I wanted to see what base statistic most correlates to runs scored. This way we know which statistics to value when looking at offensive players. I used Fangraphs customizable reports, and looked at all 30 teams from 2000-2011. I selected a few different statistics to see the correlations.
The Yankees have scored the most runs during this time period, and also have the most home runs and walks. They are 27th in Sacrifice hits and have less strikeouts than average. They have also grounded into the 2nd most double plays and are 5th in stolen bases. They are second in batting average and first in OBP. They are tied for first in slugging and tied for second in ISO. As far as BABIP goes, they are tied for 5th. The worst team in this era is the Expos/Nationals, scoring 8177 runs or 77.4% of the runs the Yankees scored (according to Sabermetric formula of 10 runs equaling a win, this is 238.3 more losses than the Yankees or almost 20 more losses a season). The Expos/Nationals were in the bottom half in baseball in homers and walks. They were 12th in baseball in strikeouts and had the second most sacrifice hits. They grounded into the 13th most double plays, and were about mid-pack in stolen bases. They were second to last in both batting average and OBP. They were 5th to last in ISO and 3rd to last in SLG with the 7th worst BABIP.
3 of the top 5 home run teams were top 5 run teams. The same ratio applied to walks. 3 of the worst home run teams were part of the bottom 5 in runs scored. 2 of the worst 5 walk teams were among the worst 5 offenses, while none of the 5 best walk teams were part of the worst 5 offenses. Only 1 of the top 5 strikeout teams were 1 of the worst 5 offensive teams, and 1 of those were actually part of the top 5 offenses. 1 of the teams with the 5 lowest strikeout totals were one of the worst 5 offenses and none of them were in the top 5. As far as sacrifice hits go, they seem to be more helpful than I originally thought, as 2 of the top 5 offenses were also in the top 5 in sacrifice hits (and of course the Expos were in the bottom 5 of offenses and top 5 of sacrifice hits). Only 1 team that were in the top 5 in grounding into double plays were 1 of the worst 5 offenses (of course the best offensive team had the second most GIDP). None of the teams that hit into the least double plays were in the top 5 offenses. The Yankees were the only team in the top 5 in stolen bases and the top 5 in runs scored. The Red Sox were among the worst teams as far as stolen bases, but also among the best offenses. Batting average had a huge correlation, all 5 teams with the most runs scored were in the top 6 in BA. 3 of the worst 5 teams in batting averages were among the worst 5 in runs. OBP also had a high correlation as 4 of the best 5 run scoring teams were among the best 5 in OBP. 4 of the worst offensive teams were also in the bottom 5 in OBP. All 5 of the top teams in runs scored were in the top 5 in Slugging, and all 5 of the bottom in runs scored were in the bottom 6 in SLG. The top 5 in Isolated Slugging contained 4 of the top 5 run scoring teams. All five of the worst offenses were in the bottom of 7 in Isolated Slugging. BABIP doesn't have quite as strong of a correlation as 2 of the top 5 offenses were also the top 5 offenses. None of the bottom 5 offenses suffered from being one of the bottom BABIPs in the league.
So it seems that offensive statistics can be ranked by importance in this order: Great correlation: OBP, BA, SLG, ISO, BB, HR,
Small correlation: SH, BABIP
No correlation: SB, GIDP, SO