Pct = 1.396*OPSDIFF + .500
Then I estimated each team's pct and calculated how many more games per 162 that they won than this equation would predict. Here are the top 10:
So the Braves in 1914 should have had a pct of .503 based on their OPS differential of .002. But it was actually .614. That gives them 17.96 more wins per 162 games than we might have expected. Maybe that is why they are called the "Miracle Braves!"
I also found a regression equation for each decade but the list of the top over achieving teams was similar to this one.
We don't have splits for things like RISP, runners on base and close and late situations for 1914. So we can't tell if the Braves did especially well in those cases, which would explain alot. The Braves were 33-20. But that is not much different than their overall pct.
They had what seems to be good fielding. Their fielding pct was .961 (the league average was .958). Their defensive efficiency rating was .701 and the league average was .698. That probably helped a bit, but I don't think that would explain their .614 pct. They stole 139 bases, as did their opponents. They turned 143 DPs and the next highest team had 119.
The 1987 Cardinals hit alot better when it counted as this table shows
It looks like their pitchers did a bit better when it counted
They stole 248 bases while their opponents stole just 100. The Cards hit into 16 fewer DPs and reached on errors 22 more times. Some of that probably helped them over achieve. They turned 172 DPs, 2nd most in the league. The league average was 146.