The Cincinnati Reds and the Boston Red Sox are tied for the most games when scoring 22+ runs, with 10 games.

Interpreted as:

team most regular-season games with 22+ runs, all-time

	TEAM	G	R	W%	W	L	AB	H	2B	3B	HR	RBI	BB	HBP	SO	SB	CS	PA	TB	XBH	SH	SF	IBB	GIDP	AVG	OBP	SLG	OPS
1	Reds	10	233	1.000	10	0	479	234	41	10	43		85	12	54	13	2	585	424	94	7	2	5	3	.489	.573	.885	1.458
2	Red Sox	10	236	1.000	10	0	470	229	52	9	33	224	89	6	40	6	1	575	398	94	3	7	0	6	.487	.566	.847	1.413
3	Giants	9	210	1.000	9	0	465	232	54	12	21	195	48	4	37	14	0	526	373	87	8	1	0	0	.499	.548	.802	1.350
4	Yankees	8	182	1.000	8	0	380	178	27	8	31	175	78	1	33	9	0	466	314	66	5	2	2	0	.468	.557	.826	1.384
5	Cubs	8	188	.875	7	1	393	192	39	4	28	175	62	3	27	2	0	463	323	71	3	2	0	7	.489	.559	.822	1.381
6	Indians	8	191	1.000	8	0	396	201	42	10	14	178	57	1	22	15	0	466	305	66	11	1	0	2	.508	.569	.770	1.339
7	Dodgers	7	158	1.000	7	0	333	162	23	11	22	149	44	5	21	2	0	386	273	56	4	0	1	6	.486	.552	.820	1.372
8	Phillies	4	94	.750	3	1	198	98	27	5	11	88	37	3	24	5	0	245	168	43	3	4	5	3	.495	.570	.848	1.419
9	Athletics	4	93	1.000	4	0	193	106	18	7	9	90	26	1	17	11	0	226	165	34	6	0	0	0	.549	.605	.855	1.459
10	Orioles	3	67	1.000	3	0	144	69	18	1	11	62	19	2	22	2	0	166	122	30	0	1	0	1	.479	.542	.847	1.389
11	Blue Jays	3	74	1.000	3	0	149	72	17	2	12	74	21	3	23	0	0	174	129	31	0	1	0	0	.483	.552	.866	1.417
12	Cardinals	3	73	1.000	3	0	153	76	11	5	5	65	21	1	11	6		179	112	21	4				.497	.560	.732	1.292
13	Pirates	3	69	1.000	3	0	147	72	11	4	8	61	18	2	6	10	0	172	115	23	4	1	0	0	.490	.548	.782	1.330
14	Nationals	2	48	1.000	2	0	96	49	9	2	12	48	14	1	12	2	0	113	98	23	1	1	4	0	.510	.571	1.021	1.592
15	Twins	2	47	1.000	2	0	96	44	10	2	6	44	19	1	9	2	0	117	76	18	0	1	2	0	.458	.547	.792	1.339
16	Rangers	2	56	1.000	2	0	95	48	7	1	11	56	21	1	13	1	1	120	90	19	0	3	0	1	.505	.583	.947	1.531
17	Mets	2	47	1.000	2	0	99	46	11	2	6	41	15	1	13	2	0	117	79	19	1	1	2	2	.465	.534	.798	1.332
18	Angels	2	49	1.000	2	0	104	54	11	2	10	48	11	1	7	0	0	117	99	23	1	0	0	5	.519	.569	.952	1.521
19	Royals	2	49	1.000	2	0	94	42	10	1	3	46	17	1	11	2	0	114	63	14	0	2	0	0	.447	.526	.670	1.197
20	Braves	2	52	1.000	2	0	100	49	7	3	9	50	14	2	12	2	0	118	89	19	0	2	0	0	.490	.551	.890	1.441
21	White Sox	2	51	1.000	2	0	105	53	11	1	8	46	9	1	13	2	2	118	90	20	1	2	2	0	.505	.538	.857	1.396
22	Padres	1	24	1.000	1	0	50	22	3	1	5	23	9	0	7	3	0	60	42	9	1	0	0	0	.440	.525	.840	1.365
23	Astros	1	23	1.000	1	0	50	25	7	0	6	21	2	0	4	0	0	52	50	13	0	0	0	3	.500	.519	1.000	1.519
24	Marlins	1	22	1.000	1	0	47	22	8	2	4	21	6	0	11	0	0	54	46	14	0	1	0	1	.468	.519	.979	1.497
25	Mariners	1	22	1.000	1	0	43	19	5	0	4	22	8	2	5	1	0	54	36	9	0	1	0	0	.442	.537	.837	1.374