Bill James has the highest career average Game Score in the postseason, with 88 per game.

Interpreted as:

most game score per game by a player playoffs

	NAME	GSC	G	W	L	W%	GS	ERA	SO	CG	SHO	SV	IP	H	ER	R	HR	BB	HBP	GF	IBB	TBF	WP	K/9	BB/9	K/BB	HR/9	K%	BB%	WHIP	BABIP	RA	H/9
1	Bill James B. James	88	2	2	0	1.000	1	0.00	9	1	1	0	11.0	2	0	0	0	6	0	1	1	37	0	7.36	4.91	1.50	0.00	24.3	16.2	0.73	.091	0.00	1.64
2	Mike Scott M. Scott	86	2	2	0	1.000	2	0.50	19	2	1	0	18.0	8	1	1	0	1	0	0	0	65	0	9.50	0.50	19.00	0.00	29.2	1.5	0.50	.178	0.50	4.00
3	Joe Coleman J. Coleman	84	1	1	0	1.000	1	0.00	14	1	1	0	9.0	7	0	0	0	3	0	0	0	37	0	14.00	3.00	4.67	0.00	37.8	8.1	1.11	.350	0.00	7.00
4	Duster Mails D. Mails	83	2	1	0	1.000	1	0.00	6	1	1	0	15.2	6	0	0	0	6	0	0	0	58	0	3.45	3.45	1.00	0.00	10.3	10.3	0.77	.130	0.00	3.45
5	Clem Labine C. Labine	81	13	2	2	.500	1	3.16	15	1	1	2	31.1	37	11	17	3	7	0	7	2	133	1	4.31	2.01	2.14	0.86	11.3	5.3	1.40	.315	4.88	10.63
6	Gene Bearden G. Bearden	81	2	1	0	1.000	1	0.00	4	1	1	1	10.2	6	0	0	0	1	0	1	0	36	0	3.38	0.84	4.00	0.00	11.1	2.8	0.66	.194	0.00	5.06
7	Ernie White E. White	81	1	1	0	1.000	1	0.00	6	1	1	0	9.0	6	0	0	0	0	0	0	0	33	0	6.00	0.00		0.00	18.2	0.0	0.67	.222	0.00	6.00
8	Homer Bailey H. Bailey	80	2	0	0		1	1.00	12	0	0	0	9.0	3	1	1	0	1	1	0	0	32	0	12.00	1.00	12.00	0.00	37.5	3.1	0.44	.167	1.00	3.00
9	Wally Bunker W. Bunker	80	1	1	0	1.000	1	0.00	6	1	1	0	9.0	6	0	0	0	1	0	0	0	33	0	6.00	1.00	6.00	0.00	18.2	3.0	0.78	.231	0.00	6.00
10	Joe Dobson J. Dobson	80	3	1	0	1.000	1	0.00	10	1	0	0	12.2	4	0	3	0	3	1	1	1	48	0	7.11	2.13	3.33	0.00	20.8	6.3	0.55	.118	2.13	2.84
11	Jimmy Ring J. Ring	80	2	1	1	.500	1	0.64	4	1	1	0	14.0	7	1	1	0	6	2	1	0	57	0	2.57	3.86	0.67	0.00	7.0	10.5	0.93	.156	0.64	4.50
12	Johnny Kucks J. Kucks	79	8	1	0	1.000	1	1.89	4	1	1	0	19.0	15	4	5	1	6	0	0	0	76	0	1.89	2.84	0.67	0.47	5.3	7.9	1.11	.215	2.37	7.11
13	Monte Pearson M. Pearson	77.5	4	4	0	1.000	4	1.01	28	3	1	0	35.2	19	4	5	1	7	0	0	0	133	0	7.07	1.77	4.00	0.25	21.1	5.3	0.73	.186	1.26	4.79
14	Dick Rudolph D. Rudolph	77.5	2	2	0	1.000	2	0.50	15	2	0	0	18.0	12	1	2	0	4	0	0	0	66	1	7.50	2.00	3.75	0.00	22.7	6.1	0.89	.255	1.00	6.00
15	LaMarr Hoyt L. Hoyt	77	1	1	0	1.000	1	1.00	4	1	0	0	9.0	5	1	1	0	0	0	0	0	31	0	4.00	0.00		0.00	12.9	0.0	0.56	.185	1.00	5.00
16	Jack Kramer J. Kramer	77	2	1	0	1.000	1	0.00	12	1	0	0	11.0	9	0	2	0	4	0	1	1	46	0	9.82	3.27	3.00	0.00	26.1	8.7	1.18	.300	1.64	7.36
17	Earl Whitehill E. Whitehill	77	1	1	0	1.000	1	0.00	2	1	1	0	9.0	5	0	0	0	2	0	0	0	34	1	2.00	2.00	1.00	0.00	5.9	5.9	0.78	.167	0.00	5.00
18	Dutch Leonard D. Leonard	76.5	2	2	0	1.000	2	1.00	9	2	0	0	18.0	8	2	3	0	4	0	0	0	67	1	4.50	2.00	2.25	0.00	13.4	6.0	0.67	.148	1.50	4.00
19	Babe Ruth B. Ruth	76.3	3	3	0	1.000	3	0.87	8	2	1	0	31.0	19	3	3	1	10	1	0	0	116	1	2.32	2.90	0.80	0.29	6.9	8.6	0.94	.188	0.87	5.52
20	Michael Soroka M. Soroka	76	1	0	0		1	1.29	7	0	0	0	7.0	2	1	1	0	0	0	0	0	23	0	9.00	0.00		0.00	30.4	0.0	0.29	.125	1.29	2.57
21	Johnny Sain J. Sain	76	6	2	2	.500	2	2.64	15	2	1	0	30.2	27	9	9	2	6	1	2	2	127	0	4.40	1.76	2.50	0.59	11.8	4.7	1.08	.243	2.64	7.92
22	Hippo Vaughn H. Vaughn	75.7	3	1	2	.333	3	1.00	17	3	1	0	27.0	17	3	3	0	5	1	0	1	97	0	5.67	1.67	3.40	0.00	17.5	5.2	0.81	.230	1.00	5.67
23	Dave Dravecky D. Dravecky	75.5	7	1	1	.500	2	0.35	24	1	1	0	25.2	12	1	1	0	5	0	1	0	88	0	8.42	1.75	4.80	0.00	27.3	5.7	0.66	.203	0.35	4.21
24	Bob Gibson B. Gibson	75.1	9	7	2	.778	9	1.89	92	8	2	0	81.0	55	17	19	6	17	2	0	3	312	2	10.22	1.89	5.41	0.67	29.5	5.4	0.89	.251	2.11	6.11
25	Logan Webb L. Webb	75	2	1	0	1.000	2	0.61	17	0	0	0	14.2	9	1	1	0	1	0	0	0	53	0	10.43	0.61	17.00	0.00	32.1	1.9	0.68	.257	0.61	5.52