Appendix: Infield Hit Model, Part 2: Use the Whole Field, Hit Line Drives

This is the online appendix to Donald Slavik’s article, “Infield Hit Model, Part 2: Use the Whole Field, Hit Line Drives,” in the Spring 2025 edition of the SABR Baseball Research Journal.

 

MODEL CONSTANTS AND EQUATIONS

Pop-Up Reference Hit Probabilities 

Adj Spray Angle (deg)	Lefty Hitter	Righty Hitter	Launch Speed Constant
>40	0.000	0.003	0
35 to 40	0.000	0.018	0
30 to 35	0.013	0.000	0
25 to 30	0.025	0.016	0
20 to 25	0.000	0.000	0
15 to 20	0.000	0.005	0
10 to 15	0.026	0.004	0
5 to 10	0.017	0.010	0
0 to 5	0.018	0.010	0
-5 to 0	0.028	0.005	0
-10 to -5	0.011	0.012	0
-15 to -10	0.014	0.012	0
-20 to -15	0.004	0.012	0
-25 to -20	0.013	0.022	0
-30 to -25	0.027	0.021	0
-35 to – 30	0.056	0.052	0
-40 to -35	0.074	0.032	0
<-40	0.000	0.000	0

Note: there was no significant impact of launch speed for pop-ups (launch speed constant = 0.0)

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Grounder Reference Hit Probabilities with Launch Speed Model Constants

	Left-Handed Hitter, Ground Balls					Right-Handed Hitter, Ground Balls
Adj Spray Angle (deg)	Shade Ref Hit %	No-Shade Ref Hit %	Lo Launch Speed Constant	Hi Launch Speed Constant		Shade Ref Hit %	No-Shade Ref Hit %	Lo Launch Speed Constant	Hi Launch Speed Constant
>40	0.231	0.269	-2.9	-1.9		0.600	0.720	-0.6	-1.1
35 to 40	0.125	0.150	5.9	3.1		0.250	0.376	-0.1	3.9
30 to 35	0.125	0.125	7.3	5.2		0.150	0.242	0.5	4.4
25 to 30	0.222	0.215	3.0	9.0		0.100	0.100	-1.1	7.6
20 to 25	0.125	0.150	3.1	9.0		0.194	0.211	2.3	12.1
15 to 20	0.125	0.111	2.7	4.3		0.150	0.162	2.1	7.8
10 to 15	0.341	0.250	3.9	4.0		0.150	0.075	1.4	3.5
5 to 10	0.556	0.520	2.8	3.3		0.600	0.272	2.8	4.8
0 to 5	0.362	0.517	3.3	3.2		0.593	0.665	2.6	1.7
-5 to 0	0.150	0.173	3.1	2.4		0.235	0.460	3.4	2.7
-10 to -5	0.150	0.073	0.6	5.1		0.100	0.133	5.0	3.3
-15 to -10	0.305	0.331	1.4	3.7		0.200	0.150	3.1	4.2
-20 to -15	0.275	0.397	1.4	3.6		0.571	0.298	1.8	1.4
-25 to -20	0.350	0.342	1.6	1.2		0.688	0.400	1.7	3.4
-30 to -25	0.696	0.341	0.0	1.8		0.300	0.364	3.1	2.6
-35 to – 30	0.786	0.957	0.9	-0.4		0.545	0.232	2.5	5.4
-40 to -35	0.875	1.000	0.6	0.0		0.545	0.240	2.3	5.0
<-40	0.500	0.400	-3.7	-0.2		0.150	0.150	-4.2	-2.3

Grounder Hit Prob = (ref hit prob) x [1 + alpha x speed constant x (launch speed – ref speed)] where  alpha = (0.051 x speed – 2.05) from 20 to 60 mph for very low launch speeds.

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Infield Liner Reference Hit Probabilities with Launch Speed Model Constants 

	Left-Handed Hitter, Infield Liners					Right-Handed Hitter, Infield Liners
Adj Spray Angle (deg)	Shade Ref Hit %	No-Shade Ref Hit %	Lo Launch Speed Constant	Hi Launch Speed Constant		Shade Ref Hit %	No-Shade Ref Hit %	Lo Launch Speed Constant	Hi Launch Speed Constant
>40	0.652	0.647	0.0	0.0		0.938	0.938	0.0	0.0
35 to 40	0.682	0.667	1.6	1.0		0.935	0.935	1.8	-0.5
30 to 35	0.537	0.563	0.2	1.6		0.520	0.520	-0.1	2.8
25 to 30	0.837	0.900	1.4	0.7		0.627	0.627	0.0	1.1
20 to 25	0.632	0.839	1.5	0.9		0.846	0.846	0.9	0.6
15 to 20	0.389	0.488	-1.4	1.4		0.674	0.674	0.9	-1.2
10 to 15	0.645	0.741	1.7	1.4		0.565	0.565	0.8	2.1
5 to 10	0.973	0.893	0.5	-0.1		0.821	0.821	0.6	1.8
0 to 5	0.907	0.945	1.4	-0.3		0.953	0.953	0.9	0.0
-5 to 0	0.391	0.792	0.9	0.8		0.772	0.772	1.5	0.2
-10 to -5	0.679	0.581	2.1	2.1		0.642	0.642	1.4	-0.7
-15 to -10	0.914	0.870	1.5	0.5		0.800	0.800	1.4	-0.5
-20 to -15	0.667	0.919	0.4	0.5		0.952	0.952	0.9	-1.1
-25 to -20	0.871	0.833	1.3	-0.5		0.878	0.878	0.8	-0.4
-30 to -25	0.941	0.854	0.6	-0.4		0.765	0.765	0.2	0.2
-35 to – 30	1.000	1.000	1.2	-0.5		0.855	0.855	0.3	0.6
-40 to -35	1.000	1.000	0.6	0.0		0.905	0.905	-0.1	-0.4
<-40	1.000	1.000	0.0	0.0		0.826	0.826	0.0	0.0

Infield Liner Hit Prob = (ref hit prob) x [1 + alpha x speed constant x (launch speed – ref speed)] where  alpha = (-0.084 x speed + 6.71) from 40 to 68 mph for very low launch speeds

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Outfield Liners and Fly Balls Reference Hit Probabilities with Model Launch Speed Constants 

	Outfield Liner (Launch Angle  15.5 deg)				Fly Balls  (Launch Angle 37.6 deg)
Adj Spray Angle (deg)	Ref Hit %	Lo Launch Speed Constant	Hi Launch Speed Constant		Ref Hit %	Lo Launch Speed Constant	Hi Launch Speed Constant
>40	1.000	0.0	0.0		0.000	0.0	0.0
35 to 40	1.000	0.0	0.0		0.000	-1.4	0.0
30 to 35	0.982	0.0	0.0		0.190	-0.7	-0.8
25 to 30	0.631	-2.0	1.2		0.029	-0.6	0.5
20 to 25	0.313	-3.4	1.3		0.059	0.6	0.2
15 to 20	0.308	-2.6	2.6		0.063	0.0	-0.2
10 to 15	0.769	0.1	1.4		0.113	0.2	-0.8
5 to 10	0.667	-2.1	0.9		0.026	-1.1	-0.1
0 to 5	0.150	-5.6	1.5		0.008	-1.0	0.0
-5 to 0	0.052	-5.2	1.5		0.007	-1.0	0.0
-10 to -5	0.286	-5.2	0.7		0.009	-1.1	0.1
-15 to -10	0.681	-1.7	0.8		0.045	-0.6	-0.2
-20 to -15	0.292	-2.9	2.1		0.046	-0.4	-0.2
-25 to -20	0.098	-4.9	1.9		0.030	-0.5	-0.5
-30 to -25	0.175	-5.4	-0.1		0.089	-0.6	-0.7
-35 to – 30	0.794	-2.9	-0.2		0.125	-1.6	-1.2
-40 to -35	1.000	0.0	0.00		0.267	-3.1	-3.6
<-40	1.000	0.0	0.00		0.000	0.0	0.0

Outfield Hit Prob = (ref hit prob) + speed constant x (launch speed – ref speed) 

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Reference Launch Speed Functions

• For popup : Reference launch speed = 0.050 x (adj spray angle) + 78.5
• For fly ball: Reference launch speed = -0.0041 x (adj spray angle)**2 + 0.0217 x (adj spray angle) + 93.2
• For outfield line drive: Reference launch speed = -0.0023 x (adj spray angle)**2 + 0.0993 x (adj spray angle) + 97.6
• For Infield line drive and adj spray angle >= -37.5 deg: Reference launch speed = -0.0041 x (adj spray angle)**2 + 0.0983 x (adj spray angle) + 95.5
• For infield line drive and adj spray angle <-37.5 deg: Reference launch speed = 3.72 x (adj spray angle) + 225.2
• For grounder and adj spray angle < -27.5 deg: Reference launch speed = 2.21 x (adj spray angle) + 146.0
• For grounder and adj spray angle -27.5 to 37.5 deg: Reference launch speed = -0.0066 x (adj spray angle)**2 + 0.0527 x (adj spray angle) + 91.6
• For grounder and adj spray angle > 37.5 deg: Reference launch speed = -4.82 x (adj spray angle) + 265.1

Outfield Line Drives Launch Angle Factors

• For launch speeds < 85 mph: Launch angle factor = 1.87 + 0.0243 x (launch speed) + 0.165 x (launch angle) – 00376 x (launch speed) x (launch angle)
• For launch speed 85 to 100 mph: Launch angle factor = 0.0200 x (launch angle)**2 – 0.990 x (launch angle) + 12.43   
• For launch speed 100 to 110 mph: Launch angle factor = 0.425 + 0.0869 x (launch speed) + 1.6934 x (launch angle) – 0.02159 x (launch speed) x (launch angle)
• For launch speed > 110 mph: Launch angle factor = 9.984 – 0.6815 x (launch angle)
• For launch speeds < 90.4 mph: Minimum launch angle factor = 0.2
• For launch speeds from 90.4 to 104.9 mph: Minimum launch angle factor = 0.069 x (launch speed) – 6.04
• For launch speeds > 104.9 mph: Minimum launch angle factor = 1.2

 Fly Balls Launch Angle Factors

• For launch speeds <= 70 mph: Launch angle factor = [(launch angle) – 50] x (-0.32)  
• For launch speeds 70 to 75 mph: Launch angle factor = [(launch angle) –  50] x [-0.008 x  (launch speed)**2 + 1.206 x (launch speed) – 45.54]
• For launch speeds 75 to 85 mph: Launch angle factor = [(launch angle) – 50] x [-0.0009 x (launch speed)**2 + 0.1515 x (launch speed) – 6.39]
• For Launch speeds 85 to 95 mph: Launch angle factor = [(launch angle) – 36.3] x [-0.003625 x (launch speed)**2 + 0.616 x (launch speed) -26.26]
• For launch speeds 95 to 100 mph Launch angle factor = [(launch angle) – 36.3] x [-0.0325 x (launch speed)**2 + 6.03 x (launch speed) – 279.9]
• For launch speeds >= 100 mph: Launch angle factor = [(launch angle) -36.3] x (-1.90)
• For launch speeds < 69.6 mph: Minimum launch angle Factor = 1.0
• For launch speeds 69.6 to 96.8 mph: Minimum launch angle factor = 0.0047 x (launch speed)**2 – 0.7895 x (launch speed) + 33.18
• For launch speeds > 96.8 mph: Minimum launch angle factor = 0.80

Pop-up Launch Angle Factors

• For launch angles <= 20.0 deg: Launch angle factor = 24.5
• For launch angles 20.0 to 55.6 deg: Launch angle factor = 0.014 x (launch angle)**2  – 1.73 x (launch angle) + 53.48
• For launch angles 55.6 to 81.8 deg: Launch angle factor = -0.022 x (launch angle) + 1.80
• For launch angles >= 81.8 deg: Launch angle factor = 0.0

Ground Ball Launch Angle Factors

• For launch angles <= -52.0 deg: Launch angle factor = 0.014 x (launch angle) + 2.24
• For launch angles -52.0 to -35.2 deg: Launch angle factor = -0.069 x (launch angle) – 2.08
• For launch angles -35.2 to -10.0 deg: Launch angle factor = 0.0007 x (launch angle)**2 + 0.045 x (launch angle) + 1.07
• For launch angles -10.0 to 10.9 deg: Launch angle factor = 0.0028 x (launch angle)**2 + 0.0757 x (launch angle) + 1.17
• For launch angles 10.9 to 28.4 deg: Launch angle factor = -0.084 x (launch angle) + 3.23
• For launch angles >= 28.4 deg: Launch angle factor = 0.85

Infield Line Drive Launch Angle Factors for Left-Handed Hitters

• For launch angles <= 0.0 deg: Launch angle factor = 1.0
• For launch angles 0.0 to 4.6 deg Launch angle factor = -0.058 x (launch angle) + 1.0
• For launch angles 4.6 to 24.3 deg: Launch angle factor = 0.044 x (launch angle) + 0.52
• For launch angles 24.3 to 39.6 deg: Launch angle factor = -0.077 x (launch angle) + 3.46
• For launch angles >= 39.6 deg: Launch angle factor = 0.41

Infield Line Drive Launch Angle Factors for Right-Handed Hitters

• For launch angles <= 0.0 deg: Launch angle factor = 1.0
• For launch angles 0.0 to 4.6 deg Launch angle factor = -0.058 x (launch angle) + 1.0
• For launch angles 4.6 to 20.6 deg: Launch angle factor = -0.0016 x (launch angle)**2 + 0.081 x (launch angle) + 0.33
• For launch angles 20.6 to 36.8 deg: Launch angle factor = -0.056 x (launch angle) + 2.47
• For launch angles >= 36.8 deg: Launch angle factor = 0.41