Rickey Henderson had the most games when stealing 4+ bases, with 19 games.

Interpreted as:

most regular-season games by a player with 4+ SB

	NAME	G	SB	AB	R	H	2B	3B	HR	RBI	BB	HBP	SO	CS	PA	TB	XBH	SH	SF	IBB	GIDP	AVG	OBP	SLG	OPS
1	Rickey Henderson R. Henderson	19	77	69	42	43	6	0	2	12	26	0	4	4	95	55	8	0	0	1	1	.623	.726	.797	1.523
2	Vince Coleman V. Coleman	10	40	36	13	17	1	3	1	4	11	0	7	1	48	27	5	1	0	0	1	.472	.596	.750	1.346
3	Ty Cobb T. Cobb	6	24	20	12	12	0	0	0	8	6	0	0		28	12	0	2				.600	.692	.600	1.292
4	Tim Raines T. Raines	5	20	21	9	12	2	0	0	2	4	0	2	1	25	14	2	0	0	0	0	.571	.640	.667	1.307
5	Davey Lopes D. Lopes	5	21	18	7	10	0	0	0	1	5	0	2	2	23	10	0	0	0	0	0	.556	.652	.556	1.208
6	Billy Hamilton B. Hamilton	4	17	15	9	10	3	0	0	1	6	0	1	1	21	13	3	0	0	0	0	.667	.762	.867	1.629
7	Scott Podsednik S. Podsednik	4	16	17	9	10	0	0	0	0	4	0	3	1	21	10	0	0	0	0	1	.588	.667	.588	1.255
8	Tony Womack T. Womack	4	16	19	7	8	1	0	0	2	3	0	0	0	22	9	1	0	0	0	0	.421	.500	.474	.974
9	Kenny Lofton K. Lofton	4	17	16	8	11	0	0	2	3	6	0	1	0	22	17	2	0	0	1	0	.688	.773	1.063	1.835
10	Max Carey M. Carey	4	16	12	7	6	0	0	0	1	6	0	0		18	6	0	0				.500	.667	.500	1.167
11	Dee Gordon D. Gordon	3	12	12	4	5	0	0	0	0	2	0	3	0	14	5	0	0	0	0	0	.417	.500	.417	.917
12	Ichiro Suzuki I. Suzuki	3	12	14	2	11	1	0	0	1	1	0	1	0	15	12	1	0	0	0	0	.786	.800	.857	1.657
13	Otis Nixon O. Nixon	3	14	14	7	7	0	0	0	0	1	0	0	0	15	7	0	0	0	0	0	.500	.533	.500	1.033
14	Ron LeFlore R. LeFlore	3	12	11	6	5	0	0	0	2	4	0	3	0	15	5	0	0	0	0	0	.455	.600	.455	1.055
15	Lou Brock L. Brock	3	12	9	6	4	0	0	0	0	6	0	0	1	15	4	0	0	0	0	0	.444	.667	.444	1.111
16	Eddie Collins E. Collins	3	17	16	9	12	0	0	0	4	0	0	0		16	12	0	0				.750	.750	.750	1.500
17	Elly De La Cruz E. De La Cruz	2	8	8	3	7	1	0	0	1	1	0	0	1	9	8	1	0	0	0	0	.875	.889	1.000	1.889
18	Trea Turner T. Turner	2	8	7	2	3	0	0	0	0	2	0	1	0	9	3	0	0	0	0	0	.429	.556	.429	.984
19	Rajai Davis R. Davis	2	8	7	1	3	0	0	0	0	1	0	2	0	8	3	0	0	0	0	0	.429	.500	.429	.929
20	Jacoby Ellsbury J. Ellsbury	2	9	6	1	4	0	0	0	0	2	2	0	0	10	4	0	0	0	0	0	.667	.800	.667	1.467
21	Carl Crawford C. Crawford	2	10	9	7	9	0	0	1	3	1	0	0	0	10	12	1	0	0	0	0	1.000	1.000	1.333	2.333
22	Roger Cedeno R. Cedeno	2	8	8	4	4	1	0	0	2	2	0	1	0	10	5	1	0	0	0	0	.500	.600	.625	1.225
23	Eric Young E. Young	2	11	10	7	6	0	0	0	1	2	0	0	0	12	6	0	0	0	0	0	.600	.667	.600	1.267
24	Brian L. Hunter B. L. Hunter	2	8	11	3	6	0	0	0	3	0	0	0	0	11	6	0	0	0	0	0	.545	.545	.545	1.091
25	Luis Polonia L. Polonia	2	8	10	1	4	0	0	0	2	1	1	1	0	12	4	0	0	0	0	1	.400	.500	.400	.900

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Some of the information used here was obtained free of charge from Retrosheet.

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DATE	MATCHUP			TIME (ET)
Fri 3/27	ATH	@	TOR	7:07 PM
Sat 3/28	ATH	@	TOR	3:07 PM
Sun 3/29	ATH	@	TOR	1:37 PM
Mon 3/30	ATH	@	ATL	7:15 PM
Tue 3/31	ATH	@	ATL	7:15 PM

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Reds - w	83	79	.512	14.0
Cardinals	78	84	.481	19.0
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Athletics	76	86	.469	14.0
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Tue 9/16	CIN	@	STL	6-2
Tue 9/16	ATL	@	WSH	9-4
Tue 9/16	ATH	@	BOS	4-5
Tue 9/16	TOR	@	TBR	1-2
Tue 9/16	SEA	@	KCR	5-7

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DATE	MATCHUP			TIME (ET)
Wed 3/25	NYY	@	SFG	8:05 PM
Thu 3/26	LAA	@	HOU	4:00 AM
Thu 3/26	WSH	@	CHC	4:00 AM
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Rickey Henderson had the most games when stealing 4+ bases, with 19 games.

Interpreted as:

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