Back to Basics: Pythagorean Expectation

As we build out our advanced rating systems (ELO, RAPM), it's crucial to have a solid "sanity check" baseline. Today, we've deployed two classical models based on the Pythagorean expectation framework.

These models are now live on the Rankings page!

The Models

1. Pythagorean Raw

This is the original formula applied to raw points scored and allowed. * Formula: $Win\% = \frac{PS^{11.5}}{PS^{11.5} + PA^{11.5}}$ * What it tells us: How dominant a team has been in terms of scoring margin interactively. * Flaw: It treats a 20-point win over a cupcake the same as a 20-point win over a contender.

2. Pythagorean Adjusted

This model adjusts efficiency for opponent strength. * Method: We use Ridge Regression to solve for "Adjusted Efficiency" (Offense and Defense) such that: $Efficiency_{Game} \approx Base + AdjO_{Team} - AdjD_{Opponent}$ * What it tells us: How well a team should perform against an average opponent.

Why It Matters: The "Strength of Schedule" Effect

The difference between these two models reveals who has played a tough schedule.

Example 1: The Battle-Tested * Oregon Ducks: Ranked #278 in raw points (brutal start?), but #140 in Adjusted. The model recognizes their opponents were elite. * San Diego State: Jumps +131 spots when adjusting for schedule.

Example 2: The Paper Tigers * Virginia St Trojans: Fall 183 spots when opponent strength is factored in.

Live Now

Check out the Rankings page to see where your team lands in the new Adjusted Efficiency column. This gives us a third independent signal alongside ELO and RAPM to evaluate team quality.