Saturday, March 18, 2006
Cardinals Probabilistic Model of Range
Probabilistic Model of Range, 2005, Runs Created Against Fielders
Used is a modified version of the runs created formula that appeared in The Bill James Handbook 2005. That formula is designed for batters. I've modified it in the following ways:
• Count any time a fielder fails to get an out as a time on base. So if there is a failed fielder's choice, or the batter reaches on an error, it's a time on base. Since we're looking at defenses, this seems appropriate.
• Total bases are based on the number of bases achieved by the batter when he earns a time on base. So a two base error in this system counts the same as a double. The weights used for the various types of hits are the same as in the Handbook.
So that makes the formula (Times On Base - GDP)* (Weighted Total Base)/(Balls in Play). I'd like to hear what you think about the formula, but I believe it's a good first approximation. It was easy to apply to teams; you're just looking at all balls in play, and the likelihood that a particular ball will end in a particular result. But I wasn't quite sure how to then apply it to individual fielders.
When I was looking just at the probability of catching the ball, I wanted to look at all balls in play. I was looking at the piece of team DER that belonged to a particular fielder. But here, I'm trying to predict runs, so I made the decision to only look at balls in play in which the fielder had a non-zero chance of making the play. If you will, I used the probabilities of various balls in play to define the zone for the fielder, and the results of those balls to define runs created against (RCA).
The results made me wish I had worked on this last year. They're conveying information much more clearly than simply looking at the probability of catching the ball.
(The player is listed with their overall MLB ranking at their position, there is a minimum of 200 fieldable balls in play per position.)
#19 1B Albert Pujols
1002 fieldable balls in play
329 actual outs by fielder
302.94 predicted outs by fielder
57.80 RCA
64.84 predicted RCA
4.74 RCA/27 outs
5.78 predicted RCA/27 outs
1.035 runs saved/27 outs
Here is what it would look like if you don’t assess penalties for balls other players catch. (no out penalties) Grounders and bunt grounders only.
2226 balls in play
243 actual outs
223.51 predicted outs
0.109 DER
0.100 predicted DER
0.00875 difference
(Smoothed visiting player model.) Grounders and bunt grounders only.
2226 balls in play
243 actual outs
222.85 predicted outs
0.109 DER
0.100 predicted DER
0.00905 difference
#28 2B Deivi Cruz
358 fieldable balls in play
112 actual outs by fielder
130.55 predicted outs by fielder
19.20 RCA
22.07 predicted RCA
4.63 RCA/27 outs
4.57 predicted RCA/27 outs
-0.063 runs saved/27 outs
#34 2B Junior Spivey
625 fieldable balls in play
223 actual outs by fielder
210.83 predicted outs by fielder
41.50 RCA
36.08 predicted RCA
5.02 RCA/27 outs
4.62 predicted RCA/27 outs
-0.403 runs saved/27 outs
Here is what it would look like if you don’t assess penalties for balls other players catch. (no out penalties) Grounders and bunt grounders only.
752 balls in play
156 actual outs
143.90 predicted outs
0.207 DER
0.191 predicted DER
0.01609 difference
(Smoothed visiting player model.) Grounders and bunt grounders only.
752 balls in play
156 actual outs
144.88 predicted outs
0.207 DER
0.193 predicted DER
0.01479 difference
#39 2B Aaron Miles
744 fieldable balls in play
246 actual outs by fielder
252.32 predicted outs by fielder
54.50 RCA
48.62 predicted RCA
5.98 RCA/27 outs
5.20 predicted RCA/27 outs
-0.779 runs saved/27 outs
Here is what it would look like if you don’t assess penalties for balls other players catch. (no out penalties) Grounders and bunt grounders only.
869 balls in play
173 actual outs
179.06 predicted outs
0.199 DER
0.206 predicted DER
-0.00697 difference
(Smoothed visiting player model.) Grounders and bunt grounders only.
869 balls in play
173 actual outs
178.71 predicted outs
0.199 DER
0.206 predicted DER
-0.00658 difference
#12 3B Scott Rolen
433 fieldable balls in play
176 actual outs by fielder
148.12 predicted outs by fielder
23.05 RCA
30.52 predicted RCA
3.54 RCA/27 outs
5.56 predicted RCA/27 outs
2.027 runs saved/27 outs
Here is what it would look like if you don’t assess penalties for balls other players catch. (no out penalties) Grounders and bunt grounders only.
799 balls in play
144 actual outs
118.75 predicted outs
0.180 DER
0.149 predicted DER
0.03161 difference
(Smoothed visiting player model.) Grounders and bunt grounders only.
799 balls in play
144 actual outs
117.29 predicted outs
0.180 DER
0.147 predicted DER
0.03342 difference
#11 SS David Eckstein
1737 fieldable balls in play
615 actual outs by fielder
617.90 predicted outs by fielder
97.98 RCA
114.19 predicted RCA
4.30 RCA/27 outs
4.99 predicted RCA/27 outs
0.688 runs saved/27 outs
Here is what it would look like if you don’t assess penalties for balls other players catch. (no out penalties) Grounders and bunt grounders only.
4109 balls in play
550 actual outs
470.45 predicted outs
0.134 DER
0.114 predicted DER
0.01936 difference
Ball hogging index.
565.01 predicted outs
470.45 predicted outs no hogs
94.562 difference
0.0230 difference per BIP
#36 LF Larry Bigbie
232 fieldable balls in play
98 actual outs by fielder
96.20 predicted outs by fielder
34.67 RCA
28.06 predicted RCA
9.55 RCA/27 outs
7.87 predicted RCA/27 outs
-1.677 runs saved/27 outs
Here is what it would look like if you don’t assess penalties for balls other players catch. (no out penalties)
1464 balls in play
98 actual outs
96.20 predicted outs
0.067 DER
0.066 predicted DER
0.00123 difference
(Smoothed visiting player model.)
1464 balls in play
98 actual outs
95.08 predicted outs
0.067 DER
0.065 predicted DER
0.00200 difference
#5 CF Jim Edmonds
673 fieldable balls in play
319 actual outs by fielder
297.21 predicted outs by fielder
69.83 RCA
98.88 predicted RCA
5.91 RCA/27 outs
8.98 predicted RCA/27 outs
3.072 runs saved/27 outs
Here is what it would look like if you don’t assess penalties for balls other players catch. (no out penalties)
3538 balls in play
319 actual outs
258.07 predicted outs
0.090 DER
0.073 predicted DER
0.01722 difference
(Smoothed visiting player model.)
3538 balls in play
319 actual outs
292.73 predicted outs
0.090 DER
0.083 predicted DER
0.00743 difference
Ball hogging index.
297.13 predicted outs
258.07 predicted outs no hogs
39.062 difference
0.0110 difference per BIP
#30 RF Juan Encarnacion
521 fieldable balls in play
216 actual outs by fielder
213.79 predicted outs by fielder
68.31 RCA
66.12 predicted RCA
8.54 RCA/27 outs
8.35 predicted RCA/27 outs
-0.189 runs saved/27 outs
Here is what it would look like if you don’t assess penalties for balls other players catch. (no out penalties)
3355 balls in play
216 actual outs
213.79 predicted outs
0.064 DER
0.064 predicted DER
0.00066 difference
(Smoothed visiting player model.)
3355 balls in play
216 actual outs
215.77 predicted outs
0.064 DER
0.064 predicted DER
0.00007 difference
C Yadier Molina
Groundballs only (grounders and bunts).
1554 balls in play
18 actual outs
16.20 predicted outs
0.012 DER
0.010 predicted DER
0.00116 difference
Smoothed visiting player model.
1554 balls in play
18 actual outs
14.51 predicted outs
0.012 DER
0.009 predicted DER
0.00225 difference
C Gary Bennett
Groundballs only (grounders and bunts).
690 balls in play
9 actual outs
9.21 predicted outs
0.013 DER
0.013 predicted DER
-0.00030 difference
Smoothed visiting player model.
690 balls in play
9 actual outs
8.73 predicted outs
0.013 DER
0.013 predicted DER
0.00039 difference
Used is a modified version of the runs created formula that appeared in The Bill James Handbook 2005. That formula is designed for batters. I've modified it in the following ways:
• Count any time a fielder fails to get an out as a time on base. So if there is a failed fielder's choice, or the batter reaches on an error, it's a time on base. Since we're looking at defenses, this seems appropriate.
• Total bases are based on the number of bases achieved by the batter when he earns a time on base. So a two base error in this system counts the same as a double. The weights used for the various types of hits are the same as in the Handbook.
So that makes the formula (Times On Base - GDP)* (Weighted Total Base)/(Balls in Play). I'd like to hear what you think about the formula, but I believe it's a good first approximation. It was easy to apply to teams; you're just looking at all balls in play, and the likelihood that a particular ball will end in a particular result. But I wasn't quite sure how to then apply it to individual fielders.
When I was looking just at the probability of catching the ball, I wanted to look at all balls in play. I was looking at the piece of team DER that belonged to a particular fielder. But here, I'm trying to predict runs, so I made the decision to only look at balls in play in which the fielder had a non-zero chance of making the play. If you will, I used the probabilities of various balls in play to define the zone for the fielder, and the results of those balls to define runs created against (RCA).
The results made me wish I had worked on this last year. They're conveying information much more clearly than simply looking at the probability of catching the ball.
(The player is listed with their overall MLB ranking at their position, there is a minimum of 200 fieldable balls in play per position.)
#19 1B Albert Pujols
1002 fieldable balls in play
329 actual outs by fielder
302.94 predicted outs by fielder
57.80 RCA
64.84 predicted RCA
4.74 RCA/27 outs
5.78 predicted RCA/27 outs
1.035 runs saved/27 outs
Here is what it would look like if you don’t assess penalties for balls other players catch. (no out penalties) Grounders and bunt grounders only.
2226 balls in play
243 actual outs
223.51 predicted outs
0.109 DER
0.100 predicted DER
0.00875 difference
(Smoothed visiting player model.) Grounders and bunt grounders only.
2226 balls in play
243 actual outs
222.85 predicted outs
0.109 DER
0.100 predicted DER
0.00905 difference
#28 2B Deivi Cruz
358 fieldable balls in play
112 actual outs by fielder
130.55 predicted outs by fielder
19.20 RCA
22.07 predicted RCA
4.63 RCA/27 outs
4.57 predicted RCA/27 outs
-0.063 runs saved/27 outs
#34 2B Junior Spivey
625 fieldable balls in play
223 actual outs by fielder
210.83 predicted outs by fielder
41.50 RCA
36.08 predicted RCA
5.02 RCA/27 outs
4.62 predicted RCA/27 outs
-0.403 runs saved/27 outs
Here is what it would look like if you don’t assess penalties for balls other players catch. (no out penalties) Grounders and bunt grounders only.
752 balls in play
156 actual outs
143.90 predicted outs
0.207 DER
0.191 predicted DER
0.01609 difference
(Smoothed visiting player model.) Grounders and bunt grounders only.
752 balls in play
156 actual outs
144.88 predicted outs
0.207 DER
0.193 predicted DER
0.01479 difference
#39 2B Aaron Miles
744 fieldable balls in play
246 actual outs by fielder
252.32 predicted outs by fielder
54.50 RCA
48.62 predicted RCA
5.98 RCA/27 outs
5.20 predicted RCA/27 outs
-0.779 runs saved/27 outs
Here is what it would look like if you don’t assess penalties for balls other players catch. (no out penalties) Grounders and bunt grounders only.
869 balls in play
173 actual outs
179.06 predicted outs
0.199 DER
0.206 predicted DER
-0.00697 difference
(Smoothed visiting player model.) Grounders and bunt grounders only.
869 balls in play
173 actual outs
178.71 predicted outs
0.199 DER
0.206 predicted DER
-0.00658 difference
#12 3B Scott Rolen
433 fieldable balls in play
176 actual outs by fielder
148.12 predicted outs by fielder
23.05 RCA
30.52 predicted RCA
3.54 RCA/27 outs
5.56 predicted RCA/27 outs
2.027 runs saved/27 outs
Here is what it would look like if you don’t assess penalties for balls other players catch. (no out penalties) Grounders and bunt grounders only.
799 balls in play
144 actual outs
118.75 predicted outs
0.180 DER
0.149 predicted DER
0.03161 difference
(Smoothed visiting player model.) Grounders and bunt grounders only.
799 balls in play
144 actual outs
117.29 predicted outs
0.180 DER
0.147 predicted DER
0.03342 difference
#11 SS David Eckstein
1737 fieldable balls in play
615 actual outs by fielder
617.90 predicted outs by fielder
97.98 RCA
114.19 predicted RCA
4.30 RCA/27 outs
4.99 predicted RCA/27 outs
0.688 runs saved/27 outs
Here is what it would look like if you don’t assess penalties for balls other players catch. (no out penalties) Grounders and bunt grounders only.
4109 balls in play
550 actual outs
470.45 predicted outs
0.134 DER
0.114 predicted DER
0.01936 difference
Ball hogging index.
565.01 predicted outs
470.45 predicted outs no hogs
94.562 difference
0.0230 difference per BIP
#36 LF Larry Bigbie
232 fieldable balls in play
98 actual outs by fielder
96.20 predicted outs by fielder
34.67 RCA
28.06 predicted RCA
9.55 RCA/27 outs
7.87 predicted RCA/27 outs
-1.677 runs saved/27 outs
Here is what it would look like if you don’t assess penalties for balls other players catch. (no out penalties)
1464 balls in play
98 actual outs
96.20 predicted outs
0.067 DER
0.066 predicted DER
0.00123 difference
(Smoothed visiting player model.)
1464 balls in play
98 actual outs
95.08 predicted outs
0.067 DER
0.065 predicted DER
0.00200 difference
#5 CF Jim Edmonds
673 fieldable balls in play
319 actual outs by fielder
297.21 predicted outs by fielder
69.83 RCA
98.88 predicted RCA
5.91 RCA/27 outs
8.98 predicted RCA/27 outs
3.072 runs saved/27 outs
Here is what it would look like if you don’t assess penalties for balls other players catch. (no out penalties)
3538 balls in play
319 actual outs
258.07 predicted outs
0.090 DER
0.073 predicted DER
0.01722 difference
(Smoothed visiting player model.)
3538 balls in play
319 actual outs
292.73 predicted outs
0.090 DER
0.083 predicted DER
0.00743 difference
Ball hogging index.
297.13 predicted outs
258.07 predicted outs no hogs
39.062 difference
0.0110 difference per BIP
#30 RF Juan Encarnacion
521 fieldable balls in play
216 actual outs by fielder
213.79 predicted outs by fielder
68.31 RCA
66.12 predicted RCA
8.54 RCA/27 outs
8.35 predicted RCA/27 outs
-0.189 runs saved/27 outs
Here is what it would look like if you don’t assess penalties for balls other players catch. (no out penalties)
3355 balls in play
216 actual outs
213.79 predicted outs
0.064 DER
0.064 predicted DER
0.00066 difference
(Smoothed visiting player model.)
3355 balls in play
216 actual outs
215.77 predicted outs
0.064 DER
0.064 predicted DER
0.00007 difference
C Yadier Molina
Groundballs only (grounders and bunts).
1554 balls in play
18 actual outs
16.20 predicted outs
0.012 DER
0.010 predicted DER
0.00116 difference
Smoothed visiting player model.
1554 balls in play
18 actual outs
14.51 predicted outs
0.012 DER
0.009 predicted DER
0.00225 difference
C Gary Bennett
Groundballs only (grounders and bunts).
690 balls in play
9 actual outs
9.21 predicted outs
0.013 DER
0.013 predicted DER
-0.00030 difference
Smoothed visiting player model.
690 balls in play
9 actual outs
8.73 predicted outs
0.013 DER
0.013 predicted DER
0.00039 difference
