Method overview¶

The problem with the existing approach¶

There are perhaps a dozen public NBA impact metrics. They disagree. A player can sit in the top ten by one and outside the top forty by another, and no metric tells you which to believe, or how firmly.

The usual response is to argue about which metric is best. This project does something else.

The reframe¶

Treat every public metric as a noisy measurement of the same unobserved quantity. Let \(\theta_p\) be player \(p\)'s true contribution to point differential, which nobody ever observes. Each metric \(m\) gives a reading:

\[ y_{p,m} = \alpha_m + \beta_m \theta_p + \varepsilon_{p,m}, \qquad \varepsilon_{p,m} \sim \mathcal{N}(0, \sigma_m^2) \]

Now the question is no longer "which metric is right." It is "how noisy is each one, and how should readings be combined given that noise." That is a measurement-error problem, and statistics has answered it.

The three steps¶

1. Own the ground truth¶

Compute RAPM from possession-level play-by-play rather than borrowing a paywalled metric. Without this the project could not be reproduced, and could not legally publish its inputs.

2. Measure reliability instead of asserting it¶

Split each player's season into odd and even games, compute each metric on both halves, and correlate. A metric that disagrees with itself is measuring noise. The details are on Measuring reliability.

This replaces the common practice of assigning reliability by expert judgment. The survey this project grew from scored metrics from 0 to 100 across six criteria, and conceded in its own limitations section that the scoring "involves some judgment." Judgment is a reasonable starting point and a poor foundation.

3. Fuse by inverse-variance weighting¶

A metric with reliability \(r_m\) carries error variance proportional to \(1 - r_m\), so its weight is

\[ w_m \propto \frac{r_m}{1 - r_m} \]

Fitting this hierarchically in NumPyro shrinks low-minute players toward the league mean automatically and yields a posterior interval for every player, not a point estimate.

The output is PIPPEN: Player Impact from Pooled Priors and Estimated Noise.

How we will know whether it worked¶

Does PIPPEN predict next-season team net rating better than any single input metric does, out of sample?

Aggregate each metric to team level weighted by minutes, predict the following season's net rating, and compare out-of-sample error. If PIPPEN does not beat its best input, the fusion added nothing, and that result gets published here.

What this is not¶

It is not a claim to beat DARKO or EPM. Those systems are excellent and use inputs this project does not have. It is a claim that combining public metrics while accounting for their measured noise is better than picking one, and that users deserve an interval alongside the number.