information presented to you, updating its probability as each round progresses. Rather than a traditional score, the final plot lets you compare your updates directly against the Bayesian baseline, allowing you to see if you are updating your beliefs too much or too little as specific pieces of evidence are revealed.