> If a program over the course of a few thousand instructions hits a branch X% of the time, then X will be the branch prediction.

This is not completely true - modern branch predictors can recognize patterns such as "this branch is taken every other time", or "every 5th time", etc. They also can, in some cases, recognize correlations between nearby branches.

However, they won't use factors like register or memory contents to predict branches, because that would require waiting for that data to be available to make the prediction -- which of course defeats the point of branch prediction.