Woody Williams had the most games pitched when allowing 4+ HR, with 8 games.

Interpreted as:

pitcher 4 or more home runs allowed most regular-season game

	NAME	G	HR	W	L	W%	GS	ERA	SO	CG	SHO	SV	IP	H	ER	R	BB	HBP	GF	IBB	TBF	WP	K/9	BB/9	K/BB	HR/9	K%	BB%	WHIP	BABIP	RA	H/9
1	Woody Williams W. Williams	8	33	1	7	.125	8	11.80	25	0	0	0	39.2	76	52	54	12	0	0	2	201	1	5.67	2.72	2.08	7.49	12.4	6.0	2.22	.328	12.25	17.24
2	Bartolo Colon B. Colon	7	28	1	6	.143	7	10.57	28	0	0	0	38.1	55	45	46	10	1	0	0	176	0	6.57	2.35	2.80	6.57	15.9	5.7	1.70	.248	10.80	12.91
3	Chris Young C. Young	6	25	0	6	.000	6	14.12	18	0	0	0	21.2	39	34	34	6	1	0	0	108	2	7.48	2.49	3.00	10.38	16.7	5.6	2.08	.241	14.12	16.20
4	Zack Greinke Z. Greinke	6	25	0	4	.000	6	13.33	21	0	0	0	26.1	52	39	41	6	0	0	0	135	0	7.18	2.05	3.50	8.54	15.6	4.4	2.20	.325	14.01	17.77
5	Brett Tomko B. Tomko	6	25	1	3	.250	5	12.74	25	0	0	0	29.2	51	42	42	10	1	0	0	150	2	7.58	3.03	2.50	7.58	16.7	6.7	2.06	.292	12.74	15.47
6	Pedro Astacio P. Astacio	6	24	1	5	.167	6	11.81	22	0	0	0	32.0	50	42	42	15	3	0	1	163	1	6.19	4.22	1.47	6.75	13.5	9.2	2.03	.263	11.81	14.06
7	Warren Hacker W. Hacker	6	25	0	5	.000	6	9.18	17	1	0	0	33.1	47	34	37	11	0	0	1	158	0	4.59	2.97	1.55	6.75	10.8	7.0	1.74	.210	9.99	12.69
8	Warren Spahn W. Spahn	6	25	1	4	.200	6	7.44	19	1	0	0	42.1	53	35	35	10	0	0	0	183	0	4.04	2.13	1.90	5.31	10.4	5.5	1.49	.217	7.44	11.27
9	Dan Haren D. Haren	5	20	2	2	.500	5	7.92	30	0	0	0	30.2	47	27	27	1	1	0	0	139	0	8.80	0.29	30.00	5.87	21.6	0.7	1.57	.310	7.92	13.79
10	Bronson Arroyo B. Arroyo	5	21	1	4	.200	5	8.58	20	0	0	0	28.1	40	27	27	9	2	0	1	132	0	6.35	2.86	2.22	6.67	15.2	6.8	1.73	.238	8.58	12.71
11	Justin Verlander J. Verlander	5	20	0	5	.000	5	10.16	30	0	0	0	28.1	39	32	33	7	1	0	0	130	1	9.53	2.22	4.29	6.35	23.1	5.4	1.62	.264	10.48	12.39
12	Josh Beckett J. Beckett	5	22	2	3	.400	5	9.58	29	0	0	0	31.0	39	33	33	5	2	0	0	138	0	8.42	1.45	5.80	6.39	21.0	3.6	1.42	.213	9.58	11.32
13	Rodrigo Lopez R. Lopez	5	20	1	4	.200	5	9.11	22	0	0	0	27.2	41	28	28	8	1	0	0	130	0	7.16	2.60	2.75	6.51	16.9	6.2	1.77	.266	9.11	13.34
14	Steve Trachsel S. Trachsel	5	20	1	3	.250	5	13.50	21	0	0	0	21.1	40	32	33	6	1	0	1	110	0	8.86	2.53	3.50	8.44	19.1	5.5	2.16	.323	13.92	16.88
15	Kenny Rogers K. Rogers	5	21	0	1	.000	5	10.33	13	0	0	0	27.0	43	31	31	11	1	0	0	132	0	4.33	3.67	1.18	7.00	9.8	8.3	2.00	.256	10.33	14.33
16	Mike Mussina M. Mussina	5	21	2	3	.400	5	9.20	26	0	0	0	29.1	51	30	31	2	0	0	0	141	1	7.98	0.61	13.00	6.44	18.4	1.4	1.81	.326	9.51	15.65
17	Rick Helling R. Helling	5	21	1	4	.200	5	12.90	21	0	0	0	22.1	47	32	32	7	1	0	1	120	0	8.46	2.82	3.00	8.46	17.5	5.8	2.42	.371	12.90	18.94
18	Phil Niekro P. Niekro	5	20	1	4	.200	5	8.04	25	1	0	0	31.1	39	28	30	7	1	0	0	139	0	7.18	2.01	3.57	5.74	18.0	5.0	1.47	.221	8.62	11.20
19	Joe Ryan J. Ryan	4	18	0	4	.000	4	15.12	20	0	0	0	16.2	34	28	28	5	1	0	0	88	0	10.80	2.70	4.00	9.72	22.7	5.7	2.34	.364	15.12	18.36
20	Jordan Lyles J. Lyles	4	16	0	3	.000	4	10.24	14	0	0	0	19.1	31	22	23	6	1	0	0	93	1	6.52	2.79	2.33	7.45	15.1	6.5	1.91	.268	10.71	14.43
21	Yu Darvish Y. Darvish	4	16	0	3	.000	4	13.03	19	0	0	0	19.1	30	28	29	7	0	0	0	95	0	8.84	3.26	2.71	7.45	20.0	7.4	1.91	.264	13.50	13.97
22	Michael Kopech M. Kopech	4	17	1	3	.250	4	11.57	18	0	0	0	18.2	33	24	24	9	1	0	0	99	2	8.68	4.34	2.00	8.20	18.2	9.1	2.25	.296	11.57	15.91
23	Mike Fiers M. Fiers	4	17	0	2	.000	4	11.37	23	0	0	0	19.0	28	24	24	3	0	0	0	88	0	10.89	1.42	7.67	8.05	26.1	3.4	1.63	.244	11.37	13.26
24	Dan Straily D. Straily	4	16	0	2	.000	3	17.76	12	0	0	0	12.2	31	25	25	5	1	0	0	74	0	8.53	3.55	2.40	11.37	16.2	6.8	2.84	.375	17.76	22.03
25	Max Scherzer M. Scherzer	4	16	1	2	.333	4	9.00	29	0	0	0	22.0	27	22	22	7	0	0	0	101	0	11.86	2.86	4.14	6.55	28.7	6.9	1.55	.224	9.00	11.05