Injury System Formulas

Base Injury Rate Calculation
`Formula: BaseRate = 0.010 + (EffectiveRating × 0.015)`
`EffectiveRating = InjuryRating + 1 for pitchers`
`EffectiveRating = InjuryRating for position players`
`InjuryRating: 0-6 from player's Strat-O-Matic card`
Usage Factor Calculation
`Formula: UsageFactor = e^(α(U - 1.1) + γ(U - 1.1)³)`
`U = UsagePct = CurrentSeasonUsage / ProRatedExpectedUsage`
`α = 0.2`
`γ = 4`
`CurrentSeasonUsage: PA or IP accumulated so far this season`
`ProRatedExpectedUsage: (ActualMLBUsage × GamesPlayed) / 162`
Block Factor Calculation
`Formula: BlockFactor = 1 - (β × B/14)`
`β = 0.2`
`B = current block number (1-14)`
Final Injury Probability Formula
`P(injury) = BaseRate × UsageFactor × BlockFactor`

Step 1: Calculate Durability-Adjusted Decay Rate
`Formula: Adjusted_λ = λ_base × DurabilityRatio^θ`
`DurabilityRatio = ActualMLBUsage / BaselineUsage`
`λ_base = 0.8`
`θ = 0.4`
`BaselineUsage for position players: 300 PA`
`BaselineUsage for starting pitchers: 75 IP`
`BaselineUsage for relief pitchers: 25 IP`
Step 2: Generate Base Duration Probabilities
`Formula for duration d (1 to 10 blocks): BaseProb(d) = e^(-Adjusted_λ × d)`
`Normalize all probabilities to sum to 1.0`
Step 3: Apply Return Compression
`RemainingBlocks = 14 - B`
`MaxReturnDuration = RemainingBlocks - 2`
`If d > MaxReturnDuration: AdjustedProb(d) = BaseProb(d) × (MaxReturnDuration / d)^ζ`
`If d ≤ MaxReturnDuration: AdjustedProb(d) = BaseProb(d)`
`If d = MaxReturnDuration: boost probability with total removed from compressed durations`
`ζ = 3`
Step 4: Season-Ending Injuries
`Base probability: 2.5% of all injuries are for the rest of the season.`
`Late-season compression naturally increases this rate`

`α (alpha) = 0.2: Usage factor linear coefficient`
`γ (gamma) = 4: Usage factor cubic coefficient`
`β (beta) = 0.2: Block factor season reduction`
`λ (lambda) = 0.8: Base duration decay rate`
`θ (theta) = 0.4: Durability adjustment exponent`
`ζ (zeta) = 3: Return compression exponent`