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Probabilistic Model of Range

This article presents a comprehensive probabilistic model for assessing fielding range in baseball. It analyzes the trajectories of different batted balls (grounders, flies, lines) and calculates vital metrics, including Defensive Efficiency Rating (DER) and Ultimate Zone Rating (UZR). By utilizing historical fielding statistics and adjusting for factors like handedness and park effects, the model ranks teams and players based on their defensive performance. The insights aim to enhance understanding of fielding dynamics and improve evaluations of player effectiveness on the field.

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Probabilistic Model of Range

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  1. Probabilistic Model of Range David F. Pinto Baseball Musings www.baseballmusings.com

  2. Construction of Model Direction p(out|D,T,S,B,P,PK) All Fielders Trajectory (Ground, Fly, Line) Weighting: Visit in Play > 0.5 Then Visit In Play Else 2*Visit in Play/All in Play p(out|D,T,S,B,P,PK) Smoothed Speed Handedness, Batters and Pitchers p(out|D,T,S,B,P,PK) Visiting Fielders Park

  3. History of Fielding Stats • Assists, Putouts, Errors, Fielding Percentage, Games at position • No Context • Range Factor (Assists + Putouts)/Game • Last 1980s (Assists + Putouts)/(9 Innings) • Zone Rating • Ultimate Zone Rating (UZR), PMR

  4. Errors Keep Disappearing

  5. Defensive Efficiency Rating • DER measures the probability that a fieldable ball in play results in at least one out. • Similar to 1- BABIP (BA on Ball in Play) • BABIP does not account for safe on errors, safe on failed fielder’s choice. • Major League DER in 2007, 0.686.

  6. DER by Vector

  7. DER by Vector, Groundballs

  8. DER by Batted Ball Type

  9. DER by Velocity

  10. DER by Handedness

  11. DER by Park

  12. Calculating Probabilities • Use visiting fielders, so one fielder does not dominate. • Sum total chances and outs for each set of six parameters. Probability = outs/chances. • Smooth against data for all fielders. • If more than 50% of chances are by visitors, visitor data get 100% of weight. Else, visitor data weighted by 2*percent of visitor chances.

  13. Ranking Teams • Count number of balls in play (BIP). • Count number turned into outs (Outs). • Calculate expected number of outs (Exp), ∑p(out|D,T,S,BH,BP,PK) • Calculate DER (Outs/BIP), Expected DER (Exp/BIP) • Rank by Difference or Ratio (DER/Exp DER) • 2007 Team PMR Rankings

  14. Probabilities for Players • Split up DER for a set of parameters by how many outs are started by a fielding position.

  15. Range Rovers

  16. Statues

  17. Shortstop Comparison

  18. Links • Range Charts • PMR on Baseball Musings

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