Does plate patience mean more runs?

Looking at runs per game and pitches per plate appearance, it becomes apparent that the two are connected. I looked at the last five seasons, and there is a definite progression of pitches/pa that corresponds with runs/game. The higher the r/g, in general, the higher the p/pa.

The difficult part is determining whether the team sees more pitches simply because it has better hitters and the pitchers are trying to be cautious; or are the hitters actually being more patient? Regardless, it's pretty clear that patience does result in a better offense.

	r/g rank	r/g	p/pa
2006 AL avg.		4.97	3.75
NYY	1	5.74	3.81
TOR	7	4.99	3.77
MIN	8	4.94	3.72
TB	14	4.25	3.69
2005 AL avg.		4.76	3.71
BOS	1	5.62	3.86
NYY	2	5.47	3.74
LAA	7	4.7	3.65
TB	8	4.63	3.6
MIN	14	4.25	3.71
		r/g	p/pa
2004 AL avg.		5.01	3.77
BOS	1	5.86	3.93
NYY	2	5.54	3.79
ANA	7	5.16	3.65
DET	8	5.1	3.74
SEA	14	4.31	3.77
2003 AL avg.		4.86	3.78
BOS	1	5.93	3.82
NYY	3	5.38	3.81
SEA	7	4.91	3.81
CHW	8	4.88	3.83
DET	14	3.65	3.67
		r/g	p/pa
2002 AL avg.		4.81	3.78
NYY	1	5.57	3.8
TOR	7	5.02	3.75
OAK	8	4.94	3.94
DET	14	3.57	3.61