This issue came up over at "The Book" blog. See Consistency is better than inconsistency?. Here is something I did several years ago. I think the results are mixed and not conclusive in any way.
I tried to estimate the value of consistency once. I ran a regression with team winning pct as the dependent variable and runs per game, runs allowed per game, the standard deviation of runs per game and the standard deviation of runs allowed per game as the independent variables. I looked at all teams from 1996. First the results just using runs and runs allowed
Pct = .502 + .9*RG - .91*RAG
Then I put in the standard deviations
Pct = .072*RG - .099*RAG + .04*STDRG + .016*STDRAG
The standard error fell only .0013. That works out to about .21 per 162 games. So bringing in consistency did not help predict winning pct very much. I have no explanation for why the coefficient on runs per game falls so much. The STDRG is positive, meaning that the less consistent you are, the higher your winning pct. The difference between the highest and lowest is STDRG was about 1.36. That times .04 is about .054. Times 162 games is 8.75 wins. The least consistent team would win alot more games. The t-value was 1.9. But again, the sign is wrong. The t-value on STDRAG was .72. The difference between the highest and lowest was 1.42. That works out to 3.62 wins per season. I also looked at all teams from 1967-68. The regression equations were
Pct = .495 + .113*RG - .111*RAG
Pct = .510 + .114*RAG - .11*RAG - .004*STDRG - .007*STDRAG
The standard error actually got higher with the 2nd regression. This time the sign is right for STDRG but not for STDRAG. The difference in STDRG between the highest and lowest was 1.41. For a whole season, that works out to about .84 wins. So the most consistent team in scoring won .84 more games than the least consistent. The t-values were -.21 and -.37 for the STDs. For STDRAG, the difference between the highest and lowest was 1.06 which works out to 1.23 wins. The most consistent team in runs allowed would win 1.23 more games than the least consistent.