Findings / Effective Sample Size
How independent is our data, really?
mlb: 78,986 residual rows carry the independent information of at most ~227 games.
ESS from the already-committed lag-1 within-game residual autocorrelation (rho); because the game outcome is terminal-constant the probability path is smooth, so consecutive rows are near-duplicates rather than independent draws. The distinct-game count is the conservative anchor and the AR(1) figure is an approximation, so the reported ess_anchor takes the minimum of the two.
| Corpus | Rows | Distinct games | Residual autocorr (rho) | Effective sample (AR1) | Honest anchor | CI must widen by |
|---|---|---|---|---|---|---|
| MLB | 78,986 | 227 | 0.9809market 0.9799 | 761 | 227 | 18.7xAR1 estimate 10.2x |
| Soccer (Intl) | 9,003 | 51 | 0.9624market 0.9489 | 172 | 51 | 13.3xAR1 estimate 7.2x |
How to read this — rows within one game are near-duplicates because the outcome is fixed and the win-probability path is smooth, so 78,986 MLB rows carry the independent information of at most ~227 games. Every confidence interval on a within-game analysis must therefore be widened by the factor in the last column.
Formula
AR(1) is a first-order approximation of a smooth terminal-constant path, not a full independence model; the distinct-game count is the conservative anchor. DESCRIPTIVE_ONLY -- this deflates our OWN sample sizes and makes no edge or ROI claim.
This exhibit deflates our own numbers on purpose — no edge or ROI is claimed anywhere here, only the honest count of what was actually measured.