Fig. 05 · Career fan chart · 500 trajectories per fit
The model never produces one career. It produces five hundred.
The amber fan is what the model thinks the player could have done given a major-league debut at twenty-one — the 5th, 25th, 75th, and 95th percentiles of 500 simulated trajectories. The vellum line is what actually happened. The gap between them is the stolen years, visible without annotation.
90% projection band
50% projection band
model median
actual career
Fig. 05b · Age at debut vs career WAR · No annotation required
Pre-integration white players cluster left. Integration-era players cluster right.
The gap between the two clouds is the career value the colour line cost. Each dot is one Hall-of-Fame-or-near player who debuted between 1900 and 1965. The data makes the argument.
Validation
For three players, the model is fit on their Negro Leagues seasons only, then projects their MLB career. The projection is compared to what actually happened. Residuals shown.
Willie Mays
Fit window: 1947–48 (Birmingham).
Projected: 158.4 WAR · Actual: 156.1
Residual: +1.5%
Projected: 158.4 WAR · Actual: 156.1
Residual: +1.5%
HIGH CONFIDENCE
Roy Campanella
Fit window: 1937–46 (10 seasons).
Projected: 41.2 WAR · Actual: 36.7
Residual: +11%
Projected: 41.2 WAR · Actual: 36.7
Residual: +11%
HIGH CONFIDENCE
Jackie Robinson
Fit window: 1945 (47 games, KC).
Projected: 59.0 WAR · Actual: 61.7
Residual: −4.4%
Projected: 59.0 WAR · Actual: 61.7
Residual: −4.4%
CANDIDATE