| Outs | Base State | Run Expectancy | Post-Play RE (Slam = +4R) | Run Value Added (RE24) |
|---|---|---|---|---|
| 0 Outs | Loaded (1-2-3) | 2.28 runs | 4.00 + 0.48 = 4.48 | +2.20 runs |
| 1 Out | Loaded (1-2-3) | 1.52 runs | 4.00 + 0.25 = 4.25 | +2.73 runs |
| 2 Outs | Loaded (1-2-3) | 0.74 runs | 4.00 + 0.10 = 4.10 | +3.36 runs |
⚾ Why Bases-Loaded Leverage Spikes
Leverage Index (LI) measures the standard deviation of win probability shifts across possible outcomes. With bases loaded and two outs late in the game, an out drops win probability near 0%, while a grand slam grants a +4 run swing, resulting in extreme leverage spikes (LI > 7.0).
🚀 Trajectory Ballistics & Aerodynamics
Batted ball distance utilizes numerical integration with air drag ($C_d \approx 0.31$) and Magnus backspin lift ($C_l \approx 0.18$). Optimal launch angles for distance occur between 26° and 30°, maximizing carry past 400+ foot outfield barriers.
📊 Run Expectancy RE24 vs WPA
While Run Expectancy assesses average runs scored from a base-out state (2 Outs Loaded = 0.74 Expected Runs), WPA directly measures context-dependent game win odds. A grand slam at 2 outs erases the highest expected failure rate.