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Baseball · Sport academy

MLB Academy

Baseball is a sequence of discrete, well-measured events. That makes it the friendliest sport for probability — and the easiest to fool yourself with small samples.

What matters

Most baseball player outcomes reduce to opportunities × rate. Opportunities are plate appearances (for hitters) or batters faced and pitch count (for pitchers). Rates come from skill, matchup and environment. Lineup position alone can move a hitter's expected plate appearances by close to a full trip.

Important data

InputWhy it matters
Plate appearances / lineup slotSets opportunities — confirmed lineups change probabilities
Contact quality (exit velocity, launch angle, barrels)More predictive of future power than past home run totals
Pitcher profile (stuff, CSW%, handedness)Strikeout and contact suppression
Park and weatherModest, real adjustments to carry and run scoring
UmpireSmall effect on called strikes and walks

Common metrics

MetricWhat it measuresHow to read it
Barrel rateShare of batted balls barreledPower indicator; stabilises faster than HR totals
xwOBAExpected quality from contact, strikeouts and walksCompare with actual wOBA for luck
CSW%Called strikes + whiffs / pitchesStrikeout indicator for pitchers
Park factorPark effect vs league average (100)Context, not a switch
Base-out stateRunners and outsSets run expectancy for the inning

Model concepts

Home runs are rare, countable events, so a Poisson-style "at least one" calculation from an expected rate is a sensible starting point — with the caveats in the Poisson lesson. Strikeout totals are counts too, but a starter's exit time caps them, so the distribution is narrower at the top than a pure Poisson suggests.

Live intelligence

Baseball's live state updates every pitch: count, outs and runners. PBEcast shows the diamond, the live pitch, the batter's split against the current pitcher's hand and the pitcher's arsenal from this game.

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Worked example

Worked example · from per-PA rate to game probability
  1. A hitter homers on about 3.5% of plate appearances; batting second he projects for about 4.4 PAs. λ ≈ 0.035 × 4.4 = 0.154.
  2. P(≥1) = 1 − e^(−0.154) = 14.3% → fair about +601.
  3. Dropped to 8th (about 3.8 PAs): λ = 0.133 → 12.5% → fair +703.
Lineup position alone moved the fair price from +601 to +703. Opportunities matter.

Glossary

Related lessons