RUN VALUE & WIN PROBABILITY IN AMATEUR DIAMOND SPORTS
Document Code: DOC-13-AMATEUR-ANALYTICS
Author: M. Wanjiru & ProActa Analytics Lab
1. The Base-Out Run Expectancy Matrix ($RE_{24}$)
Every baseball and softball inning consists of 24 distinct states ($3 \text{ out states: } 0, 1, 2 \times 8 \text{ base runner configurations}$).
Amateur run expectancy baseline (runs expected to end of inning):
- Bases empty, 0 outs: $\approx 0.52$ runs
- Runner on 1st, 0 outs: $\approx 0.88$ runs
- Runner on 2nd, 0 outs: $\approx 1.10$ runs
- Bases loaded, 0 outs: $\approx 2.30$ runs
- Runner on 2nd, 1 out: $\approx 0.67$ runs
- Bases empty, 2 outs: $\approx 0.11$ runs
2. Tactical Evaluation: The Mathematical Flaw of the Sacrifice Bunt
- The Scenario: Runner on 1st base, 0 outs ($RE = 0.88$).
- A Successful Bunt: Moves the runner to 2nd, but concedes 1 out ($RE$ drops to $0.67$).
- Conclusion: In non-walk-off scenarios, the standard sacrifice bunt reduces total expected runs by $0.21$ runs per occurrence. It should only be used when 1 single run wins the game in the final frame.
3. Leverage Index (LI) & Win Probability Added (WPA)
- Leverage Index (LI): Quantifies how critical a single pitch or at-bat is to the final outcome ($LI = 1.0$ is average; $LI > 3.0$ is high-leverage late-inning drama).
- Bullpen Strategy: High-strikeout relievers should enter during high-LI situations (bases loaded, 1 out in the 6th inning) rather than being saved rigidly for an empty 9th-inning save.