most games with 4+ total bases by a catcher

Ivan Rodriguez had the most games by a catcher when collecting 4+ total bases, with 433 games.

Interpreted as:

most regular-season games with 4+ total bases by a catcher

	NAME	G	TB	AB	R	H	2B	3B	HR	RBI	BB	HBP	SO	SB	CS	PA	XBH	SH	SF	IBB	GIDP	AVG	OBP	SLG	OPS
1	Ivan Rodriguez I. Rodriguez	433	2,199	1,873	593	980	228	38	305	697	79	8	182	20	18	1,974	571	3	11	10	52	.523	.541	1.174	1.715
2	Mike Piazza M. Piazza	412	2,155	1,656	559	834	122	4	397	842	178	2	179	5	8	1,840	523	0	4	45	29	.504	.551	1.301	1.852
3	Carlton Fisk C. Fisk	404	2,016	1,572	542	785	124	27	351	715	135	22	177	21	14	1,742	502	3	10	16	28	.499	.542	1.282	1.824
4	Johnny Bench J. Bench	360	1,773	1,426	468	671	108	8	326	692	140	4	176	13	8	1,589	442	0	19	28	20	.471	.513	1.243	1.756
5	Yogi Berra Y. Berra	346	1,727	1,398	474	657	102	22	308	722	111	13	47	3	8	1,529	432	1	6	6	23	.470	.511	1.235	1.746
6	Gary Carter G. Carter	332	1,676	1,292	430	639	114	16	297	608	115	8	86	3	7	1,423	427	0	8	12	21	.495	.535	1.297	1.833
7	Lance Parrish L. Parrish	327	1,618	1,307	429	607	84	15	299	600	107	6	177	4	6	1,429	398	2	7	14	29	.464	.505	1.238	1.743
8	Gabby Hartnett G. Hartnett	312	1,578	1,225	417	654	158	35	232	560	108	7	95	3		1,354	425	14			1	.534	.574	1.288	1.862
9	Bill Dickey B. Dickey	308	1,566	1,289	407	717	138	54	201	595	103	2	30	11		1,398	393	4			3	.556	.590	1.215	1.805
10	Brian McCann B. McCann	307	1,516	1,212	369	588	111	2	271	605	102	11	162	3	1	1,336	384	1	10	15	34	.485	.525	1.251	1.776
11	Jorge Posada J. Posada	288	1,471	1,123	387	580	133	7	248	588	139	7	182	3	5	1,279	388	0	10	11	26	.516	.568	1.310	1.878
12	Ted Simmons T. Simmons	277	1,348	1,140	346	594	125	22	195	493	98	3	66	0	4	1,257	342	2	14	21	25	.521	.554	1.182	1.736
13	Javy Lopez J. Lopez	268	1,385	1,069	344	536	93	12	244	504	62	6	120	3	7	1,144	349	0	7	10	25	.501	.528	1.296	1.824
14	A.J. Pierzynski	266	1,295	1,096	313	578	133	16	184	415	36	6	89	2	2	1,150	333	3	9	9	20	.527	.541	1.182	1.722
15	Benito Santiago B. Santiago	264	1,300	1,050	318	516	99	23	213	488	56	4	148	15	10	1,122	335	3	9	5	19	.491	.515	1.238	1.753
16	Ernie Lombardi E. Lombardi	262	1,302	1,088	291	591	122	20	183	467	49	6	40	1		1,143	325	0			14	.543	.565	1.197	1.762
17	Salvador Perez S. Perez	260	1,289	1,046	313	505	92	7	226	485	49	7	138	1	0	1,109	325	0	7	4	29	.483	.506	1.232	1.738
18	Roy Campanella R. Campanella	252	1,295	994	336	488	63	12	240	529	93	4	93	5	4	1,098	315	3	4	6	24	.491	.534	1.303	1.837
19	Yadier Molina Y. Molina	246	1,206	994	294	549	123	6	174	429	50	7	68	12	4	1,065	303	6	8	4	18	.552	.572	1.213	1.786
20	Jason Varitek J. Varitek	225	1,127	856	293	437	97	7	193	391	88	13	131	2	4	963	297	3	3	13	14	.511	.560	1.317	1.877
21	Bill Freehan B. Freehan	224	1,108	874	270	434	72	25	184	368	59	14	75	2	4	957	281	6	4	8	21	.497	.533	1.268	1.801
22	Walker Cooper W. Cooper	222	1,106	911	290	473	86	20	169	431	60	8	53	5	0	985	275	6	0	0	14	.519	.553	1.214	1.767
23	Mickey Cochrane M. Cochrane	217	1,099	901	340	529	133	40	119	357	106	5	22	10		1,029	292	17				.587	.632	1.220	1.852
24	Russell Martin R. Martin	212	1,026	822	284	388	64	5	188	393	80	11	131	9	7	920	257	0	7	8	14	.472	.521	1.248	1.769
25	J.T. Realmuto	206	1,048	844	289	429	84	17	167	361	59	10	119	19	5	915	268	0	2	2	12	.508	.544	1.242	1.786