The New York Yankees put up the most runs by a team in 1956, with 857 runs.

	TEAM	R	SEASON	G	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	Yankees	857	1956	154	.630	97	57	5,312	1,433	193	55	190	788	615	30	755	51	37	6,075	2,306	438	82	36	40	102	.270	.347	.434	.781
2	Tigers	789	1956	155	.532	82	72	5,364	1,494	209	50	150	745	643	28	618	43	26	6,143	2,253	409	58	50	30	133	.279	.356	.420	.776
3	Red Sox	780	1956	155	.545	84	70	5,349	1,473	261	45	139	752	727	25	689	28	19	6,215	2,241	445	68	46	41	153	.275	.362	.419	.781
4	White Sox	776	1956	154	.552	85	69	5,286	1,412	218	43	128	726	619	75	658	70	33	6,122	2,100	389	86	56	30	130	.267	.349	.397	.746
5	Redlegs	775	1956	155	.591	91	63	5,291	1,406	201	32	221	734	528	51	760	45	22	6,003	2,334	454	90	43	69	112	.266	.336	.441	.777
6	Dodgers	720	1956	154	.604	93	61	5,098	1,315	212	36	179	680	649	17	738	65	37	5,884	2,136	427	86	34	91	146	.258	.342	.419	.761
7	Indians	712	1956	155	.571	88	66	5,148	1,256	199	23	153	677	681	40	764	40	32	5,988	1,960	375	81	38	35	110	.244	.335	.381	.715
8	Braves	709	1956	155	.597	92	62	5,207	1,350	212	54	177	667	486	20	714	29	20	5,897	2,201	443	142	42	76	99	.259	.323	.423	.745
9	Cardinals	678	1956	156	.494	76	78	5,378	1,443	234	49	124	628	503	33	622	41	35	5,986	2,147	407	41	31	53	128	.268	.333	.399	.732
10	Phillies	668	1956	154	.461	71	83	5,204	1,313	207	49	121	616	585	27	673	45	23	5,910	1,981	377	52	42	62	132	.252	.329	.381	.709
11	Senators	652	1956	155	.383	59	95	5,202	1,302	198	62	112	612	690	41	877	37	34	6,043	1,960	372	75	35	42	142	.250	.341	.377	.717
12	Athletics	619	1956	154	.338	52	102	5,256	1,325	204	41	112	584	479	20	725	40	30	5,859	1,947	357	67	37	31	127	.252	.315	.370	.685
13	Cubs	597	1956	157	.390	60	94	5,260	1,281	202	50	142	563	446	13	776	55	38	5,852	2,009	394	87	46	60	99	.244	.302	.382	.684
14	Pirates	588	1956	157	.429	66	88	5,221	1,340	199	57	110	546	383	18	752	24	33	5,757	1,983	366	95	40	43	124	.257	.307	.380	.687
15	Orioles	571	1956	154	.448	69	85	5,090	1,242	198	34	91	515	561	22	725	39	42	5,788	1,781	323	84	31	30	133	.244	.320	.350	.670
16	Giants	540	1956	154	.435	67	87	5,190	1,268	192	45	145	497	402	21	659	67	34	5,709	1,985	382	59	37	50	114	.244	.299	.382	.682