The Boston Red Sox had the most runs by a team in 2003, with 961 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	Red Sox	961	2003	162	.586	95	67	5,769	1,667	371	40	238	932	620	53	943	88	35	6,530	2,832	649	24	64	61	126	.289	.360	.491	.851
2	Braves	907	2003	162	.623	101	61	5,670	1,608	321	31	235	872	545	49	933	68	22	6,378	2,696	587	65	49	46	124	.284	.349	.475	.824
3	Blue Jays	894	2003	162	.531	86	76	5,661	1,580	357	33	190	853	546	90	1,081	37	25	6,364	2,573	580	11	56	40	146	.279	.349	.455	.803
4	Yankees	877	2003	163	.623	101	61	5,605	1,518	304	14	230	845	684	81	1,042	98	33	6,430	2,540	548	25	35	54	154	.271	.356	.453	.810
5	Cardinals	876	2003	162	.525	85	77	5,672	1,580	342	32	196	827	580	73	952	82	32	6,466	2,574	570	87	54	68	136	.279	.350	.454	.804
6	Rockies	853	2003	162	.457	74	88	5,518	1,472	330	31	198	814	619	52	1,134	63	37	6,282	2,458	559	55	38	46	140	.267	.344	.445	.790
7	Royals	836	2003	162	.512	83	79	5,568	1,526	288	39	162	781	476	75	926	120	42	6,239	2,378	489	63	57	32	128	.274	.336	.427	.763
8	Rangers	826	2003	162	.438	71	91	5,664	1,506	274	36	239	799	488	75	1,052	65	25	6,293	2,569	549	24	42	31	115	.266	.330	.454	.784
9	Astros	805	2003	162	.537	87	75	5,583	1,466	308	30	191	763	557	81	1,021	66	30	6,320	2,407	529	61	38	44	125	.263	.336	.431	.767
10	Twins	801	2003	162	.556	90	72	5,655	1,567	318	45	155	755	512	63	1,027	94	44	6,324	2,440	518	42	52	36	139	.277	.341	.431	.772
11	Mariners	795	2003	162	.574	93	69	5,561	1,509	290	33	139	759	586	53	989	108	37	6,281	2,282	462	35	46	34	130	.271	.344	.410	.754
12	Phillies	791	2003	162	.531	86	76	5,543	1,448	325	27	166	757	651	55	1,155	72	29	6,333	2,325	518	46	38	56	120	.261	.343	.419	.762
13	White Sox	791	2003	162	.531	86	76	5,487	1,445	303	19	220	766	519	58	916	77	29	6,148	2,446	542	43	41	27	132	.263	.331	.446	.777
14	Athletics	768	2003	162	.593	96	66	5,497	1,398	317	24	176	742	556	59	898	48	14	6,187	2,291	517	22	53	52	118	.254	.327	.417	.743
15	Giants	755	2003	161	.621	100	61	5,456	1,440	281	29	180	713	593	40	980	53	37	6,204	2,319	490	76	39	79	130	.264	.338	.425	.763
16	Pirates	753	2003	162	.463	75	87	5,581	1,492	275	45	163	711	529	87	1,049	86	37	6,314	2,346	483	79	38	42	112	.267	.338	.420	.758
17	Marlins	751	2003	162	.562	91	71	5,490	1,459	292	44	157	709	515	57	978	150	74	6,185	2,310	493	82	41	44	114	.266	.333	.421	.754
18	Orioles	743	2003	163	.438	71	91	5,665	1,516	277	24	152	695	431	54	902	89	36	6,241	2,297	453	51	40	32	123	.268	.323	.405	.729
19	Angels	736	2003	162	.475	77	85	5,487	1,473	276	33	150	687	476	56	838	129	61	6,119	2,265	459	50	50	42	125	.268	.330	.413	.743
20	Cubs	724	2003	162	.543	88	74	5,519	1,431	302	24	172	691	492	50	1,158	73	31	6,187	2,297	498	80	46	40	135	.259	.323	.416	.739
21	Diamondbacks	717	2003	162	.519	84	78	5,570	1,467	303	47	152	696	531	45	1,006	76	38	6,261	2,320	502	63	52	63	126	.263	.330	.417	.746
22	Devil Rays	715	2003	162	.389	63	99	5,654	1,501	298	38	137	678	420	56	1,030	142	42	6,212	2,286	473	32	50	46	108	.265	.320	.404	.724
23	Brewers	714	2003	162	.420	68	94	5,548	1,423	266	24	196	685	547	71	1,221	99	39	6,268	2,325	486	62	40	41	158	.256	.329	.419	.748
24	Expos	711	2003	162	.512	83	79	5,437	1,404	294	25	144	682	522	45	990	100	39	6,116	2,180	463	72	40	58	143	.258	.326	.401	.727
25	Indians	699	2003	162	.420	68	94	5,572	1,413	296	26	158	660	466	62	1,062	86	61	6,187	2,235	480	46	41	25	128	.254	.316	.401	.717