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

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

4. 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

5. Errors Keep Disappearing

7. 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.

8. DER by Vector

9. DER by Vector, Groundballs

10. DER by Batted Ball Type

11. DER by Velocity

12. DER by Handedness

13. DER by Park

14. 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.

15. 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

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

17. Range Rovers FielderOuts SavedRatio, 100*DER/Exp. DER Chris Sampson, P9157.55 Yadir Molina, C5119.33 Albert Pujols, 1B40113.01 Brandon Phillips, 2B46110.38 Ryan Zimmerman, 3B45111.23 Troy Tulowitzki, SS50108.94 Jay Payton, LF16107.52 Coco Crisp, CF31108.14 Shane Victorino, RF18108.72

18. Statues FielderOuts MissedRatio, 100*DER/Exp. DER Curt Schilling, P654.40 Victor Martinez, C289.76 Dmitri Young, 1B2387.66 Craig Biggio, 2B2591.79 Garrett Atkins, 3B4886.53 Derek Jeter, SS4191.20 Pat Burrell, LF2288.75 Bill Hall, CF2093.76 Brad Hawpe, RF2092.48

19. Shortstop Comparison

20. Links Range Charts PMR on Baseball Musings