Probabilistic Model of Range

David F. PintoBaseball Musings

www.baseballmusings.com

Construction of ModelDirection

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 ThenVisit In PlayElse2*Visit in Play/All in Play

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

Errors Keep Disappearing

1900 1920 1940 1960 1980 20000.920

0.930

0.940

0.950

0.960

0.970

0.980

0.990

Fielding Percentage Over Time

FPCT

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.

DER by Vector

3B LF CF RF 1B 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

In Play

In Play

DER by Vector, Groundballs

3B RF CF RF 1B 0.00.10.20.30.40.50.60.70.80.91.0

DER

DER

DER by Batted Ball Type

Bunt Fly Fly Bunt Grounder

Grounder Fliner (Fly)

Fliner (Liner)

Liner0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

DER

DER by Velocity

Soft Medium Hard0.00.10.20.30.40.50.60.70.80.9

Grounders and Low Line Drives

DER

0-99 100-199

200-299

300-399

400+0.00.10.20.30.40.50.60.70.80.91.0

Fly Balls and High Line Drives

DER

DER by Handedness

Right vs. Right Right vs. Left Left vs. Right Left vs. Left0.665

0.670

0.675

0.680

0.685

0.690

0.695

Batter vs. Pitcher

DER

DER by Park

Fenway

Park

The Ballpark

in Arlin

gton

Minute M

aid Park

Angel S

tadium of A

naheim

Great Americ

an Ball

park

Yanke

e Stad

ium

Tropica

na Field

Coors Fie

ld

Comerica P

ark

Oriole Park

at Cam

den Yards

Cellular

One Fi

eld

Turner F

ield

AT&T Park

Chase Fi

eld

PETCO Park0.54

0.58

0.62

0.66

0.70

Leftfield Vectors, No Groundballs or Bunts

DER

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.

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

Probabilities for Players

3B SS 2B 1B0

0.10.20.30.40.50.60.70.80.9

1

Predicted DER on Grounders for Infielders

Third BaseShortStopSecond BaseFirst Base

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

Range RoversFielder Outs Saved Ratio, 100*DER/Exp. DER

Chris Sampson, P 9 157.55

Yadir Molina, C 5 119.33

Albert Pujols, 1B 40 113.01

Brandon Phillips, 2B 46 110.38

Ryan Zimmerman, 3B 45 111.23

Troy Tulowitzki, SS 50 108.94

Jay Payton, LF 16 107.52

Coco Crisp, CF 31 108.14

Shane Victorino, RF 18 108.72

StatuesFielder Outs Missed Ratio, 100*DER/Exp. DER

Curt Schilling, P 6 54.40

Victor Martinez, C 2 89.76

Dmitri Young, 1B 23 87.66

Craig Biggio, 2B 25 91.79

Garrett Atkins, 3B 48 86.53

Derek Jeter, SS 41 91.20

Pat Burrell, LF 22 88.75

Bill Hall, CF 20 93.76

Brad Hawpe, RF 20 92.48

Shortstop Comparison

Links

• Range Charts• PMR on Baseball Musings