Zones of Scoring: Using Hit F/X to Find the Linear Weights for the Vertical and Horizontal Angle for a Fair Ball.

by Jeff Zimmerman on Jun 18, 2009 7:21 PM EDT

Zones of Scoring: Using Hit F/X to Find the Linear Weights for the Vertical and Horizontal Angle of a Ball Hit into Play.

Using Hit F/X data, I created 10 degree vertical and horizontal zones and looked at the linear weight for each ball hit into those zones. The data is in a 90 degree horizontal range and an 180 degree vertical range. I used -45 degrees for the 3^rd base line and 45 degrees for the 1^st base line. To create Linear weights values I used the following linear weights for the complete retrosheet era.

Event	Linear Weight
Home Run	1.40
Triple	1.03
Double	0.76
Single	0.46
Fielding Error	0.48
Out	-0.27

In future analysis, the zone angle interval and the linear weight values may need to be adjusted to get better information..

There ended up initially being 162 zones. Here is the zones with the number of balls (excluding bunts) hit in each zone.

Degrees	-45 to -35	-35- to -25	-25 to -15	-15 to -5	-5 to 5	5 to 15	15 to 25	25 to 35	35 to 45
80 to 90	3	6	1	7	2	8	8	7	3
70 to 80	18	35	27	21	25	39	43	31	16
60 to 70	19	39	46	50	49	49	46	45	23
50 to 60	14	50	79	92	94	95	80	43	13
40 to 50	2	64	125	144	167	170	133	77	10
30 to 40	6	108	199	289	338	260	232	139	15
20 to 30	12	132	275	327	375	347	162	162	14
10 to 20	36	173	277	330	373	358	343	250	43
0 to 10	73	171	262	261	305	296	298	246	111
0 to -10	120	193	191	218	236	236	244	226	173
-10 to -20	116	155	170	211	197	239	229	228	138
-20 to -30	49	74	99	96	86	90	111	106	86
-30 to -40	22	27	30	28	35	34	35	31	40
-40 to -50	8	6	7	4	16	7	9	20	11
-50 to -60	2	3	8	2	3	8	3	2	0
-60 to -70	0	0	3	1	0	5	2	1	5
-70 to -80	0	1	1	2	0	0	0	0	0
-80 to -90	0	0	1	0	0	0	0	0	0

I needed at some the more vertical angle to combine zones do to lack of hits in the zone and got the following zones:

Degrees	-45 to -35	-35- to -25	-25 to -15	-15 to -5	-5 to 5	5 to 15	15 to 25	25 to 35	35 to 45
> 70	21	41	28	28	27	47	51	38	19
60 to 70	19	39	46	50	49	49	46	45	23
50 to 60	14	50	79	92	94	95	80	43	13
40 to 50	2	64	125	144	167	170	133	77	10
30 to 40	6	108	199	289	338	260	232	139	15
20 to 30	12	132	275	327	375	347	162	162	14
10 to 20	36	173	277	330	373	358	343	250	43
0 to 10	73	171	262	261	305	296	298	246	111
0 to -10	120	193	191	218	236	236	244	226	173
-10 to -20	116	155	170	211	197	239	229	228	138
-20 to -30	49	74	99	96	86	90	111	106	86
-30 to -40	22	27	30	28	35	34	35	31	40
< -40	10	10	20	9	19	20	14	23	16

By using the above linear weights here is a graph of the zones the the run value for each ball hit into that zone:

Degrees	-45 to -35	-35- to -25	-25 to -15	-15 to -5	-5 to 5	5 to 15	15 to 25	25 to 35	35 to 45
> 70	-0.270	-0.252	-0.270	-0.270	-0.242	-0.232	-0.255	-0.270	-0.270
60 to 70	-0.270	-0.270	-0.270	-0.270	-0.270	-0.270	-0.231	-0.224	-0.270
50 to 60	-0.270	-0.226	-0.270	-0.262	-0.262	-0.241	-0.239	-0.253	-0.270
40 to 50	0.096	0.005	-0.168	-0.227	-0.238	-0.235	-0.211	-0.069	0.009
30 to 40	-0.026	0.265	0.157	-0.056	-0.068	-0.098	0.133	0.523	0.188
20 to 30	0.653	0.594	0.215	0.197	0.125	0.228	0.572	0.572	0.739
10 to 20	0.515	0.482	0.215	0.350	0.242	0.379	0.257	0.525	0.571
0 to 10	0.209	0.202	0.093	0.051	0.284	0.150	0.161	0.119	0.233
0 to -10	-0.081	-0.018	-0.144	-0.114	0.111	0.111	-0.068	-0.019	-0.047
-10 to -20	-0.231	-0.159	-0.162	-0.200	-0.095	-0.193	-0.161	-0.092	-0.122
-20 to -30	-0.255	-0.210	-0.196	-0.224	-0.133	-0.205	-0.158	-0.228	-0.147
-30 to -40	-0.236	-0.161	-0.196	-0.191	-0.145	-0.119	-0.039	-0.127	-0.123
< -40	-0.270	-0.197	-0.233	-0.270	-0.115	-0.159	0.096	0.048	0.233

Linear Weght
> 0.6
0.4 to 0.6
0.2 to 0.4
0.0 to 0.2
0.0 to -0.2
-0.2 to -0.4

There is quite a bit going on there but here are some observations:

Looking at the 0 to -10 horizontal zone, the gaps between the fielders can be seen as the run values go up and down. I believe this can be used to determine how well certain player field. There could be certain zones a 3^rd baseman is responsible for and weight averages of the zones could be used to evaluate the defense.
The best hits are hit at 10 to 30 degrees vertically. Horizontally, > 25 degrees and < -25 degrees are the money spots.
It can be seen that balls hit <-20 vertically have a better chance to be fielded on right side of the infield vice on left side. I think this is due to right handed pitchers falling off to the right side after they throw and can't get to the ball as well. A chart of right vs. left handers would help determine if this is true.
Put more than 50 degrees of loft on a ball and it is almost guaranteed to be an out.

Future research.

Right vs. left handed pitchers and hitters.
Different views for speed off bat to see if there is any patterns
For the zones that are located near where fielder would have a play, maybe more zones used here where there are plenty of sample and use wider zones for other parts of the field where there aren't as many samples.
Different views for different speeds off bat.
Put image with it that shows a field from home plate for better understanding where the ball goes.

Let me know what you think because for now I really like the potential of the data viewed this way for ease of understand and usefulness of the data.

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Comments

Did you see the thread at Tango's?

Good discussion on hitting and pitching weights, and labeling conventions, too.
http://www.insidethebook.com/ee/index.php/site/comments/linear_weights_by_batted_ball_speed/

by Harry Pavlidis on Jun 18, 2009 7:38 PM EDT reply actions

Yes, took some from there (-45 to 45)

I really wanted to look at location and see if it can be used for a defensive metric. There just doesn’t seem like there is enough data yet break it down by team yet with this method.

Jeff Zimmerman - Protecting the world from RBI's and Wins from my mom's guest house.

by Jeff Zimmerman on Jun 18, 2009 7:52 PM EDT up reply actions

I think

I’m going to do a little more learning about metrics and such, and I need to take a few more math classes before I’ll understand all this.

You and I are gonna live forever

by Original Six on Jun 18, 2009 9:33 PM EDT reply actions

I (or Harry) should so a basics of Hit F/X

With each ball that is hit into play there are 3 numbers that matter associated with it.

- The speed of the ball off the bat (I didn’t use it)
- Horizontal direction (-45 is to 3rd base line, 0 is to pitcher and 45 is the first base line)
-Vertical direction (0 is even with the ground and positive number is hit up in the air and negative is hit down)

So if a ball is hit (100,0,0) it is hit right back at the pitcher

Now if it is hit (100, 40, 20), the ball is hit down first line at a 20 degree loft which could be anything from a double to a home run.

Let me know if you have any more questions.

Jeff Zimmerman - Protecting the world from RBI's and Wins from my mom's guest house.

by Jeff Zimmerman on Jun 18, 2009 11:58 PM EDT up reply actions

I understand how this works...

but if you could put the horizontal directions overlayed on a baseball diamond that would help, as would putting a vertical angle cross-section in front of a home plate, so you can get an idea of trajectory.

See what I mean? If there was a picture that you could link to so that everyone can get the hang of how this works.

"I just wish that the late Harry Caray were still around so I could hear him mispronounce 'Kosuke Fukudome' every fukun' night" -- Dennis Miller

by fourstick on Jun 19, 2009 5:08 PM EDT up reply actions