Lou Gehrig had the most games when scoring 4+ runs, with 18 games.

Interpreted as:

most regular-season games by a player with 4 or more runs a game

	NAME	G	R	AB	H	2B	3B	HR	RBI	BB	HBP	SO	SB	CS	PA	TB	XBH	SH	SF	IBB	GIDP	AVG	OBP	SLG	OPS
1	Lou Gehrig L. Gehrig	18	75	81	63	13	3	26	70	16	1	2	0		98	160	42	0				.778	.816	1.975	2.792
2	Alex Rodriguez A. Rodriguez	16	66	69	51	8	0	23	50	15	1	7	2	0	86	128	31	0	1	1	0	.739	.779	1.855	2.634
3	Jimmie Foxx J. Foxx	15	63	65	46	5	2	20	46	20	0	0	2		85	115	27	0			0	.708	.776	1.769	2.546
4	Ty Cobb T. Cobb	14	58	64	48	9	5	6		12	0	1	11		78	85	20	2				.750	.789	1.328	2.118
5	Paul Molitor P. Molitor	12	49	55	36	8	2	5	17	10	0	0	4	0	65	63	15	0	0	1	0	.655	.708	1.145	1.853
6	Ted Williams T. Williams	12	48	44	33	2	0	11	38	21	0	2	1	0	65	68	13	0	0		0	.750	.831	1.545	2.376
7	Mel Ott M. Ott	12	53	35	29	4	1	9	20	27	1	1	2		63	62	14	0			0	.829	.905	1.771	2.676
8	Earle Combs E. Combs	12	49	61	41	12	7	1	11	11	0	1	2		72	70	20	0				.672	.722	1.148	1.870
9	Frankie Frisch F. Frisch	12	48	58	41	10	3	2	23	6	0	0	8		65	63	15	1				.707	.734	1.086	1.821
10	Jimmy Rollins J. Rollins	11	45	51	35	8	2	7	20	9	1	4	1	0	61	68	17	0	0	0	0	.686	.738	1.333	2.071
11	Al Simmons A. Simmons	11	46	61	44	6	0	13	36	4	0	3	2		65	89	19	0				.721	.738	1.459	2.197
12	Charlie Gehringer C. Gehringer	11	44	43	32	7	1	3	15	16	0	0	2		59	50	11	0			0	.744	.814	1.163	1.976
13	Babe Ruth B. Ruth	11	45	43	31	6	1	12	31	19	0	5	1		63	75	19	1				.721	.806	1.744	2.551
14	Eddie Collins E. Collins	11	44	43	29	5	2	0		16	2	1	11		62	38	7	1				.674	.770	.884	1.654
15	Craig Biggio C. Biggio	10	43	43	28	7	0	5	12	10	2	0	7	0	55	50	12	0	0	0	0	.651	.727	1.163	1.890
16	Ryne Sandberg R. Sandberg	10	40	45	34	4	0	13	20	7	1	2	4	0	53	77	17	0	0	1	1	.756	.792	1.711	2.504
17	Arky Vaughan A. Vaughan	10	40	37	24	7	5	2	9	16	0	2	1		53	47	14	0			0	.649	.755	1.270	2.025
18	Paul Waner P. Waner	10	41	42	33	7	5	5	22	8	1	2	0		52	65	17	1			0	.786	.824	1.548	2.371
19	Kiki Cuyler K. Cuyler	10	42	45	34	6	4	6	26	9	4	1	1		58	66	16	0				.756	.810	1.467	2.277
20	George Grantham G. Grantham	10	41	37	25	5	1	10	31	18	0	0	4		56	62	16	1				.676	.782	1.676	2.457
21	Bobby Abreu B. Abreu	9	36	35	26	6	3	6	21	12	0	2	5	0	49	56	15	0	2	0	0	.743	.776	1.600	2.376
22	Kenny Lofton K. Lofton	9	37	39	30	4	5	3	10	8	0	2	15	0	47	53	12	0	0	2	0	.769	.809	1.359	2.167
23	Barry Bonds B. Bonds	9	38	27	19	4	0	8	14	21	0	0	3	0	48	47	12	0	0	4	0	.704	.833	1.741	2.574
24	Rickey Henderson R. Henderson	9	36	29	24	7	0	3	9	15	1	3	19	1	45	40	10	0	0	0	0	.828	.889	1.379	2.268
25	Pete Rose P. Rose	9	36	48	30	4	1	4	17	4	0	1	1	0	52	48	9	0	0	1	0	.625	.654	1.000	1.654