Barry Bonds had the most games with 3+ balls, with 2,086 games.

Interpreted as:

most regular-season games by a player with 10 three or more balls

	NAME	G	BALL	AB	H	2B	3B	HR	RBI	BB	HBP	SO	PA	TB	XBH	SH	SF	IBB	AVG	OBP	SLG	OPS
1	Barry Bonds B. Bonds	2,086	11,595	1,492	427	99	13	131	318	2,359	6	335	3,865	945	243	0	8	666	.286	.722	.633	1.356
2	Jim Thome J. Thome	1,920	10,086	1,646	437	90	3	140	360	1,699	6	615	3,362	953	233	0	11	171	.265	.637	.579	1.216
3	Albert Pujols A. Pujols	1,911	8,718	1,520	449	92	3	91	306	1,368	6	212	2,906	820	186	0	12	312	.295	.627	.539	1.167
4	Alex Rodriguez A. Rodriguez	1,850	8,628	1,520	420	83	3	108	325	1,333	14	427	2,876	833	194	0	9	97	.276	.614	.548	1.162
5	Frank Thomas F. Thomas	1,824	9,591	1,545	437	85	2	104	324	1,630	6	333	3,197	838	191	0	15	164	.283	.649	.542	1.191
6	Bobby Abreu B. Abreu	1,807	9,216	1,585	469	95	18	64	292	1,470	4	354	3,072	792	177	0	13	115	.296	.632	.500	1.132
7	Miguel Cabrera M. Cabrera	1,740	7,647	1,285	326	66	0	71	216	1,250	4	392	2,549	605	137	0	10	230	.254	.620	.471	1.091
8	David Ortiz D. Ortiz	1,738	8,511	1,499	443	117	3	105	339	1,318	2	372	2,837	881	225	0	18	209	.296	.621	.588	1.209
9	Chipper Jones C. Jones	1,734	8,424	1,308	381	66	7	76	278	1,489	0	301	2,808	689	149	0	11	176	.291	.666	.527	1.193
10	Ken Griffey Jr. K. Griffey Jr.	1,733	8,040	1,367	343	63	4	99	277	1,298	3	370	2,680	711	166	0	12	244	.251	.613	.520	1.134
11	Derek Jeter D. Jeter	1,716	7,764	1,502	457	75	9	49	241	1,073	9	353	2,588	697	133	1	3	38	.304	.595	.464	1.059
12	Rafael Palmeiro R. Palmeiro	1,713	7,905	1,348	376	64	8	97	273	1,264	6	247	2,635	747	169	0	17	163	.279	.625	.554	1.179
13	Gary Sheffield G. Sheffield	1,676	7,977	1,200	312	63	1	62	227	1,436	12	265	2,659	563	126	0	11	127	.260	.662	.469	1.131
14	Carlos Beltran C. Beltran	1,641	7,284	1,337	361	68	15	60	196	1,084	2	307	2,428	639	143	0	5	104	.270	.596	.478	1.074
15	Fred McGriff F. McGriff	1,630	7,881	1,387	404	69	3	80	271	1,223	1	369	2,627	719	152	0	16	163	.291	.620	.518	1.138
16	Todd Helton T. Helton	1,605	7,821	1,255	371	89	7	66	241	1,331	3	259	2,607	672	162	0	16	185	.296	.655	.535	1.190
17	Carlos Santana C. Santana	1,598	8,064	1,383	345	65	4	67	231	1,293	1	357	2,688	619	136	0	11	50	.249	.610	.448	1.057
18	Manny Ramirez M. Ramirez	1,597	7,779	1,271	381	84	6	86	289	1,296	10	391	2,593	735	176	0	16	215	.300	.651	.578	1.229
19	Omar Vizquel O. Vizquel	1,582	6,708	1,203	330	66	13	14	153	1,014	0	131	2,236	464	93	3	16	25	.274	.602	.386	.988
20	Jason Giambi J. Giambi	1,568	7,773	1,214	323	69	1	94	305	1,349	11	333	2,591	676	164	0	17	96	.266	.650	.557	1.206
21	Jeff Bagwell J. Bagwell	1,551	7,968	1,288	373	81	2	87	280	1,342	12	361	2,656	719	170	0	14	143	.290	.650	.558	1.208
22	Luis Gonzalez L. Gonzalez	1,547	7,008	1,193	317	65	7	49	194	1,125	7	224	2,336	543	121	1	10	146	.266	.621	.455	1.076
23	Joey Votto J. Votto	1,544	7,938	1,267	360	73	4	69	243	1,357	8	360	2,646	648	146	0	14	140	.284	.652	.511	1.163
24	Adam Dunn A. Dunn	1,529	8,082	1,367	292	49	3	96	254	1,317	4	581	2,694	635	148	0	6	122	.214	.599	.465	1.063
25	Andrew McCutchen A. McCutchen	1,522	7,404	1,310	332	67	6	45	172	1,142	4	394	2,468	546	118	0	12	70	.253	.599	.417	1.016