Exponential Smoothing of Batting Statistics

In this blog post, I will describe how I used exponential smoothing to weight the four seasons of batting statistics I have on my fastball team.

The point of exponential smoothing, in this case, is predict the player’s performance using all the data available but give the most current data greater weight than older data.  This is based on the assumption that players get better with experience or worse with age.

Here is the four years of data I have on the players' batting in reverse chronological order.

2014
Player	AB	R	H	2B	3B	HR	RBI	SB	CS	BB	SO	HBP	SAC
A	28	5	9	1	0	0	2	4	0	5	7	3	0
B	25	3	8	0	1	1	4	0	0	1	9	0	1
C	6	0	0	0	0	0	0	0	0	0	5	1	0
D	32	7	10	1	0	0	7	2	1	1	8	1	0
E	36	10	9	4	0	1	10	1	0	6	12	0	0
F	28	5	6	1	1	0	3	0	0	3	8	1	0
G	53	13	15	3	0	0	5	5	0	10	19	0	1
H	36	7	11	1	0	2	5	0	0	3	9	0	0
I	46	6	11	2	0	1	8	0	0	2	14	0	0
J	31	6	10	1	2	1	3	1	0	0	11	0	1
K	14	3	6	4	0	0	1	0	0	1	5	0	0
L	29	2	11	4	0	0	5	0	0	1	10	0	1
M	42	9	10	1	0	5	15	0	0	5	9	0	0

2013
Player	AB	R	H	2B	3B	HR	RBI	SB	CS	BB	SO	HBP	SAC
A	38	15	14	4	1	1	4	4	0	7	8	0	0
B	40	17	17	3	2	5	15	0	0	5	6	0	1
C	23	3	2	1	0	0	1	0	0	0	7	0	1
D	31	4	10	3	0	1	4	1	0	3	6	0	0
E	38	5	11	2	1	3	7	0	1	3	7	0	0
F	32	4	10	3	0	0	6	0	0	0	5	1	0
G	44	13	18	1	3	2	6	3	0	4	10	4	1
H
I	42	3	14	3	0	0	7	0	0	2	16	1	0
J	38	9	11	1	1	0	2	8	0	1	7	2	1
K	22	1	4	0	0	1	6	0	0	3	10	0	0
L	25	5	9	1	0	1	3	0	0	7	10	0	1
M	40	4	14	2	0	0	1	0	0	4	14	1	0

2012
Player	AB	R	H	2B	3B	HR	RBI	SB	CS	BB	SO	HBP	SAC
A	37	8	12	2	1	0	5	5	0	6	10	1	1
B	44	11	15	1	1	3	15	1	0	5	8	0	1
C	15	1	2	0	0	0	0	0	0	0	4	1	0
D	24	5	7	0	0	0	1	3	0	1	8	0	2
E	24	6	6	0	0	1	6	0	0	3	4	0	2
F	44	4	13	5	0	0	5	0	0	5	10	0	0
G	21	4	4	0	0	0	1	5	0	9	10	0	0
H	31	5	7	1	0	0	0	1	0	2	9	0	1
I	48	4	10	0	1	0	3	1	0	0	24	0	1
J	49	15	27	4	1	1	9	10	1	3	8	0	2
K	37	5	10	0	1	1	14	0	0	2	8	1	1
L	33	6	10	0	0	1	3	0	0	5	14	1	2
M	39	6	12	1	1	0	8	0	0	2	7	0	0

2011
Player	AB	R	H	2B	3B	HR	RBI	SB	CS	BB	SO	HBP	SAC
A	14	3	2	0	0	1	2	0	0	2	2	0	0
B	46	9	12	3	1	1	8	1	0	6	14	1	0
C	16	0	2	0	0	0	0	0	0	0	8	0	0
D	38	8	12	3	0	0	0	1	0	1	2	1	0
E	39	7	17	1	0	1	8	1	0	4	7	1	0
F	29	4	4	0	0	1	4	0	0	3	13	1	2
G	37	4	10	1	0	0	5	2	0	2	10	0	0
H	26	4	7	2	1	2	4	0	0	0	10	0	1
I	40	8	9	1	2	0	3	1	0	2	15	0	0
J	44	9	17	2	1	0	3	8	0	5	14	2	0
K	15	3	3	0	0	0	1	0	0	3	9	0	0
L	20	3	6	1	0	1	6	0	0	2	7	0	0
M	43	9	15	0	1	2	10	0	0	7	13	0	0

Here are the results of an exponential smoothing with a constant of 0.5

Player	AB	R	H	2B	3B	HR	RBI	SB	CS	BB	SO	HBP	SAC
A	29.9	7.6	9.8	1.8	0.4	0.4	2.9	3.6	0.0	5.3	7.0	1.6	0.1
B	33.8	8.3	11.6	1.3	1.3	2.3	8.6	0.3	0.0	3.1	8.8	0.1	0.9
C	12.6	0.9	1.0	0.3	0.0	0.0	0.3	0.0	0.0	0.0	5.8	0.6	0.3
D	31.5	6.1	9.9	1.6	0.0	0.3	4.6	1.8	0.5	1.5	6.8	0.6	0.3
E	35.4	7.9	10.1	2.6	0.3	1.5	8.5	0.6	0.3	4.6	9.1	0.1	0.3
F	31.1	4.5	7.6	1.9	0.5	0.1	4.1	0.0	0.0	2.5	8.1	0.9	0.3
G	44.8	10.8	13.8	1.9	0.8	0.5	4.8	4.1	0.0	7.4	14.5	1.0	0.8
H	25.1	4.6	7.3	0.9	0.1	1.3	3.0	0.1	0.0	1.8	6.9	0.0	0.3
I	44.5	5.3	11.4	1.9	0.4	0.5	6.5	0.3	0.0	1.8	15.9	0.3	0.1
J	36.6	8.3	13.3	1.5	1.5	0.6	3.5	4.8	0.1	1.3	10.0	0.8	1.0
K	19.0	2.8	5.6	2.0	0.1	0.4	3.9	0.0	0.0	1.9	7.1	0.1	0.1
L	27.4	3.4	9.8	2.4	0.0	0.5	4.4	0.0	0.0	3.1	10.1	0.1	1.0
M	41.3	7.4	11.9	1.1	0.3	2.8	10.0	0.0	0.0	4.6	10.5	0.3	0.0

Here are the results of an exponential smoothing with a constant of 0.75 which gives more weight to the most recent data.

Player	AB	R	H	2B	3B	HR	RBI	SB	CS	BB	SO	HBP	SAC
A	30.1	7.0	10.0	1.6	0.2	0.2	2.5	4.0	0.0	5.4	7.3	2.3	0.0
B	29.0	6.1	10.1	0.7	1.2	1.8	6.6	0.1	0.0	2.0	8.5	0.0	1.0
C	9.8	0.6	0.5	0.2	0.0	0.0	0.2	0.0	0.0	0.0	5.4	0.8	0.2
D	31.5	6.4	9.9	1.4	0.0	0.2	6.0	1.8	0.8	1.4	7.5	0.8	0.1
E	35.9	8.8	9.4	3.4	0.2	1.4	9.2	0.8	0.2	5.3	10.6	0.0	0.1
F	29.5	4.8	7.0	1.5	0.8	0.0	3.7	0.0	0.0	2.5	7.6	1.0	0.0
G	49.6	12.4	15.0	2.5	0.6	0.4	5.0	4.6	0.0	8.7	16.8	0.8	0.9
H	28.9	5.5	8.7	0.8	0.0	1.5	3.8	0.0	0.0	2.3	7.3	0.0	0.1
I	45.3	5.4	11.5	2.1	0.1	0.8	7.5	0.1	0.0	1.9	14.9	0.2	0.0
J	33.4	7.0	11.1	1.2	1.8	0.8	3.1	2.8	0.0	0.4	10.2	0.4	1.0
K	16.6	2.7	5.8	3.0	0.0	0.2	2.5	0.0	0.0	1.5	6.1	0.0	0.0
L	28.3	2.8	10.5	3.2	0.0	0.3	4.5	0.0	0.0	2.3	10.1	0.0	1.0
M	41.5	7.9	10.9	1.2	0.1	3.8	12.0	0.0	0.0	4.7	9.9	0.2	0.0

Here is a comparison of the statistics based on a smoothing constant of 0.75 which puts more weight on the recent seasons and the statistics based on a smoothing constant of 0.5 which puts extra weight on the earlier seasons.

		0.75			0.5			difference
Player	oba	slg	ops	oba	slg	ops	oba	slg	ops
A	0.467	0.420	0.888	0.452	0.448	0.900	0.015	-0.027	-0.013
B	0.390	0.642	1.032	0.402	0.656	1.058	-0.012	-0.013	-0.026
C	0.123	0.070	0.193	0.123	0.099	0.222	0.000	-0.029	-0.028
D	0.357	0.375	0.732	0.357	0.389	0.746	0.000	-0.014	-0.014
E	0.356	0.481	0.837	0.371	0.502	0.872	-0.015	-0.021	-0.036
F	0.319	0.344	0.663	0.319	0.349	0.668	0.000	-0.006	-0.006
G	0.414	0.397	0.811	0.416	0.416	0.833	-0.003	-0.019	-0.022
H	0.354	0.490	0.844	0.335	0.483	0.817	0.019	0.007	0.026
I	0.287	0.353	0.640	0.288	0.348	0.636	-0.001	0.005	0.004
J	0.348	0.544	0.892	0.395	0.536	0.931	-0.046	0.008	-0.038
K	0.402	0.576	0.978	0.363	0.474	0.837	0.038	0.103	0.141
L	0.420	0.511	0.931	0.424	0.498	0.922	-0.005	0.013	0.008
M	0.341	0.568	0.909	0.363	0.527	0.890	-0.022	0.040	0.018

Notice that player K is hitting well above his average in recent years especially in slugging percentage. 

Players B and E are hitting somewhat below average in recent years.

Player M is hitting somewhat worse in terms of on-base average and somewhat better in terms of slugging percentage in recent years. 

Players A and C are hitting somewhat worse with regards to their slugging percentage in recent years.