Thanks for the comments Eric. I know this thread isn't going to get a lot of attention, but I thought I'd add a little bit more.
The first step above was trying to show there's no relation between good offenses (defined by EQA) and the consistency of the principal hitters.
Another step is to look at team consistency in general. This was done a while ago in the
Live Nude Girls thread, but revisited here. What this does is take, by team, the runs scored for every game, and then get a standard deviation from that.
Here are the data
Table
| LG | TEAM | stdev | R/G | "Consistency" | "Balance" | EQR | R | R diff |
| NL | SLN | 3.04 | 4.85 | 62.71% | 14.05% | 770 | 781 | 11 |
| NL | COL | 3.67 | 5.02 | 73.14% | 13.55% | 799 | 813 | 14 |
| AL | CHA | 3.37 | 5.36 | 62.91% | 12.84% | 859 | 868 | 9 |
| NL | PHI | 3.27 | 5.34 | 61.22% | 12.49% | 855 | 865 | 10 |
| NL | HOU | 3.08 | 4.54 | 67.91% | 12.47% | 745 | 735 | -10 |
| AL | BOS | 3.12 | 5.06 | 61.56% | 12.31% | 842 | 820 | -22 |
| AL | MIN | 3.41 | 4.94 | 68.94% | 12.30% | 795 | 801 | 6 |
| NL | CHN | 3.33 | 4.42 | 75.35% | 12.03% | 722 | 716 | -6 |
| NL | SFN | 3.03 | 4.63 | 65.31% | 11.80% | 724 | 746 | 22 |
| NL | FLO | 3.31 | 4.69 | 70.55% | 11.66% | 765 | 759 | -6 |
| AL | CLE | 3.66 | 5.37 | 68.11% | 11.58% | 854 | 870 | 16 |
| AL | KCA | 3.20 | 4.67 | 68.59% | 10.65% | 744 | 757 | 13 |
| NL | SDN | 3.02 | 4.51 | 66.93% | 10.31% | 758 | 731 | -27 |
| NL | WAS | 2.86 | 4.60 | 62.10% | 9.96% | 767 | 746 | -21 |
| NL | NYN | 3.35 | 5.15 | 65.10% | 9.76% | 812 | 834 | 22 |
| AL | NYA | 3.69 | 5.74 | 64.20% | 9.44% | 921 | 930 | 9 |
| NL | PIT | 3.01 | 4.27 | 70.49% | 9.13% | 701 | 691 | -10 |
| NL | ATL | 3.38 | 5.24 | 64.57% | 9.12% | 810 | 849 | 39 |
| AL | TBA | 3.03 | 4.25 | 71.35% | 8.88% | 712 | 689 | -23 |
| AL | SEA | 3.13 | 4.67 | 67.09% | 8.71% | 754 | 756 | 2 |
| AL | ANA | 3.13 | 4.73 | 66.25% | 8.22% | 778 | 766 | -12 |
| AL | OAK | 2.98 | 4.76 | 62.52% | 8.14% | 771 | 771 | 0 |
| AL | TEX | 3.33 | 5.15 | 64.64% | 7.21% | 813 | 835 | 22 |
| AL | DET | 3.39 | 5.07 | 66.75% | 6.44% | 787 | 822 | 35 |
| NL | LAN | 3.37 | 5.06 | 66.56% | 5.96% | 822 | 820 | -2 |
| NL | MIL | 2.93 | 4.51 | 64.94% | 5.65% | 726 | 730 | 4 |
| AL | BAL | 3.29 | 4.74 | 69.41% | 4.95% | 787 | 768 | -19 |
| NL | ARI | 2.98 | 4.77 | 62.47% | 4.90% | 765 | 773 | 8 |
| AL | TOR | 3.00 | 4.99 | 60.03% | 4.59% | 853 | 809 | -44 |
| NL | CIN | 3.21 | 4.62 | 69.45% | 4.20% | 790 | 749 | -41 |
| | | | | | | | | |
| | | | | | | | | |
| AL: correlation of %stdev to R-Diff (team): .23 | | | | | | 0.11 | | |
| NL: correlation of %stdev to R-Diff (team): -.029 | | | | | | -0.2 | | |
| | | | | | | | | |
| AL: correlation of %stdev (team) to %stdev (principal hitters): .06 | | | | | | | | 0.012 |
| NL: correlation of %stdev (team) to %stdev (principal hitters): .16 | | | | | | | | 0.147 |
| | | | | | | | | |
| AL: correlation of %stdev (principal) to R-Diff: .28 | | | | | | 0.28 | | |
| NL: correlation of %stdev (principal) to R-Diff: .28 | | | | | | 0.28 | | |
stdev = the standard deviation of the runs scored in every game played by a team that year
r/g = the average number of runs scored per game
"Consistency" = relative consistency of the team's performance overall. Basically, the standard deviation of the runs they scored in every game, divided by the average number of runs per game
"Balance" = the relative consistency of the team's principal hitters. The standard deviation of the the EQAs of the 10 players with most plate appearances, divided by average EQA. Derived from post above.
EQR = expected runs for the team based on component batting lines (from B-P)
R diff = difference between actual runs and expected runs. A measure of over/under offensive performance
The table is reverse sorted by "Balance", with more unbalanced teams (eg. St. Louis) at the top and balanced teams (eg. Toronto and Cincinnati) at the bottom.
Results: in the AL less consistent teams tend to outperform, while in the NL less consistent teams tend to underperform. On average, no particular relationship is visible.
While "balanced" doesn't have any strong relation with "consistency" (a little, maybe), it does seem to have some relation to worse performance judged by R-Diff, where negative numbers indicate possible under-performance. The correlation is slightly positive, but my "balanced" is in reverse order (smaller numbers = more balanced). More balanced teams tend to do worse with regard to R diff.
I'm sure the study is too small, and I'm probably just seeing sample effects (though there are 30 teams and thousands of games involved). Is there an interleague play issue here? I wish I could subtract all interleague games, but that would be a total pita. Maybe the DH is a factor.
Here are some charts of team consistency. Haven't charted with the principal hitter variance data yet, but this is what I have:

AL Volatility vs. Relative Offensive Performance

NL Volatility vs. Relative Offensive Performance
Anyway, just a sketch of a study I guess, but at least within this study, consistent offenses overall (on a game to game run-scoring basis) might not do better, but "balanced" teams do a bit worse, overall, or at least they did in 2006.
Here's the chart with combined NL and AL data for 2006 with a scatterplot of "Balance" against R-Diff. The downward slope of the trend line suggests that more balanced teams did relatively worse than a metric like B-Ps EQR indicated they would. The trend is not strong, and obviously subject to small sample skew. Cincinnati and Toronto were both very balanced lineups that distinctly under-performed by EQR.

edit: fixed errors
edit2: I wonder if we aren't seeing here the effect of lineup? In an unbalanced lineup, the better hitters will tend to get more at bats by being higher up in the order, so that more balanced lineups need better offense on average to counterweight the greater leverage of the better players.
Edited by Worst Trade Evah, 05 December 2006 - 12:50 AM.